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Big Ideas Math Book 3rd Grade Answer Key Chapter 9 Multiples and Problem Solving

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Lesson – 1: Use Number Lines to Multiply by Multiples of 10

• Lesson 9.1 Use Number Lines to Multiply by Multiples of 10
• Use Number Lines to Multiply by Multiples of 10 Homework & Practice 9.1

Lesson – 2: Use Place Value to Multiply by Multiples of 10

• Lesson 9.2 Use Place Value to Multiply by Multiples of 10
• Use Place Value to Multiply by Multiples of 10 Homework & Practice 9.2

Lesson – 3: Use Properties to Multiply by Multiples of 10

• Lesson 9.3 Use Properties to Multiply by Multiples of 10
• Use Properties to Multiply by Multiples of 10 Homework & Practice 9.3

Lesson – 4: Problem Solving: Multiplication and Division

• Lesson 9.4 Problem Solving: Multiplication and Division
• Problem Solving: Multiplication and Division Homework & Practice 9.4

Lesson – 5: Problem Solving: All Operations

• Lesson 9.5 Problem Solving: All Operations
• Problem Solving: All Operations Homework & Practice 9.5

Performance Task

• Multiples and Problem Solving Performance Task
• Multiples and Problem Solving Activity
• Multiples and Problem Solving Chapter Practice

Lesson 9.1 Use Number Lines to Multiply by Multiples of 10

Explore and Grow

Show 5 jumps of 3. Write a multiplication equation shown by the number line.

____ × _____ = _____

Answer: 5 × 3 = 15

Explanation:
The count starts from 0.
You have put 5 jumps of 3 on the number line.
Skip by 3 five times.
That means from 0 to 3, 3 to 6, 6 to 9, 9 to 12, 12 to 15.
5 × 3 = 15

Show 5 jumps of 30. Write a multiplication equation shown by the number line.

____ × ____ = _____
Answer: 5 × 30 = 150

Explanation:

The count starts from 0.
You have put 5 jumps of 30 on the number line.
Skip by 30 five times.
That means from 0 to 30, 30 to 60, 60 to 90, 90 to 120, 120 to 150.
5 × 30 = 150

Structure
Compare the models. How are they the same? How are they different?
Answer: The Multiplication equation for both the models are the same but counts are different.

Think and Grow: Number Lines and Multiples of 10

Example
Find 3 × 50.
3 × 50 means 3 groups of 50.
Number of jumps: ______
Size of each jump: ______
Start at 0. Skip count by 50 three times.

Answer: 3 × 50 = 150

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 3 jumps of 50.
The count starts at 0. Skip 50 three times.
Number of jumps = 3
Size of each jump = 50
3 × 50 = 150

Show and Grow

Question 1.
Find 8 × 20.
Number of jumps: ______
Size of each jump: ______

8 × 20 = _____
Answer: 160

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 8 jumps of 20.
The count starts at 0. Skip 20 eight times.
Number of jumps = 8
Size of each jump = 20
8 × 20 = 160

Question 2.
Find 4 × 30
Number of jumps: _______
Size of each jump: _______

4 × 30 = _____
Answer: 120

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 4 jumps of 30.
The count starts at 0. Skip 30 four times.
Number of jumps = 4
Size of each jump = 30
4 × 30 = 120

Apply and Grow: Practice

Question 3.
Find 2 × 60.
Number of jumps: _______
Size of each jump: _______

2 × 60 = _____
Answer: 120

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 2 jumps of 60.
The count starts at 0. Skip 60 two times.
Number of jumps = 2
Size of each jump = 60
2 × 60 = 120

Question 4.
Find 5 × 50

5 × 50 = _____
Answer: 250

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 5 jumps of 50.
The count starts at 0. Skip 50 five times.
Number of jumps = 5
Size of each jump = 50
5 × 50 = 250

Question 5.
Find 3 × 70.
3 × 70 = _____
Answer: 210

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 3 jumps of 70.
The count starts at 0. Skip 70 three times.
Number of jumps = 3
Size of each jump = 70
3 × 70 = 210

Question 6.
Find 30 × 6.
30 × 6 = _____
Answer: 180

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 6 jumps of 30.
The count starts at 0. Skip 30 six times.
Number of jumps = 6
Size of each jump = 30
30 × 6 = 180

Question 7.
Structure
Show 2 × 40 on one number line and 4 × 20 on the other. What is the same about the number lines? What is different?

Answer: The model is the same on the number line. The counts are different and the number of jumps on the number line is different.

Think and Grow: Modeling Real Life

A section of an airplane has 20 rows of seats. Each row has 7 seats. Can the section seat more than 150 people? Explain.

Model:

The section ______ seat more than 150 people.
Explain:

Answer:
Given that,
A section of an airplane has 20 rows of seats. Each row has 7 seats.
20 × 7 = 140 seats
Thus the section cannot seat more than 150 people.

Show and Grow

Question 8.
There are 9 rows of seats in an auditorium. Each row has 30 seats. Can the auditorium seat more than 250 people? Explain.
Answer:
Given that,
There are 9 rows of seats in an auditorium. Each row has 30 seats.
9 × 30 = 270 seats
270 – 250 = 20
Thus the auditorium seat more than 250 people.

Question 9.
A mechanic installs new tires on 20 cars and 20 pickup trucks. How many new tires does the mechanic install in all?

Answer:
Given that,
A mechanic installs new tires on 20 cars and 20 pickup trucks.
20 × 4 = 80 cars
20 × 4 = 80 trucks
80 + 80 = 160 new tires
Thus the mechanic install 160 new tires.

Question 10.
DIG DEEPER!
Newton saves $5 each week for 20 weeks. How much more money does he need to buy a new bike that costs $130? If he continues to save the same amount each week, how many more weeks does he need to save to buy the bike? Explain.
Answer:
Given that,
Newton saves $5 each week for 20 weeks.
5 × 20 = $100
$130 – $100 = $30
Thus Newton need to save $30 to buy the bike.

Use Number Lines to Multiply by Multiples of 10 Homework & Practice 9.1

Question 1.
Find 3 ×30.
Number of jumps: _______
Size of each jump: _______

3 × 30 =

Answer: 90

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 3 jumps of 30.
The count starts at 0. Skip 30 three times.
Number of jumps = 3
Size of each jump = 30
3 × 30 = 90

Question 2.
Find 7 × 60.
Number of jumps: _______
Size of each jump: _______

7 × 60 = _____
Answer: 420

Explanation:
From the figure, we can observe that the count starts from 0.
It means that there are 7 jumps of 60.
The count starts at 0. Skip 60 seven times.
Number of jumps = 7
Size of each jump = 60
7 × 60 = 420

Question 3.
Find 4 × 40.
4 × 40 = ____
Answer: 160

Explanation:
We can find the product by using the distributive property.
4 × 40 = 4 × (20 + 20)
4 × 40 = (4 × 20) + (4 × 20)
4 × 40 = 80 + 80
4 × 40 = 160

Question 4.
Find 80 × 3.
80 × 3 = _____
Answer: 240

Explanation:
We can find the product by using the associative property.
80 × 3 = (8 × 10) × 3
80 × 3 = 8 × 3 × 10
80 × 3 = 24 × 10
80 × 3 = 240

Question 5.
Structure
Complete the number line. Then write the multiplication equation shown on the number line.

____ × ____ = _____
Answer: 5 × 30 = 150
By using the number line you can write the multiplication equation.
30 + 30 + 30 + 30 + 30 = 150

Question 6.
Modeling Real Life
A gymnasium has 9 rows of seats. Each row has 50 seats. Can the gymnasium seat more than 500 people? Explain.
Answer:
Given,
A gymnasium has 9 rows of seats. Each row has 50 seats.
9 × 50 = 450 seats
450 – 500 = -50 people
No the gymnasium cannot seat more than 500 people.

Question 7.
Modeling Real Life
Ten adults and 20 children fill their bike tires at a public pump. How many tires are filled in all?

Answer:
Given that,
Ten adults and 20 children fill their bike tires at a public pump.
10 × 2 = 20
20 × 2 = 40
20 + 40 = 60
Thus 60 tires are filled in all.

Review & Refresh

Question 8.
There are 35 counters. The counters are in 7 equal rows. How many counters are in each row?
7 rows of _____
35 ÷ 7 = _____

Answer: 5

Explanation:
There are 35 counters.
The counters are in 7 equal rows.
35/7 = 5
7 rows of 5
35 ÷ 7 = 5
Thus there are 5 counters in each row.

Question 9.
You have 32 counters. You arrange them with 8 counters in each row. How many rows of counters do you make?
_____ rows of 8
32 ÷ 8 = ____
Answer: 4

Explanation:
Given that,
You have 32 counters. You arrange them with 8 counters in each row.
32/8 = 4
Thus you can make 4 rows of 8.

Lesson 9.2 Use Place Value to Multiply by Multiples of 10

Explore and Grow

Use models to find each product. Draw your models.
4 × 6 = _____
4 × 60 = _____
Answer: 24, 240

i.
Multiply the rows and columns
4 × 6 = 24
ii. Multiply the two numbers 4 and 60
4 × 60 = 240

Structure
Compare the models. How are they the same? How are they different?
Answer: The models for both the problem are the same but the columns are different.

Think and Grow: Place Value and Multiples of 10

Example
Find 4 × 70.
Step 1:
Make a quick sketch to model the product.
Think: 4 groups of 70, or 7 tens.

4 × 70 = 4 × ____ tens
4 × 70 = ____ tens

Answer:
4 × 70 = 4 × 7 tens
4 × 70 = 28 tens

Step 2:
Regroup ____ tens

There are _____ hundreds and _____ tens.
So, 4 × 70 = _____.
Answer:
There are 2 hundred and 8 tens.
Now regroup tens.
There are 2 tens
So, group the tens.
2 tens are grouped and the remaining is 8.
4 × 70 = 280

Show and Grow

Make a quick sketch to find the product
Question 1.
3 × 80 = ______
Answer: 240

There are 2 hundred and 4 tens.

Question 2.
5 × 40 = _____
Answer: 200

5 × 40 = 20 tens
There are 2 hundred and 0 tens.

Apply and Grow: Practice

Use place value to find the product.
Question 3.
3 × 90 = 3 × ____ tens
3 × 90 = ____ tens
3 × 90 = _____
Answer:
3 × 90 = 3 × 9 tens
3 × 90 = 27 tens
3 × 90 = 270

Question 4.
6 × 60 = 6 × ____ tens
6 × 60 = ____ tens
6 × 60 = _____
Answer:
6 × 60 = 6 × 6 tens
6 × 60 = 36 tens
6 × 60 = 360

Question 5.
2 × 70 = 2 × ____ tens
2 × 70 = ____ tens
2 × 70 = _____
Answer:
2 × 70 = 2 × 7 tens
2 × 70 = 14 tens
2 × 70 = 140

Question 6.
9 × 20 = 9 × ____ tens
9 × 20 = ____ tens
9 × 20 = _____
Answer:
9 × 20 = 9 × 2 tens
9 × 20 = 18 tens
9 × 20 = 180

Find the product
Question 7.
3 × 30 = ____
Answer: 90

Explanation:
3 × 30 = 3 × 3 tens
3 × 30 = 9 tens
3 × 30 = 90

Question 8.
6 × 80 = ____
Answer: 480

Explanation:
6 × 80 = 6 × 8 tens
6 × 80 = 48 tens
6 × 80 = 480

Question 9.
4 × 40 = _____
Answer: 160

Explanation:
4 × 40 = 4 × 4 tens
4 × 40 =  16 tens
4 × 40 = 160

Question 10.
7 × 50 = _____
Answer: 350

Explanation:
7 × 50 = 7 × 5 tens
7 × 50 = 35 tens
7 × 50 = 350

Question 11.
8 × 70 = _____
Answer: 560

Explanation:
8 × 70 = 8 × 7 tens
8 × 70 = 56 tens
8 × 70 = 560

Question 12.
5 × 90 = _____
Answer: 450

Explanation:
5 × 90 = 5 × 9 tens
5 × 90 = 45 tens
5 × 90 = 450

Question 13.
Reasoning
Explain why the product of 6 and 30 has 1 zero and the product of 4 and 50 has 2 zeros.
Answer:
6 × 30 = 180
4 × 50 = 200
4 and 50 has two zeros because it is multiplied by 50 If the number is multiplied by 5 or 10 you will get two zeros.

Question 14.
YOU BE THE TEACHER
Is Descartes correct? Explain.

Answer: Yes, Descartes is correct.
3 × 7 = 21
3 × 70 = 210
So the product of 3 and 70 is equal to the product of 3 and 7 with a 0 written after it.

Think and Grow: Modeling Real Life

Newton saves $30 each month for 6 months. Does he have enough money to buy the drone? Explain.
Newton _______ have enough money to buy the drone.$189

Answer:
Given that,
Newton saves $30 each month for 6 months.
6 × $30 = $180
The cost of the drone is $189.
180 – 189 = -9
Therefore Newton does not have enough money to buy the drone.

Show and Grow

Question 15.
Descartes saves $20 each month for 8 months. Does he have enough money to buy the remote control jeep? Explain.

Answer:
Given that,
Descartes saves $20 each month for 8 months.
8 × $20 = $160
The cost of remote control jeep is $129
160 – 129 = $31
Thus Descartes has enough money to buy the remote control jeep.

Question 16.
You practice playing the guitar for 40 minutes every day. How many minutes do you practice in one week?
Answer:
Given that,
You practice playing the guitar for 40 minutes every day.
1 week = 7 days
7 × 40 = 280
Thus you practice 280 minutes in one week.

Question 17.
A box of snacks has 25 bags of pretzels and 25 bags of peanuts. How many bags are in 9 boxes?
Answer:
Given that,
A box of snacks has 25 bags of pretzels and 25 bags of peanuts.
25 + 25 = 50
50 × 9 = 450
Thus there are 450 bags in 9 boxes.

Use Place Value to Multiply by Multiples of 10 Homework & Practice 9.2

Make a quick sketch to find the product.
Question 1.
5 × 70 = _____
Answer: 350

Question 2.
3 × 60 = ____
Answer: 180

Use place value to find the product
Question 3.
8 × 50 = 8 × ____ tens
8 × 50 = ____ tens
8 × 50 = _____
Answer:
8 × 50 = 8 × 5 tens
8 × 50 = 40 tens
8 × 50 = 400

Question 4.
7 × 60 = 7 × ____ tens
7 × 60 = ____ tens
7 × 60 = _____
Answer:
7 × 60 = 7 × 6 tens
7 × 60 = 42 tens
7 × 60 = 420

Find the product.
Question 5.
6 × 90 = _____
Answer: 540

Explanation:
6 × 90 = 6 × 9 tens
6 × 90 = 54 tens
6 × 90 = 540

Question 6.
8 × 30 = _____
Answer: 240

Explanation:
8 × 30 = 8 × 3 tens
8 × 30 = 24 tens
8 × 30 = 240

Question 7.
5 × 40 = _____
Answer: 200

Explanation:
5 × 40 = 5 × 4 tens
5 × 40 = 20 tens
5 × 40 = 200

Question 8.
Is Newton correct? Explain.

Answer: Newton is incorrect

Explanation:
6 × 50 = 6 × 5 tens
6 × 50 = 30 tens
6 × 50 = 300
By this we can say that Newton is incorrect.

Question 9.
Structure
Write an equation for the quick sketch.

Answer: 2 × 60 = 120
There are 1 group of tens and 2 are remaining.
So, 2 × 60 = 120

Question 10.
Modeling Real Life
Descartes saves $50 each month for 5 months. Does he have enough money to buy the game system? Explain.

Answer:
Given that,
Descartes saves $50 each month for 5 months.
5 × $50 = $250
The cost of the game system is $205.
$250 – $205 = $45
Thus Descartes has enough money to buy the game system.

Question 11.
Modeling Real Life
A group of staff members packs coolers for a field trip. Each cooler has 15 peanut butter sandwiches and 15 turkey sandwiches. How many sandwiches are in 7 coolers?
Answer:
Given that,
A group of staff members packs coolers for a field trip.
Each cooler has 15 peanut butter sandwiches and 15 turkey sandwiches.
15 + 15 = 30
7 × 30 = 210
Thus there are 210 sandwiches in 7 coolers.

Review & Refresh

Question 12.
Round 282 to the nearest ten and to the nearest hundred.
Nearest ten: ____
Nearest hundred: _____
Answer:
First, 282 rounded to the nearest ten is 280.
The number nearest hundred to 282 is 300.

Lesson 9.3 Use Properties to Multiply by Multiples of 10

Explore and Grow

Use the colored rectangles to find 5 × 30.

So, 5 × 30 = ______
Answer: 50 + 50 + 50 = 150

Explanation:
The multiplication equation for the yellow-colored rectangle is 5 × 10 = 50
The multiplication equation for the blue-colored rectangle is 5 × 10 = 50
The multiplication equation for the red-colored rectangle is 5 × 10 = 50
50 + 50 + 50 = 150

Reasoning
How does this model relate to the Distributive Property?
Answer:
Yes, you can relate the above equation to the distributive property.
5 × 30 = 5 × (10 + 20)
5 × 30 = (5 × 10) + (5 × 20)
5 × 30 = 50 + 100
5 × 30 = 150

Think and Grow: Properties and Multiples of 10

Example:
Find 6 × 20
One Way:
Use the Associative Property of Multiplication

6 × 20 = 6 × (_____ × 10)
6 × 20 = (6 × ____) × 10
6 × 20 = ____ × 10
6 × 20 = ____
Rewrite 20 as _____ × 10
Associative Property of Multiplication

Answer:
Rewrite 20 as 2× 10
6 × 20 = 6 × (2 × 10)
6 × 20 = (6 × 2) × 10
6 × 20 = 12 × 10
6 × 20 = 120

Another Way:
Use the Distributive Property

6 × 20 = 6 × (10 × _____)
6 × 20 = (6 × 10) × (6 × ____)
6 × 20 = ____ + _____
6 × 20 = ____

Answer:
Rewrite 20 as 10 + 10
By using the Distributive Property we can find the product.
6 × 20 = 6 × (10 + 10)
6 × 20 = (6 × 10) × (6 × 10)
6 × 20 = 60 + 60
6 × 20 = 120

Show and Grow

Question 1.
Use the Associative Property of Multiplication to find 4 × 60.
4 × 60 = 4 × (_____ × 10)
4 × 60 = (4 × ____) × 10
4 × 60 = ____ × 10
4 × 60 = ____
Answer:
You have to find the product by using the Associative Property of Multiplication.
4 × 60 = 4 × (6 × 10)
4 × 60 = (4 × 6) × 10
4 × 60 = 24 × 10
4 × 60 = 240
Thus the product of 4 × 60 = 240.

Question 2.
Use the Distributive Property to find 9 × 20.
9 × 20 = 9 × (10 × _____)
9 × 20 = (9 × 10) × (9 × ____)
9 × 20 = ____ + _____
9 × 20 = ____
Answer:
You have to find the product by using the Distributive Property of Multiplication.
9 × 20 = 9 × (10 + 10)
9 × 20 = (9 × 10) + (9 × 10)
9 × 20 = 90 + 90
9 × 20 = 180

Apply and Grow: Practice

Use properties to find the product
Question 3.
7 × 30 = _____
Answer: 210

Explanation:
You have to find the product by using the Associative Property of Multiplication.
7 × 30 = 7 × (3 × 10)
7 × 30 = (7 × 3) × 10
7 × 30 = 21 × 10
7 × 30 = 210

Question 4.
5 × 80 = _____
Answer: 400

Explanation:
You have to find the product by using the Associative Property of Multiplication.
5 × 80 = 5 × (8 × 10)
5 × 80 = (5 × 8) × 10
5 × 80 = 40 × 10
5 × 80 = 400

Question 5.
5 × 20 = _____
Answer: 100

Explanation:
You have to find the product by using the Associative Property of Multiplication.
5 × 20 = 5 × (10 × 2)
5 × 20 = (5 × 2) × 10
5 × 20 = 10 × 10
5 × 20 = 100

Question 6.
3 × 90 = _____
Answer: 270

Explanation:
You have to find the product by using the Associative Property of Multiplication.
3 × 90 = 3 × (9 × 10)
3 × 90 = (3 × 9) × 10
3 × 90 = 27 × 10
3 × 90 = 270

Find the missing factor.
Question 7.
8 × ____ = 320
Answer: 40

Explanation:
Let the missing factor be x.
8 × x = 320
x = 320/8
x = 40
Thus the missing factor is 40.

Question 8.
____ × 50 = 300
Answer: 6

Explanation:
Let the missing factor be y.
y × 50 = 300
y = 300/50
y = 6
Thus the missing factor is 6.

Question 9.
_____ × 30 = 270
Answer: 9

Explanation:
Let the missing factor be z.
z × 30 = 270
z = 270/30
z = 9
Thus the missing factor is 9.

Question 10.
Number Sense
Use the Associative Property of Multiplication to show why
4 × 20 = 8 × 10.
Answer:
You have to find the product by using the Associative Property of Multiplication.
4 × 20 = 8 × 10
4 × (2 × 10) = 8 × 10
8 × 10 = 8 × 10
By this we can say that 4 × 20 = 8 × 10.

Question 11.
Open-Ended
Write three expressions equal to 240.

Answer:
The three expressions equal to 240 is
240/3 = 80
2 × 40 | 2 × 40 | 2 × 40
80 + 80 + 80 = 240

Question 12.
Number Sense
Which equations show the Distributive Property?
2 × 20 = (2 × 10) + (2 × 10)
4 × (3 × 10) = (4 × 3) × 10
(7 × 10) + (7 × 10) = 7 × 20
Answer:
2 × 20 = (2 × 10) + (2 × 10) is the distributive property.
4 × (3 × 10) = (4 × 3) × 10 shows the associative property.

Think and Grow: Modeling Real Life

There are 8 tables in the classroom. There are 5 students at each table. Each student has 10 markers. How many markers do the students have in all?

There are ______ markers at each table.
The students have ______ markers in all.

Answer:
Given that,
There are 8 tables in the classroom.
There are 5 students at each table.
8 × 5 = 40
Each student has 10 markers.
40 × 10 = 400

Show and Grow

Question 13.
Your teacher buys 5 boxes of pens. Each box has 6 bundles of 10 pens. How many pens does your teacher buy in all?
Answer:
Given that,
Your teacher buys 5 boxes of pens. Each box has 6 bundles of 10 pens.
6 × 10 = 60
60 × 5 = 300 pens
Thus the teacher buy 300 pens.

Question 14.
DIG DEEPER!
Newton earns $30 each work shift. He wants to buy Descartes a cat tree. The tree costs $150. After how many work shifts can Newton buy the tree?

Answer:
Given,
Newton earns $30 each work shift. He wants to buy Descartes a cat tree. The tree costs $150.
To find how many work shifts can Newton buy the tree, you need to divide the cost of the tree by newton’s earned amount.
150/30 = 5
After 5 work shifts, Newton can buy the tree.

Use Properties to Multiply by Multiples of 10 Homework & Practice 9.3

Question 1.
Use the Associative Property of Multiplication to find 6 × 70.
6 × 70 = 6 × (_____ × 10)
6 × 70 = (6 × ____) × 10
6 × 70 = ____ × 10
6 × 70 = ____
Answer:
6 × 70 = 6 × (7 × 10)
6 × 70 = (6 × 7) × 10
6 × 70 = 42 × 10
6 × 70 = 420

Question 2.
Use the Distributive Property to find 3 × 20.
3 × 20 = 3 × (10 × _____)
3 × 20 = (3 × 10) × (3 × ____)
3 × 20 = ____ + _____
3 × 20 = ____
Answer:
3 × 20 = 3 × (10 × 2)
3 × 20 = (3 × 10) × (1 × 2)
3 × 20 = 30 × 2
3 × 20 = 60

Use properties to find the product.
Question 3.
9 × 20 = _____
Answer: 180

Explanation:
We can find the product by using the distributive property.
9 × 20 = 9 × (10 + 10)
9 × 20 = (9 × 10) + (9 × 10)
9 × 20 = 90 + 90
9 × 20 = 180

Question 4.
5 × 30 = ____
Answer: 150

Explanation:
We can find the product by using the associative property.
5 × 30 = (5 × 3) × 10
5 × 30 = 15 × 10
5 × 30 = 150

Find the missing factor
Question 5.
____ × 60 = 180
Answer: 3

Explanation:
Let the missing factor be x.
x × 60 = 180
x = 180/60
x = 3
Thus the missing factor is 3.

Question 6.
6 × ____ = 240
Answer: 40

Explanation:
Let the missing factor be y.
6 × y = 240
y = 240/6
y = 40
Thus the missing factor is 40.

Question 7.
____ × 80 = 720
Answer: 9

Explanation:
Let the missing factor be z.
z × 80 = 720
z = 720/80
z = 9
Thus the missing factor is 9.

Question 8.
YOU BE THE TEACHER
Your friend draws a model to find 4 × 20. Is your friend correct? Explain.

4 × 10 = 40 4 × 10 = 40
40 + 40 = 80
So, 4 × 20 = 80
Answer: Yes your friend is correct.
There are 4 rows and 20 shaded blocks
4 × 20 = 80

Question 9.
Number Sense
How can you tell whether 7 × 40 or 8 × 70 is greater without finding the products?
Answer: We can find a greater number by seeing the numbers.
7 < 8
40 < 70
7 × 40 = 280
8 × 70 = 560
So, 7 × 40 < 8 × 70

Question 10.
Modeling Real Life
There are 9 teams in a math competition. Each team has 6 students. Each student answers 10 questions. How many questions are answered in all?
Answer:
Given that,
There are 9 teams in a math competition. Each team has 6 students.
9 × 6 = 54 students
Each student answers 10 questions.
54 × 10 = 540
Thus the students answered 540 questions in all.

Question 11.
DIG DEEPER!
A soccer team earns $40 each week washing cars. The team wants to buy an inflatable field for $240. After how many weeks can the team buy the field?
Answer:
Given that,
A soccer team earns $40 each week washing cars.
The team wants to buy an inflatable field for $240.
240/40 = 6
It takes 6 weeks to buy the field.

Review & Refresh

Find the quotient
Question 12.

Answer: 6

Explanation:
Divide the two numbers 3 and 18.
18/3 = 6
Thus the quotient is 6.

Question 13.

Answer: 8

Explanation:
Divide the two numbers 4 and 32
32/4 = 8
Thus the quotient is 8.

Question 14.

Answer: 9

Explanation:
Divide the two numbers 27 and 3
27/3 = 9
Thus the quotient is 9.

Question 15.

Answer: 4

Explanation:
Divide the two numbers 4 and 16.
16/4 = 4
Thus the quotient is 4.

Lesson 9.4 Problem Solving: Multiplication and Division

Explore and Grow

Use any strategy to solve the problem.
Descartes uses 72 blocks to build ships. He uses 9 blocks for each ship. Each ship has 2 fabric sails. How many sails does Descartes use?

Descartes uses _____ fabric sails.
Answer:
Given that,
Descartes uses 72 blocks to build ships. He uses 9 blocks for each ship.
72/9 = 8
Each ship has 2 fabric sails.
8 × 2 = 16 sails
Therefore Descartes uses 16 fabric sails.

Structure
What equations did you use to solve? How can you write the equations using a letter to represent the number of fabric sails?
Answer:
I used the division and multiplication equation to solve the problem.
First, you have to divide the number of blocks by the number of blocks for each ship.
72/9 = 8
After that multiply the blocks by the number of fabric sails.
8 × 2 = 16

Think and Grow: Using the Problem-Solving Plan

Example
A box of 8 burritos costs $9. How much does it cost a group of friends to buy 40 burritos?
Understand the Problem

What do you need to find?
• A box has ______ burritos.
• The box costs _____.
• A group of friends wants to buy ______ burritos.

Answer:

• A box has 8 burritos.
• The box costs $9.
• A group of friends wants to buy 40 burritos.

What do you know?
• You need to find how much it _____ costs to buy.

Answer:
You can find the answer by using the above question.
• You need to find how much burritos cost to buy.

Make a Plan
How will you solve?
• Divide _____ by _____ to find how many _____ the group needs to buy.
• Then multiply the quotient by _____ to find the total cost.

Answer:

• Divide 40 by 8 to find how many burritos the group needs to buy.
• Then multiply the quotient by 9 to find the total cost.

Solve
Step 1:
How many boxes does the group need to buy?

Step 2:
Use to find the total cost.

It costs $ _____ for 40 burritos.

Answer:

First divide 40/8 = 5
b = 5

c = 5 × 9 = 45
Thus the total cost is $45.

Show and Grow

Question 1.
You make 9 shots in a basketball game. Each shot is worth 2 points. Your friend has the same number of points. All of her shots are worth 3 points. How many shots does your friend make?
Answer:
Given that,
You make 9 shots in a basketball game. Each shot is worth 2 points.
9 × 2 = 18 points
Your friend has the same number of points. All of her shots are worth 3 points.
18/3 = 6
Thus your friend needs to make 6 shots.

Apply and Grow: Practice

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.
Question 2.
You read 3 chapters. Each chapter has 8 pages. Your friend reads the same number of pages. All of her chapters have 6 pages. How many chapters does your friend read?
Answer:
Given that,
You read 3 chapters. Each chapter has 8 pages.
3 × 8 pages = 24 pages
Your friend reads the same number of pages. All of her chapters have 6 pages.
24/6 = 4
Thus your friend reads 4 pages.

Question 3.
There are 42 players in a basketball tournament. The players are divided into teams of 7 players. The teams are divided equally among 3 basketball courts. How many teams are at each basketball court?
Answer:
Given that,
There are 42 players in a basketball tournament. The players are divided into teams of 7 players.
42/7 = 6 teams
The teams are divided equally among 3 basketball courts.
6/3 = 3
Thus there are 3 teams at each basketball court.

Question 4.
You have 2 dream catcher kits. Each kit makes 4 dream catchers. You make all of the dream catchers and sell them for $9 each. How much money do you earn?

Answer:
Given that,
You have 2 dream catcher kits. Each kit makes 4 dream catchers.
2 × 4 = 8 dream catchers
You make all of the dream catchers and sell them for $9 each.
8 × 9 = $72
Thus you earn $72.

Question 5.
A box of 4 test tubes costs $6. How much does it cost to buy 20 test tubes?

Answer:
Given that,
A box of 4 test tubes costs $6.
20/4 = 5
5 × $6 = $30
Thus it costs $30 to buy 20 test tubes.

Think and Grow: Modeling Real Life

There are 4 crates of milk bottles. Each crate holds 20 bottles. You hand out an equal number of bottles to 10 tables of students. How many bottles of milk does each table of students get?

Understand the problem:
Make a plan:
Solve:
Each table of students gets _____ bottles of milk.

Answer:
Given that,
There are 4 crates of milk bottles. Each crate holds 20 bottles.
4 × 20 = 80 bottles
You hand out an equal number of bottles to 10 tables of students.
80/10 = 8
Therefore each table of students gets 8 bottles of milk.

Show and Grow

Question 6.
Six groups of hikers have 2 cases of water to share equally. Each case has 30 bottles of water. How many bottles of water does each group get?

Answer:
Given,
Six groups of hikers have 2 cases of water to share equally. Each case has 30 bottles of water.
2 × 30 = 60 bottles of water
There are 6 groups so divide 60 by 6.
60/6 = 10
Thus each group gets 10 bottles of water.

Question 7.
DIG DEEPER!
Newton and Descartes decide to buy 2 pet toys that cost $20 each. Newton saves $5 each week. Descartes saves $3 each week. If they combine their money, how long does it take them to save enough money to buy the toys?
Answer:
Given that,
Newton and Descartes decide to buy 2 pet toys that cost $20 each.
2 × 20 = $40
Newton saves $5 each week. Descartes saves $3 each week.
5 + 3 = 8
40/8 = 5
Thus it takes 5 weeks to buy the toys.

Problem Solving: Multiplication and Division Homework & Practice 9.4

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.
Question 1.
Your friend saves $5 each week for 8 weeks. He spends all of the money on 4 toys that each cost the same amount. How much does each toy cost?
Answer:
Given that,
Your friend saves $5 each week for 8 weeks.
He spends all of the money on 4 toys that each cost the same amount.
To find the cost of the toy we need to multiply your friend savings and the number of weeks.
8 × 5 = 40
Thus the cost of the toy is $40.

Question 2.
There are 3 trees. Each tree has 2 birdhouses. Each birdhouse has 4 birds. How many birds are there in all?

Answer:
Given that,
There are 3 trees. Each tree has 2 birdhouses.
3 × 2 = 6 birdhouses
Each birdhouse has 4 birds.
6 × 4 = 24 birds
Therefore there are 24 birds in all.

Question 3.
There are 54 students at a field day who are divided equally into teams of 6 students. The teams are divided equally among 3 stations. How many teams are at each station?
Answer:
Given that,
There are 54 students at a field day who are divided equally into teams of 6 students.
54/6 = 9 teams
The teams are divided equally among 3 stations.
Again the teams are divided into 3 stations.
9/3 = 3
Thus there are 3 teams at each station.

Question 4.
Newton runs an equal number of miles 2 days each week. He runs 8 miles each week. One mile is equal to 4 laps around the track. Which equation can you use to find how many laps Newton runs each day?
r = 8 ÷ 4
r = 4 ÷ 4
r = 4 × 4
r = 2 × 4
Answer:
Given that,
Newton runs an equal number of miles 2 days each week. He runs 8 miles each week. One mile is equal to 4 laps around the track.
8/2 = 4
To find how many laps Newton runs each day you need to divide 4 by 4
r = 4 ÷ 4
Thus the correct answer is option b.

Question 5.
Modeling Real Life
Ten classrooms have 3 boxes of white boards to share equally. Each box has 30 white boards. How many white boards does each classroom get?

Answer:
Given that,
Ten classrooms have 3 boxes of white boards to share equally.
Each box has 30 white boards.
1 box = 30 whiteboards
3 boxes = 3 × 30 = 90 white boards
Now divide the whiteboards by number of classrooms.
90/10 = 9
Thus each classroom gets 9 whiteboards.

Question 6.
DIP DEEPER!
Newton and Descartes decide to buy 2 amusement park tickets that cost $30 each. Newton saves $2 each week. Descartes saves $4 each week. If they combine their money, how long does it take them to save enough money to buy the tickets?
Answer:
Given that,
Newton and Descartes decide to buy 2 amusement park tickets that cost $30 each.
Newton saves $2 each week. Descartes saves $4 each week.
2 + 4 = 6
Now divide the ticket cost by their savings.
30/6 = 5
Therefore it takes 5 weeks to save enough money to buy the tickets.

Review & Refresh

Round to the nearest ten to estimate the difference
Question 7.

Answer:
58 round to the nearest ten is 60.
27 round to the nearest ten is 30.
60
-30
30
Thus the estimated difference is 30.

Question 8.

Answer:
763 round to the nearest ten is 760.
415 round to the nearest ten is 420.
760
-420
340
Thus the estimated difference is 340.

Question 9.

Answer:
686 round to the nearest ten is 690.
24 round to the nearest ten is 20.
690
-20
670
Thus the estimated difference is 670.

Lesson 9.5 Problem Solving: All Operations

Explore and Grow

Use any strategy to solve the problem.
You are making 6 fruit baskets. Each basket has 3 pieces of fruit in it to start. You buy 18 bananas and divide them equally among the baskets. How many pieces of fruit are in each fruit basket now?
There are ______ pieces of fruit in each fruit basket now.
Answer:
Given that,
You are making 6 fruit baskets. Each basket has 3 pieces of fruit in it to start.
6 × 3 = 18
You buy 18 bananas and divide them equally among the baskets.
18/18 = 1
Thus there are 4 pieces of fruit in each fruit basket now.

Structure
How can you solve this problem using one equation?
Answer:
We can solve the above problem by using the multiplication equation.
First, you need to multiply the number of fruit baskets by the number of pieces of fruit.
After that divide the number of pieces by the number of bananas.

Think and Grow: One Equation with Two Operations

Example
Newton buys 3 DVDs for $4 each. He pays with a $20 bill. What is his change?
You can write one equation with two operations to solve this problem.
The equation is shown.
20 – 3 × 4 = c ← c is the amount of change.
When solving a problem with more than one type of operation, use the rules below.
• First, multiply or divide as you read the equation from left to right.
• Then add or subtract as you read the equation from left to right.
Step 1:
Multiply from left to right.
20 – 3 × 4 = c
20 – ____ = c

Step 2: Subtract from left to right.
20 – ____ = c
____ = c
His change is ____.

Answer:
Step 1:
Multiply from left to right.
20 – 3 × 4 = c
20 – 12 = c
Step 2: Subtract from left to right.
20 – 12 = c
8 = c
His change is 8.

Show and Grow

Question 1.
There are 8 tomato plants. You pick 9 tomatoes from each plant. You give away 35 of them. Use the equation 8 × 9 – 35 to find how many tomatoes you have left.

Answer:
Given that,
There are 8 tomato plants. You pick 9 tomatoes from each plant.
8 × 9 = 72
You give away 35 of them.
We can find the number of tomatoes left by using the equation.
8 × 9 – 35
72 – 35 = 37
Thus 37 tomatoes are left.

Question 2.
A family buys 5 tickets for a musical. Each ticket costs $9. They spend $28 at the musical on snacks. Write and solve an equation to find how much they spend in all at the musical. Use to represent the total amount spent.
Answer:
Given that,
A family buys 5 tickets for a musical. Each ticket costs $9.
5 × $9 = $45
They spend $28 at the musical on snacks.
45 – 28 = 17
The equation to find how much they spend in all at the musical is 5 × 9 – 45

Apply and Grow: Practice

Write an equation to solve. Use a letter to represent the unknown number. Check whether your answer is reasonable.
Question 3.
Newton buys 2 movie tickets. Each ticket costs $7. Descartes spends $23 at the movie on snacks. How much money do they spend in all at the movie?
Answer:
Given,
Newton buys 2 movie tickets. Each ticket costs $7.
2 × 7 = $14
Descartes spends $23 at the movie on snacks.
23 + 2 × 7
23 + 14 = $37

Question 4.
Newton has 28 cards. Descartes has 24 cards. Newton divides his cards into 4 equal stacks and gives Descartes one stack. How many cards does Descartes have now?
Answer:
Given,
Newton has 28 cards. Descartes has 24 cards. Newton divides his cards into 4 equal stacks and gives Descartes one stack.
28/4 = 7
Thus there are 7 cards in each stack.
24 + 7 = 31 cards
Therefore Descartes has 31 cards now.

Question 5.
There are 12 apps divided into 3 equal rows on a smart phone. One row of apps is removed. How many apps are left?

Answer:
Given that,
There are 12 apps divided into 3 equal rows on a smart phone.
12/3 = 4
There are 4 apps in each row
One row of apps is removed.
12 – 4 = 8
Thus 8 apps are left.

Question 6.
It costs $240 each week to rent a car. Newton has a coupon that saves him $10 each day he rents the car. How much will it cost him to rent the car for a week with the coupon?

Answer:
Given that,
It costs $240 each week to rent a car. Newton has a coupon that saves him $10 each day he rents the car.
1 week – 7 days
1 day – $10
7 × 10 = $70
240 – 70 = $170

Question 7.
YOU BE THE TEACHER
Your friend says 24 – 6 ÷ 2 = 9. Is your friend correct? Explain.
Answer:
No, because you need to solve the equation from the left.
24 – (6 ÷ 2) = 24 – 12
= 12
Thus your friend is incorrect.

Think and Grow: Modeling Real Life

Newton has $135. He saves $20 each week for 8 weeks. How much money does he have now?

Understand the problem:
Make a plan:
Solve:
Newton now has _____.

Answer:
Given,
Newton has $135. He saves $20 each week for 8 weeks.
20 × 8 = 160
$135 + $160 = $295
Thus Newton now gas $295.

Show and Grow

Question 8.
Your teacher buys 3 packages of napkins for a class party. Each package has 50 napkins. The class uses 79 napkins. How many napkins are left?

Answer:
Given,
Your teacher buys 3 packages of napkins for a class party. Each package has 50 napkins.
1 pack – 50 napkins
3 packs – 3 × 50 = 150
The class uses 79 napkins.
150 – 79 = 71
Thus 71 napkins are left.

Question 9.
There are 60 seconds in one minute. It takes you 2 minutes and 16 seconds to run from your home to your friend’s home. How many seconds does it take you?
Answer:
Given,
There are 60 seconds in one minute. It takes you 2 minutes and 16 seconds to run from your home to your friend’s home.
1 min – 60 seconds
2 mins – 2 × 60 = 120 seconds
120 + 16 = 136 seconds
Thus it takes 136 seconds to run from your home to your friend’s home.

Question 10.
A store is selling comic books for $5 each. The store sells 33 superhero comic books and 57 science-fiction comic books. How much money does the store earn?
Answer:
Given,
A store is selling comic books for $5 each.
The store sells 33 superhero comic books and 57 science-fiction comic books.
33 + 57 = 90
5 × 90 = $450
Thus the store earn $450.

Problem Solving: All Operations Homework & Practice 9.5

Question 1.
There are 20 math problems divided into 4 equal columns on a worksheet. Your teacher has you cross out one column of problems. Use the equation 20 – 20 ÷ 4 = p to find how many problems are left.
Answer:
Given that,
There are 20 math problems divided into 4 equal columns on a worksheet. Your teacher has you cross out one column of problems.
20 – 20 ÷ 4 = p
20 – 5 = p
15 = p
Thus 15 problems are left.

Question 2.
Newton has 42 blocks. Descartes has 48 blocks. Newton divides his blocks into 6 equal groups and gives Descartes one group. How many blocks does Descartes have now? Use d to represent how many blocks Descartes has now.
Answer:
Given,
Newton has 42 blocks. Descartes has 48 blocks. Newton divides his blocks into 6 equal groups and gives Descartes one group.
42/6 = 7 blocks
48 + 7 = 55 blocks
Thus Descartes has 55 blocks now.

Question 3.
There are 6 palm trees. An islander gathers 8 coconuts from each tree. She gives away 19 of them. How many coconuts does she have now? Write an equation to solve. Use a letter to represent the unknown number. Check whether your answer is reasonable.

Answer:
Given,
There are 6 palm trees. An islander gathers 8 coconuts from each tree. She gives away 19 of them.
6 × 8 – 19 = p
48 – 19 = p
29 = p
Thus the unknown number is 29.

Question 4.
DIG DEEPER!
Find the number that makes 5 × ____ – 15 = 5 true. Explain.
Answer:
5 × ____ – 15 = 5
5 × p – 15 = 5
p – 15 = 5/5
p – 15 = 1
p = 1 + 15
p = 16
Thus the value of the number is 16.

Question 5.
Number Sense
Which equations are true?

Answer:
3 + 5 × 2 = 13
Solve from left to right.
3 + 10 = 13
13 = 13 (true)
20 – 10 × 2 = 20
20 – 20 = 0 (false)
36 ÷ 6 + 3 = 4
36 ÷ 9 = 4
4 = 4 (true)
26 – 8 ÷ 2 = 22
26 – 4 = 22
22 = 22 (true)

Question 6.
Modeling Real Life
A school nurse orders 7 packages of bandages. Each package has 20 bandages. The nurse uses 53 bandages. How many bandages are left?
Answer:
Given,
A school nurse orders 7 packages of bandages. Each package has 20 bandages.
7 × 20 = 140 bandages
The nurse uses 53 bandages.
140 – 53 = 87 bandages
Thus 87 bandages are left.

Question 7.
Modeling Real Life
There are 60 seconds in one minute. You record a video that is 3 minutes and 48 seconds long. How many seconds long is the video?
Answer:
Given,
There are 60 seconds in one minute. You record a video that is 3 minutes and 48 seconds long.
3 mins = 3 × 60 = 180 seconds
180 + 48 = 228 seconds
Thus the video is 228 seconds long.

Review & Refresh

Estimate. Then find the sum. Check whether your answer is reasonable.
Question 8.
Estimate: _____

Answer:
The estimated number for 23 is 20.
The estimated number for 358 is 360.
The estimated number for 172 is 170.
360
170
+20
550

Question 9.
Estimate: _____

Answer:
The estimated number for 202 is 200.
The estimated number for 64 is 60.
The estimated number for 545 is 550.
550
200
+60
810

Question 10.
Estimate: _____

Answer:
The estimated number for 21 is 20
The estimated number for 15 is 20
The estimated number for 837 is 840
840
20
+20
880

Multiples and Problem Solving Performance Task

Question 1.
a. You read 120 minutes from Monday through Thursday this week. How many minutes do you read on Thursday? Complete the picture graph for Thursday.

Answer:
Given,
You read 120 minutes from Monday through Thursday this week.
Each star = 10 minutes
There are 9 stars
9 × 10 = 90 minutes
120 – 90 = 30 minutes
Thus you read 30 minutes on Thursday.

b. Last week you read 30 minutes each day for 5 days. Your goal this week is to read the same number of minutes as last week. How many minutes do you need to read on Friday to reach your goal? Complete the picture graph for Friday.
Answer:
Given,
Last week you read 30 minutes each day for 5 days. Your goal this week is to read the same number of minutes as last week.
30 × 5 = 150 minutes
150 – 120 = 30 minutes
Thus to reach your goal you need to read 30 minutes on Friday.

Question 2.
Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.
a. There are 60 minutes in one hour. Your friend reads 2 hours and 38 minutes during the week. How many minutes does your friend read in all?

Answer:
Given,
There are 60 minutes in one hour. Your friend reads 2 hours and 38 minutes during the week.
1 hour – 60 min
2 hour – 2 × 60 = 120 min
120 + 38 = 158 min
Thus your friend read 158 minutes in all.

b.Your cousin earns 2 stars on her graph each day for 5 days. How many minutes does your cousin read in all?
Answer:
Given,
Your cousin earns 2 stars on her graph each day for 5 days.
2 × 5 = 10 stars
1 star = 10 min
10 stars = 10 × 10 min = 100 min
Thus your cousin read 100 min in all.

Question 3.
Use the information above. Order the numbers of minutes you, your friend, and your cousin read from least to greatest. The person with the least number of minutes wants to read the same amount as the person with the greatest number of minutes. How many more minutes does the person need to read?

Answer:
Given that,
you read 150 minutes in all.
your friend read 158 minutes in all
your cousin read 100 min in all.
The order from least to greatest is 100, 150, 158.

Multiples and Problem Solving Activity

Multiplication Flip and Find
Directions:
1. Place the Multiplication Flip and Find Cards face down in the boxes.
2. Players take turns flipping two cards.
3. If your cards show a matching expression and product, then keep the cards. If your cards do not show a matching expression and product, then flip the cards back over.
4. Play until all matches are made.
5. The player with the most matches wins!

Answer:
Total number of cards = 12
There are 2 matching flip cards in boxes
To find the most matches we have to divide the total number of flip cards by matching cards.
12/2 = 6
Thus the player with the most matches wins is 6.

Multiples and Problem Solving Chapter Practice

9.1 Use Number Lines to Multiply by Multiples of 10

Question 1.
Find 8 × 20
Number of jumps: ______
Size of each jumps: _____

8 × 20 = _____
Answer: 160
Number of jumps: 8
Size of each jump: 20
8 jumps of 20 = 160

Question 2.
Find 7 × 40

7 × 40 = ____
Answer: 280

Explanation:
Number of jumps: 7
Size of each jump: 40
7 jumps of 40 = 7 × 40 = 280

Question 3.
Find 30 × 9
30 × 9 = ____
Answer: 270

Explanation:
Number of jumps: 9
Size of each jump: 30
30 × 9 = 270

Question 4.
Structure
Complete the number line. Then write the multiplication equation for the number line.

____ × ____ = ____
Answer: 3 × 40 = 120

Explanation:
By seeing the above number line we can say that there are
3 jumps of 40
That means 3 × 40
40 + 40 + 40 = 120
Thus the multiplication equation is 3 × 40 = 120

9.2 Use Place Value to Multiply by Multiples of 10

Make a quick sketch to find the product
Question 5.
6 × 40 = _____
Answer: 240
Number of jumps: 6
Size of each jump: 40
We can find the product by using the number line.
6 jumps of 40.
6 × 40 = 240

Question 6.
5 × 20 = ____
Answer: 100
Number of jumps: 5
Size of each jump: 20
We can find the product by using the number line.
5 jumps of 20.
5 × 20 = 100

Use place value to find the product
Question 7.
4 × 50 = 4 × ____ tens
4 × 50 = ____ tens
4 × 50 = ____
Answer:
4 × 50 = 4 × 5 tens
4 × 50 = 20 tens
4 × 50 = 20 × 10
4 × 50 = 200

Question 8.
3 × 60 = 3 × ____ tens
3 × 60 = ____ tens
3 × 60 = ____
Answer:
3 × 60 = 3 × 6 tens
3 × 60 = 18 tens
3 × 60 = 18 × 10
3 × 60 = 180

Question 9.
7 × 70 = 7 × ____ tens
7 × 70 = ____ tens
7 × 70 = ____
Answer:
7 × 70 = 7 × 7 tens
7 × 70 = 49 tens
7 × 70 = 49 × 10
7 × 70 = 490

Question 10.
9 × 80 = 9 × ____ tens
9 × 80 = ____ tens
9 × 80 = ____
Answer:
9 × 80 = 9 × 8 tens
9 × 80 = 72 tens
9 × 80 = 72 × 10
9 × 80 = 720

Find the product
Question 11.
2 × 60 = _____
Answer: 120

Explanation:
We can write 60 as 6 tens.
2 × 60 = 2 × 6 tens
2 × 60 = 12 tens
2 × 60 = 12 × 10
2 × 60 = 120

Question 12.
8 × 40 = ____
Answer: 320

Explanation:
We can write 40 as 4 tens.
8 × 40 = 8 × 4  tens
8 × 40 = 32 tens
8 × 40 = 32 × 10
8 × 40 = 320

Question 13.
5 × 90 = _____
Answer: 450

Explanation:
We can write 90 as 9 tens.
5 × 90 = 5 × 9 tens
5 × 90 = 45 tens
5 × 90 = 45 × 10
5 × 90 = 450

Question 14.
Modeling Real Life
You practice ballet for 30 minutes every day. How many minutes do you practice in one week?

Answer: 210 minutes

Explanation:
Given that,
You practice ballet for 30 minutes every day.
Convert from week to days.
1 week – 7 days
7 × 30 min = 210 minutes
Thus you practice 210 minutes in one week.

9.3 Use Properties to Multiply by Multiples of 10

Question 15.
Use the Associative Property of Multiplication to find 4 × 90.
4 × 90 = 4 × (____ × 10)
4 × 90 = (4 × ____) × 10
4 × 90 = ____ × 10
4 × 90 = ____
Answer:
We can find the product by using the Associative property.
4 × 90 = 4 × (9 × 10)
4 × 90 = (4 × 9) × 10
4 × 90 = 36 × 10
4 × 90 = 360

Question 16.
Use the Distributive Property to find 8 × 20.
8 × 20 = 8 × (10 + ____)
8 × 20 = (8 × 10) + (8 × ____)
8 × 20 = ___ + ____
8 × 20 = ____
Answer:
We can find the product by using the distributive property.
8 × 20 = 8 × (10 + 10)
8 × 20 = (8 × 10) + (8 × 10)
8 × 20 = 80 + 80
8 × 20 = 160

Use properties to find the product
Question 17.
7 × 20 = ____
Answer: 140

Explanation:
We can find the product by using the distributive property.
7 × 20 = 7 × (10 + 10)
7 × 20 = (7 × 10) + (7 × 10)
7 × 20 = 70 + 70
7 × 20 = 140

Question 18.
5 × 70 = ____
Answer: 350

Explanation:
We can find the product by using the Associative property.
5 × 70 = 5 × (7 × 10)
5 × 70 = (5 × 7) × 10
5 × 70 = 35 × 10
5 × 70 = 350

Find the missing factor
Question 19.
____ × 20 = 180
Answer: 9

Explanation:
Let the missing factor be x.
x × 20 = 180
x = 180/20
x = 9
Thus the missing factor is 9

Question 20.
7 × ___ = 350
Answer: 50

Explanation:
Let the missing factor be y.
7 × y = 350
y = 350/7
y = 50
Thus the missing factor is 50.

Question 21.
____ × 80 = 240
Answer: 3

Explanation:
Let the missing factor be z.
z × 80 = 240
z = 240/80
z = 3
Thus the missing factor is 3.

Question 22.
Open-Ended
Write three expressions equal to 120.
_____ × ______
_____ × ______
_____ × _______
Answer:
The three expressions equal to 120 are given below,
1 × 120 = 120
2 × 60 = 120
3 × 40 = 120

9.4 Problem Solving: Multiplication and Division

Write equations to solve. Use letters to represent the unknown numbers. Check whether your answer is reasonable.
Question 23.
There are 2 bookcases. Each bookcase has 3 shelves of 5 books. How many books are there in all?
Answer: 30

Explanation:
Given,
There are 2 bookcases.
Each bookcase has 3 shelves of 5 books.
3 × 5 = 15 books in one bookcase
15 × 2 = 30 books
Thus there are 30 books in 2 bookcases.

Question 24.
Four veterinarians share 2 boxes of ear wipes. Each box has 20 packs of ear wipes. How many packs of ear wipes does each veterinarian get?
Answer:
Given,
Four veterinarians share 2 boxes of ear wipes.
Each box has 20 packs of ear wipes.
2 × 20 = 40 packs
There are 4 veterinarians.
40/4 = 10
Thus each veterinarian gets 10 packs of ear wipes.

9.5 Problem Solving: All Operation

Write an equation to solve. Use a letter to represent the unknown number. Check whether your answer is reasonable.
Question 25.
Newton has 30 beads. Descartes has 22 beads. Newton divides his beads into 3 equal groups and gives Descartes one group. How many beads does Descartes have now?

Answer: 32 beads

Explanation:
Given that,
Newton has 30 beads. Descartes has 22 beads.
Newton divides his beads into 3 equal groups and gives Descartes one group.
30/3 = 10 beads
Thus there are 10 beads in each group.
22 + 10 = 32
Therefore Descartes has 32 beads now.

Question 26.
It costs $166 to rent a bounce house for 7 hours. Descartes has a coupon that saves him $5 each hour he rents the bounce house. How much will it cost him to rent the bounce house for 7 hours with the coupon?

Answer:
Given,
It costs $166 to rent a bounce house for 7 hours.
Descartes has a coupon that saves him $5 each hour he rents the bounce house.
7 × $5 = $35
$166 – $35 = $131 for 7 hours with the coupon.
Thus it will cost $131 to rent the bounce house for 7 hours with the coupon.

Final Words:

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Lesson – 1: Use Arrays to Divide

• Lesson 4.1 Use Arrays to Divide
• Use Arrays to Divide Homework & Practice 4.1

Lesson – 2: Relate Multiplication and Division

• Lesson 4.2 Relate Multiplication and Division
• Relate Multiplication and Division Homework & Practice 4.2

Lesson – 3: Divide by 2, 5, or 10

• Lesson 4.3 Divide by 2, 5, or 10
• Divide by 2, 5, or 10 Homework & Practice 4.3

Lesson – 4: Divide by 3 or 4

• Lesson 4.4 Divide by 3 or 4
• Divide by 3 or 4 Homework & Practice 4.4

Lesson – 5: Divide by 6 or 7

• Lesson 4.5 Divide by 6 or 7
• Divide by 6 or 7 Homework & Practice 4.5

Lesson – 6: Divide by 8 or 9

• Lesson 4.6 Divide by 8 or 9
• Divide by 8 or 9 Homework & Practice 4.6

Lesson – 7: Divide by 0 or 1

• Lesson 4.7 Divide by 0 or 1
• Divide by 0 or 1 Homework & Practice 4.7

Lesson – 8: Practice Division Strategies

• Lesson 4.8 Practice Division Strategies
• Practice Division Strategies Homework & Practice 4.8

Lesson – 9: Problem Solving: Division

• Lesson 4.9 Problem Solving: Division
• Problem Solving: Division Homework & Practice 4.9

Performance Task

• Division Facts and Strategies Performance Task
• Division Facts and Strategies Activity
• Division Facts and Strategies Chapter Practice
• Division Facts and Strategies Cumulative Practice
• Division Facts and Strategies STEAM Performance Task

Lesson 4.1 Use Arrays to Divide

Explore and Grow

Build an array to model 12. Draw the array.
Number of rows: _______
Number in each row: ______
Answer:
Number of rows: 4
Number in each row: 3

Structure
Compare your array with your partner’s array. How are they the same? How are they different?
Answer: The number of counters is the same but the rows and columns are different.

Think and Grow: Division and Arrays

Example
There are 40 counters. The counters are in5 equal rows. How many counters are in each row?

There are ______ counters in each row.

Answer: 8

Explanation:
Number of rows = 5
Total number of counters = 40
So, the division equation is 40 ÷ 5 = 8
There are 8 counters in each row.

Show and Grow

Find the quotient.
Question 1.

14 ÷ 2 = _____
Answer: 7

Explanation:
Number of counters = 14
Number of rows = 2
To find the quotient you have to divide the number of counters by the number of rows.
14 ÷ 2 = 7
Thus the number of columns in each row = 7

Question 2.

12 ÷ 3 = ______
Answer: 4

Explanation:
Number of counters = 12
Number of rows = 3
To find the quotient you have to divide the number of counters by the number of rows.
12 ÷ 3 = 4
Thus the number of columns in each row = 4

Question 3.
There are 20 counters. The counters are in 4 equal rows. How many counters are in each row?
4 rows of _____
20 ÷ 4 = _____
Answer: 5

Explanation:
Given,
There are 20 counters. The counters are in 4 equal rows.
To find the quotient you have to divide the number of counters by the number of rows.
20 ÷ 4 = 5
4 rows of 5
There are 5 counters in each row.

Question 4.
You have 21 counters. You arrange them with 7 counters in each row. How many rows of counters do you make?
____ rows of 7
21 ÷ 7 = _____
Answer: 3

Explanation:
Given,
You have 21 counters. You arrange them with 7 counters in each row.
21 ÷ 7 = 3
3 rows 7
Thus you make 3 rows of 7 counters.

Apply and Grow: Practice

Question 5.
There are 25 counters. The counters are in 5 equal rows. How many counters are in each row?
5 rows of _____
25 ÷ 5 = _____
Answer: 5

Explanation:
Given,
There are 25 counters.
The counters are in 5 equal rows.
To find the quotient you have to divide the number of counters by the number of rows.
25 ÷ 5 = 5
There are 5 counters in each row.

Question 6.
There are 48 counters. The counters are in 8 equal rows. How many counters are in each row?
8 rows of _____
48 ÷ 8 = _____
Answer: 6

Explanation:
Given,
There are 48 counters. The counters are in 8 equal rows.
To find the quotient you have to divide the number of counters by the number of rows.
48 ÷ 8 = 6
8 rows of 6 counters
There are 6 counters in each row.

Question 7.
You have 42 counters. You arrange them with 6 counters in each row. How many rows of counters do you make?
____ rows of 6
42 ÷ 6 = _____
Answer: 7

Explanation:
Given,
You have 42 counters. You arrange them with 6 counters in each row.
7 rows of 6
42 ÷ 6 = 7
There are 7 rows of counters.

Question 8.
You have 27 counters. You arrange them with 9 counters in each row. How many rows of counters do you make?
____ rows of 9
27 ÷ 9 = _____
Answer: 3

Explanation:
Given that,
You have 27 counters. You arrange them with 9 counters in each row.
27 ÷ 9 = 3
3 rows of 9.
There are 3 rows of counters.

Write a division equation for the array.
Question 9.

_____ ÷ _____ = _____
Answer: 4 ÷ 2 = 2

Explanation:
There are 4 rows and 2 counters.
The division equation for the array is 4 ÷ 2 = 2

Question 10.

____ ÷ _____ = _____
Answer: 40 ÷ 4 = 10

Explanation:
There are 4 rows and 40 counters.
The division equation for the array is 40 ÷ 4 = 10

Question 11.
YOU BE THE TEACHER
Your friend has 63 counters in 7 equal rows. Your friend says that finding 7 ÷ 63 will give the number of columns. Is your friend correct? Explain.
Answer: No your friend is incorrect.

Explanation:
Given,
Your friend has 63 counters in 7 equal rows.
Your friend says that finding 7 ÷ 63 will give the number of columns.
Your friend is incorrect because you have to divide the number of counters by a number of equal rows.
63 ÷ 7 = 9
There are 9 columns.

Think and Grow: Modeling Real Life

Two groups of students are playing a flip and find game. Your group arranges 48 cards in 8 equal rows. The other group arranges 28 cards in 4 equal rows. Which group has rows with more cards?
Draw:
Division equations:
_______ has rows with more cards.

Explanation:
Given,
Two groups of students are playing a flip and find game.
Your group arranges 48 cards in 8 equal rows.
48 ÷ 8 = 6 in each row
The other group arranges 28 cards in 4 equal rows.
28 ÷ 4 = 7 in each row.
The second group has 7 rows with more cards.

Show and Grow

Question 12.
Newton arranges 12 magnets in 6 equal rows. Descartes arranges 15 magnets in 3 equal rows. Who has rows with more magnets?

Answer:
Given,
Newton arranges 12 magnets in 6 equal rows.
12 ÷ 6 = 2
Descartes arranges 15 magnets in 3 equal rows.
15 ÷ 3 = 5
Thus Descartes has 5 rows with more magnets.

Question 13.
You have 18 jars of green slime and 12 jars of purple slime at a party. Each guest takes 3 jars. There are none left. How many guests are at the party?

Answer:
Given that,
You have 18 jars of green slime and 12 jars of purple slime at a party.
18 + 12 = 30 jars
Each guest takes 3 jars. There are none left.
30 ÷ 3 = 10
Thus there are 10 guests at the party.

Use Arrays to Divide Homework & Practice 4.1

Find the quotient.
Question 1.

10 ÷ 2 = _____
Answer: 5

Explanation:
Number of counters = 10
Number of rows = 2
To find the quotient you have to divide the number of counters by the number of rows.
10 ÷ 2 = 5
Thus there are 5 counters in each row.

Question 2.

35 ÷ 5 = _____
Answer: 7

Explanation:
Number of counters = 35
Number of rows = 5
To find the quotient you have to divide the number of counters by the number of rows.
35 ÷ 5 = 7
Thus there are 7 counters in each row.

Question 3.
There are 9 counters. The counters are in 3 equal rows. How many counters are in each row?
3 rows of ____
9 ÷ 3 = ____
Answer: 3

Explanation:
Given that,
There are 9 counters. The counters are in 3 equal rows.
To find the quotient you have to divide the number of counters by the number of rows.
9 ÷ 3 = 3
3 rows of 3
Thus there are 3 counters in each row.

Question 4.
There are 60 counters. The counters are in 6 equal rows. How many counters are in each row?
6 rows of _____
60 ÷ 6 = ____
Answer: 10.

Explanation:
Given,
There are 60 counters.
The counters are in 6 equal rows.
To find the number of counters in each row you have to divide the total number of counters by the number of rows.
60 ÷ 6 = 10
6 rows of 10 counters
Thus there are 10 counters in each row.

Question 5.
You have 72 counters. You arrange them with 8 counters in each row. How many rows of counters do you make?
____ rows of 8
72 ÷ 8 = ____
Answer: 9

Explanation:
Given,
You have 72 counters. You arrange them with 8 counters in each row.
To find the number of counters in each row you have to divide the total number of counters by the number of rows.
72 ÷ 8 = 9
9 rows of 8.
Thus there are 9 counters in each row.

Question 6.
You have 24 counters. You arrange them with 6 counters in each row. How many rows of counters do you make?
____ rows of 6
24 ÷ 6 = ____
Answer: 4

Explanation:
Given,
You have 24 counters. You arrange them with 6 counters in each row.
24 ÷ 6 = 4
4 rows of 6
Thus there are 4 counters in each row.

Question 7.
Writing
How can you use an array to find 35 ÷ 7?
Answer: 5

Explanation:
Number of counters = 35
Number of rows = 7
To find the number of counters in each row you have to divide the total number of counters by the number of rows.
35 ÷ 7 = 5

Question 8.
Precision
Label the parts of the division problem using quotient, dividend and divisor.

Answer:
12 is dividend
6 is divisor and
2 is quotient

Question 9.
Modeling Real Life
Your apartment building has 40 mailboxes in 5 equal rows. Your friend’s apartment building has 40 mailboxes in 4 equal rows. Which apartment building has rows with more mailboxes?
Answer: Your friend’s apartment building 10 rows with more mailboxes

Explanation:
Given,
Your apartment building has 40 mailboxes in 5 equal rows.
40 ÷ 5 = 8
Your friend’s apartment building has 40 mailboxes in 4 equal rows.
40 ÷ 4 = 10
Thus Your friend’s apartment building 10 rows with more mailboxes.

Question 10.
Modeling Real Life
There are 8 snack bags of pretzels and 10 snack bags of popcorn. The bags are divided equally between 9 friends. How many snack bags does each friend get?

Answer:
Given,
There are 8 snack bags of pretzels and 10 snack bags of popcorn.
8 + 10 = 18 snack bags
The bags are divided equally between 9 friends.
18 ÷ 9 = 2
Thus each friend gets 2 snack bags.

Review & Refresh

Find the missing factor
Question 11.
____ × 2 = 20
Answer: 10

Explanation:
Let the missing factor be a.
a × 2 = 20
a = 20/2
a = 10
Thus the missing factor is 10.

Question 12.
1 × ____ = 5
Answer: 5

Explanation:
Let the missing factor be b.
1 × b = 5
b = 5/1
b = 5
Thus the missing factor is 5.

Question 13.
____ × 6 = 0
Answer: 0

Explanation:
Let the missing factor be c.
c × 6 = 0
c = 0/6
c = 0
Thus the missing factor is 0.

Question 14.
1 × ___ = 0
Answer: 0

Explanation:
Let the missing factor be d.
1 × d = 0
d = 0/1
d = 0
Thus the missing factor is 0.

Question 15.
____ × 4 = 40
Answer: 10

Explanation:
Let the missing factor be e.
e × 4 = 40
e = 40/4
e = 10
Thus the missing factor is 10.

Question 16.
7 × ____ = 7
Answer: 1

Explanation:
Let the missing factor be f.
7 × f = 7
f = 7/7
f = 1
Thus the missing factor is 1.

Lesson 4.2 Relate Multiplication and Division

Explore and Grow

Use 24 counters to make an array. Draw the array. Write a multiplication equation and a division equation for the array.
____ × ____ = _____
_____ ÷ ____ = ____
Answer: 6 × 4 = 24
24 ÷ 6 = 4

Explanation:

The division equation is 24 ÷ 6 = 4 or 24 ÷ 4 = 6

Structure
Compare your equations to your partner’s equations. How are they the same? How are they different?
Answer:
Both the equations are the same but the rows and columns are different.

Think and Grow: Multiplication and Division

A fact family is a group of related facts that uses the same numbers.

Answer:
Multiplication:
5 rows of 6 counters
5 × 6 = 30
30 counters
Division:
30 counters in 5 equal rows
30 ÷ 5 = 6
60 counters in each row.
Fact family for 5, 6 and 30:
5 × 6 = 30
6 × 5 = 30
30 ÷ 5 = 6
30 ÷ 6 = 5

Show and Grow

Use the array to complete the equations.
Question 1.

3 × ____ = 24
24 ÷ 3 = ____
Answer: 8

Explanation:
Number of rows = 3
Number of counters = 24
To find the number of counters in each row you have to divide the total number of counters by the number of rows.
24 ÷ 3 = 8
3 × x = 24
x = 24/3
x = 8

Question 2.

4 × ____ = 20
20 ÷ 4 = _____
Answer: 5

Explanation:
Number of rows = 4
Number of counters = 20
To find the number of counters in each row you have to divide the total number of counters by the number of rows.
4 × x = 20
x = 20/4
x = 5
20 ÷ 4 = 5

Question 3.
Draw an array to find 2 × 7. Write the other facts in the fact family.
2 × 7 = _____
___________
___________
___________
Answer: 14

Explanation:

The fact family for the numbers 2, 7 and 14
2 × 7 = 14
7 × 2 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2

Apply and Grow: Practice

Question 4.
Draw an array to find 3 × 6.
Write the other 3 facts in the fact family.
3 × 6 = ______
____________
_____________
____________
Answer: 18

Explanation:

The fact family for 3, 6 and 18 are
3 × 6 = 18
6 × 3 = 18
18 ÷ 3 = 6
18 ÷ 6 = 3

Complete the fact family.
Question 5.
7 × ____ = 70
____ × 7 = 70
70 ÷ 10 = ____
70 ÷ ___ = 10
Answer:
The fact family for 7, 10 and 70 are:
7 × 10 = 70
10 × 7 = 70
70 ÷ 10 = 7
70 ÷ 7 = 10

Question 6.
5 × ____ = 40
____ × 5 = 40
40 ÷ 8 = _____
40 ÷ ____ = 8
Answer:
The fact family for 5, 8 and 40 are:
5 × 8 = 40
8 × 5 = 40
40 ÷ 8 = 5
40 ÷ 5 = 8

Write the fact family for the numbers.
Question 7.
2, 5, 10
Answer:
The fact family for 2, 5 and 10 are:
2 × 5 = 10
5 × 2 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2

Question 8.
4, 3, 12
Answer:
The fact family for 3, 4 and 12 are:
4 × 3 = 12
3 × 4 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3

Question 9.
Structure
Find each product. Then match the multiplication fact with the related division fact.

Answer:

Question 10.
DIG DEEPER!
Is 4 × 6 = 24 part of the fact family for 3 × 8 = 24? Explain.
Answer: No. Because the rows and columns are different.

Think and Grow: Modeling Real Life

Your teacher divides the items shown equally among 9 students. Write two equations that you can use to show how many straws each student gets.

Division equation:
Multiplication equation:

Answer:
Your teacher divides the items shown equally among 9 students.
Straws – 54
54 ÷ 9 = 6
Thus each student gets 6 straws.
Division Equation is 54 ÷ 9 = 6
Multiplication equation 9 × 6 = 54

Show and Grow

Question 11.
Use the table above to write two equations that you can use to show how many containers of clay each student gets.
Answer:
Your teacher divides the items shown equally among 9 students.
Containers of the day – 27
27 ÷ 9 = 3
Division Equation is 27 ÷ 9 = 3
Multiplication equation is 3 × 9 = 27

Question 12.
Use the table above to find how many more toothpicks students will get than straws.

Answer:
Your teacher divides the items shown equally among 9 students.
Toothpicks – 72
72 ÷ 9 = 8
Each student gets 8 toothpicks
Straws – 54
54 ÷ 9 = 6
Thus each student gets 6 straws.
8 – 6 = 2
Thus Each student will get 2 toothpicks more than the straws.

Question 13.
Explain how a multiplication fact can help you solve 30 ÷ 3 = _____.
Answer: 10 × 3 = 30

Explanation:
The multiplication fact to help you to solve 30 ÷ 3 is 10 × 3.
By using the multiplication fact you can get the solution for 30 ÷ 3 = 10

Relate Multiplication and Division Homework & Practice 4.2

Use the array to complete the equations
Question 1.

2 × ___ = 8
8 ÷ 2 = _____
Answer: 4

Explanation:
Number of counters = 8
Number of rows = 2
8 ÷ 2 = 4
2 × x = 8
x = 8/2
x = 4

Question 2.

3 × ____ = 9
9 ÷ 3 = ____
Answer: 3

Explanation:
Number of counters = 9
Number of rows  = 3
3 × x = 9
x = 9/3
x = 3
9 ÷ 3 = 3

Question 3.
Draw an array to find 5 × 7. Write the other 3 facts in the fact family.
5 × 7 = _____
___________
___________
___________
Answer: 35

Explanation:
The other 3 facts are
5 × 7 = 35
7 × 5 = 35
35 ÷ 5 = 7
35 ÷ 7 = 5

Complete the fact family
Question 4.

Answer: 1, 9

Explanation:
9 × 1 = 9
9 ÷ 1 = 9
1 × 9 = 9
9 ÷ 9 = 1

Question 5.

Answer: 7, 6

Explanation:
6 × 7 = 42
42 ÷ 7 = 6
7 × 6 = 42
42 ÷ 6 = 7

Write the fact family for the numbers.
Question 6.
4, 8, 32
Answer: 8 × 4 = 32, 32 ÷ 4 = 8, 32 ÷ 8 = 4

Explanation:
The facts family for the numbers are
4 × 8 = 32
8 × 4 = 32
32 ÷ 8 = 4
32 ÷ 4 = 8

Question 7.
6, 7, 42
Answer: 6 × 7 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6

Explanation:
The facts family for the numbers are
6 × 7 = 42
7 × 6 = 42
42 ÷ 7 = 6
42 ÷ 6 = 7

Question 8.
Which One Doesn’t Belong?
Which equation does not belong with the other three?
3 × 7 = 21
7 × 3 = 21
21 ÷ 7 = 3
7 + 3 = 10
Answer: 7 + 3 = 10

Explanation:
The equation that does not belong to other three equation is 7 + 3 = 10.

Question 9.
DIG DEEPER!
Newton has 16 pennies. He wants to put them in stacks that are the same height. How many stacks does he make?

Answer: 2

Explanation:
Given,
Newton has 16 pennies. He wants to put them in stacks that are the same height.
16 ÷ 8 = 2
Thus he makes 2 stacks.

Question 10.
Modeling Real Life
Your art teacher divides the items shown equally among 6 students. Write two equations that you can use to show how many pieces of paper each student gets.

Answer:
Given
Your art teacher divides the items shown equally among 6 students.
48 ÷ 6 = 8 paintbrushes
42 ÷ 6 = 7 pieces of paper
Thus each student gets 7 pieces of paper.

Question 11.
Modeling Real Life
Use the table above to find how many more paintbrushes students will get than paint trays.
Answer:
Your art teacher divides the items shown equally among 6 students.
18 ÷ 6 = 3 paint trays
48 ÷ 6 = 8 paintbrushes
8 – 3 = 5
Thus the students will get 5 more paintbrushes than paint trays.

Review & Refresh

Find the missing factor.
Question 12.
5 × ____ = 45
Answer: 9

Explanation:

Let the missing factor be g.
5 × g = 45
g = 45/5
g = 9
Thus the missing factor is 9.

Question 13.
2 × ____ = 16
Answer: 8

Explanation:
Let the missing factor be h.
2 × h = 16
h = 16/2
h = 8
Thus the missing factor is 8.

Question 14.
_____ × 2 = 4
Answer: 2

Explanation:
Let the missing factor be i.
i × 2 = 4
i = 4/2
i = 2
Thus the missing factor is 2.

Question 15.
____ × 3 = 15
Answer: 5

Explanation:
Let the missing factor be j.
j × 3 = 15
j = 15/3
j = 5
Thus the missing factor is 5.

Question 16.
5 × ____ = 10
Answer: 2

Explanation:
Let the missing factor be k.
5 × k = 10
k = 10/5
k = 2
Thus the missing factor is 2.

Question 17.
5 × ____ = 5
Answer: 1

Explanation:
Let the missing factor be l.
5 × l = 5
l = 5/5
l = 1
Thus the missing factor is 1.

Lesson 4.3 Divide by 2, 5, or 10

Explore and Grow

Use the number line to model 10 ÷ 2.

10 ÷ 2 = _____
Answer: 5

Structure
In your number line model, does 2 represent the number of equal groups or the size of the groups? Explain.
Answer: Yes, the number line model 2 represents the number of equal groups or the size of the groups.

Think and Grow: Divide by 2, 5, or 10

Example
Find 16 ÷ 2.

Answer:
Number of rows = 2
Number of counters = 16
Division equation is 16 ÷ 2 = 8
Multiplication equation is 2 × 8 = 16

Example
Find 20 ÷ 5.
Think: 5 times what number is 20?
5 × ____ = 20

Answer:
Number of rows = 5
Number of counters = 20
Division equation is 20 ÷ 5 = 4
Multiplication equation is 5 × 4 = 20

Example
Find 30 ÷ 10.
Think: 10 times what number is 30?
10 × _____ = 30

Answer:
Number of rows = 10
Number of counters = 30
Division equation is 30 ÷ 10 = 3
Multiplication equation is 10 × 3 = 30

Show and Grow

Write the related multiplication fact. Then find the quotient
Question 1.
Find 60 ÷ 10.
10 × ____ = 60
60 ÷ 10 = ____
Answer: 6, 6

Explanation:
The related multiplication fact for 60 and 10 is
10 × x = 60
x = 60/10
x = 6
60 ÷ 10 = 6
Thus the quotient is 6.

Question 2.
Find 14 ÷ 2
2 × ____ = 14
14 ÷ 2 = _____
Answer: 7, 7

Explanation:
The related multiplication fact for 14 and 2 is
2 × x = 14
x = 14/2
x = 7
14 ÷ 2 = 7
Thus the quotient is 7.

Question 3.
Find 35 ÷ 5
5 × ___ = 35
35 ÷ 5 = ____
Answer: 7, 7

Explanation:
The related multiplication fact for 5 and 35 is
5 × x = 35
x = 35/5
x = 7
35 ÷ 5 = 7
Thus the quotient is 7.

Write the related multiplication fact. Then find the quotient
Question 4.
Find 4 ÷ 2.
2 × ____ = 4
4 ÷ 2 = ____
Answer: 2, 2

Explanation:
The related multiplication fact for 2 and 4 is
2 × x = 4
x = 4/2
x = 2
4 ÷ 2 = 2
Thus the quotient is 2.

Question 5.
Find 15 ÷ 5.
5 × ____ = 15
15 ÷ 5 = ____
Answer: 3, 3

Explanation:
The related multiplication fact for 5 and 15 is
5 × x = 15
x = 15/5
x = 3
15 ÷ 5 = 3
Thus the quotient is 3.

Question 6.
Find 10 ÷ 10.
10 × ____ = 10
10 ÷ 10 = ____
Answer: 1, 1

Explanation:
The related multiplication fact for 10 and 10 is
10 × x = 10
x = 10/10
x = 1
10 ÷ 10 = 1
Thus the quotient is 1.

Find the quotient
Question 7.
70 ÷ 10 = _____
Answer: 7
Divide both the numbers 70 and 10
70/10 = 7
Thus 7 is the quotient.

Question 8.
25 ÷ 5 = _____
Answer: 5
Divide both the numbers 25 and 5.
25/5 = 5
Thus 5 is the quotient.

Question 9.
18 ÷ 2 = ____
Answer: 6
Divide both the numbers 18 and 2.
18/2 = 9
Thus 9 is the quotient.

Question 10.

Answer: 6
Divide both the numbers 30 and 5.
30/5 = 6
Thus 6 is the quotient.

Question 11.

Answer: 8
Divide both the numbers 16 and 2.
16/2 = 8
Thus 8 is the quotient.

Question 12.

Answer: 9
Divide both the numbers 10 and 90.
90/10 = 9
Thus 9 is the quotient.

Question 13.
Divide 60 by 10.
Answer: 6
Divide both the numbers 60 and 10.
60/10 = 6
Thus 6 is the quotient.

Question 14.
Divide 14 by 2.
Answer: 7
Divide both the numbers 2 and 14.
14/2 = 7
Thus 7 is the quotient.

Question 15.
Divide 45 by 5.
Answer: 9
Divide both the numbers 45 and 5.
45/5 = 9
Thus 9 is the quotient.

Find the missing divisor.
Question 16.
12 ÷ ____ = 6
Answer: 2

Explanation:
Let the missing divisor is x
12 ÷ x = 6
12/x = 6
12 = 6 × x
x = 12/6
x = 2
Thus the missing divisor is 2.

Question 17.
10 ÷ ____ = 2
Answer: 5

Explanation:
Let the missing divisor is y
10 ÷ y = 2
10/y = 2
10 = 2 × y
y = 10/2
y = 5
Thus the missing divisor is 5.

Question 18.
50 ÷ ____ = 5
Answer: 10

Explanation:
Let the missing divisor is z.
50 ÷ z = 5
50/z = 5
50 = 5 × z
z = 50/5
z = 10
Thus the missing divisor is 10.

Question 19.
You make 2 batches of pancakes. You use 6 cups of flour. How many cups of flour are in 1 batch?

Answer: 3

Explanation:
Given that,
You make 2 batches of pancakes.
You use 6 cups of flour.
6/2 = 3 cups of flour
There are 3 cups of flour in 1 batch.

Question 20.
DIG DEEPER!
I am an even number. If you multiply me by 5, then divide the product by 10, the quotient is 2. What number am I?
Answer: 20

Explanation:
I am an even number. If you multiply me by 5, then divide the product by 10, the quotient is 2.
Let 4 be the even number.
4 × 5 = 20
20/10 = 2
Thus the number is 4.

Think and Grow: Modeling Real Life

Fourteen students say a dog is their favorite pet. How many symbols should you draw to complete the picture graph?

Division equation:
You should draw _____ symbols

Answer:
Given,
Fourteen students say a dog is their favorite pet.

🙂 = 2 students
14 ÷ 2 = 7 pictures

Show and Grow

Question 21.
Twenty-five students say riding a bike is their favorite summer activity. How many symbols should you draw to complete the picture graph?

Answer:
Given,
Twenty-five students say riding a bike is their favorite summer activity.
🙂 = 5 students
25 = 🙂 🙂🙂🙂🙂
25 ÷ 5 = 5

Question 22.
Erasers cost 10¢ each. How many erasers can you buy with 70¢?
Answer:
Given that,
Erasers cost 10¢ each.
You need to buy with 70¢
10 × x = 70
x = 70/10
x = 7
Therefore you can buy 7 erasers for 70¢.

Question 23.
You have 26 red linking cubes and 24 blue linking cubes. You use all of the linking cubes to make towers with 10 linking cubes each. How many towers do you make?
Answer: 5

Explanation:
Given that,
You have 26 red linking cubes and 24 blue linking cubes.
26 + 24 = 50 linking cubes
You use all of the linking cubes to make towers with 10 linking cubes each.
50 ÷ 10 = 5 towers
Thus you can make 5 towers.

Divide by 2, 5, or 10 Homework & Practice 4.3

Write the related multiplication fact. Then find the quotient.
Question 1.
Find 20 ÷ 10
10 × ____ = 20
20 ÷ 10 = ____
Answer: 2, 2

Explanation:
Let x be the unknown factor.
10 × x  = 20
x = 20/10
x = 2
First, we need to check whether the divisor or dividend is the related multiplication fact or not.
Next check whether the divisor or the dividend the product in the related multiplication fact or not.
If both are the same then the quotient is the unknown factor.
20/10 = 2
Thus the quotient is 2.

Question 2.
Find 8 ÷ 2.
2 × ___ = 8
8 ÷ 2 = ____
Answer: 4, 4

Explanation:
Let y be the unknown factor.
First, we need to check whether the divisor or dividend is the related multiplication fact or not.
Next check whether the divisor or the dividend the product in the related multiplication fact or not.
If both are the same then the quotient is the unknown factor.
2 × y = 8
y = 8/2
y = 4
Thus the quotient is 4.

Question 3.
Find 50 ÷ 5
5 × ___ = 50
50 ÷ 5 = ____
Answer: 10, 10

Explanation:
Let z be the unknown factor.
First, we need to check whether the divisor or dividend is the related multiplication fact or not.
Next check whether the divisor or the dividend the product in the related multiplication fact or not.
If both are the same then the quotient is the unknown factor.
5 × z = 50
z = 50/5
z = 10
Thus the quotient is 10.

Find the quotient
Question 4.
100 ÷ 10 = _____
Answer: 10

Explanation:
100/10 = 10
The quotient is 10.

Question 5.
45 ÷ 5 = _____
Answer: 9

Explanation:
45/5 = 9
The quotient is 9.

Question 6.
14 ÷ 2 = _____
Answer: 7

Explanation:
14/2 = 7
The quotient is 7.

Question 7.

Answer: 6

Explanation:
12/2 = 6
The quotient is 6.

Question 8.

Answer: 6

Explanation:
60/10 = 6
The quotient is 6.

Question 9.

Answer: 2

Explanation:
10/5 = 2
The quotient is 2.

Find the missing divisor
Question 10.
20 ÷ ___ = 5
Answer: 4

Explanation:
Let x be the missing divisor
20 ÷ x = 5
20/x = 5
20 = x × 5
x = 20/5
x = 4
Thus the missing divisor is 4.

Question 11.
40 ÷ ____ = 10
Answer: 4

Explanation:
Let x be the missing divisor.
40 ÷ x = 10
40/x = 10
40 = 10 × x
x = 40/10
x = 4
Thus the missing divisor is 4.

Question 12.
4 ÷ ____ = 2
Answer: 2

Explanation:
Let x be the missing divisor.
4 ÷ x = 2
4/x = 2
4 = 2 × x
x = 4/2
x = 2
Thus the missing divisor is 2.

Question 13.
Number Sense
The American flag has 50 stars. It has 10 times as many stars as the Chinese flag. How many stars are on the Chinese flag?
Answer:
Given,
The American flag has 50 stars. It has 10 times as many stars as the Chinese flag.
50/10 = 5
Thus there are 5 stars on the Chinese flag.

Question 14.
Open-Ended Write a division equation for each description.

Answer: 10 ÷ 2 = 5
In this equation 2 is the divisor, 5 is the quotient and 10 is the dividend.

Question 15.
Repeated Reasoning
Complete the table.

Answer:

Question 16.
You buy 20 flowers. You want an equal number of flowers in each of the 5 pots. How many flowers do you put in each pot?

Answer:
Given,
You buy 20 flowers. You want an equal number of flowers in each of the 5 pots.
20/5 = 4
Thus there are 4 flowers in each pot.

Question 17.
Modeling Real Life
Fifty students say they have traveled on an airplane. How many symbols should you draw to complete the picture graph?

Answer:
Given that,
Fifty students say they have traveled on an airplane.
🙂 = 10 students
50 = 10 × 5
= 🙂 × 5

Question 18.
Modeling Real Life
A jeweler has 17 gold rings and 18 silver rings. She puts them in a ring tray in 5 rows. How many rings are in each row?
Answer:  7 rings

Explanation:
Given that,
A jeweler has 17 gold rings and 18 silver rings.
17 + 18 = 35
She puts them in a ring tray in 5 rows.
35/5 = 7
Therefore there are 7 rings in each row.

Review & Refresh

Compare.
Question 19.

Answer: >

Explanation:
8 × 3 = 24
7 × 3 = 21
24 > 21
So, 8 × 3 > 7 × 3

Question 20.

Answer: =

Explanation:
5 × 3 = 15
15 = 15
So, 15 = 5 × 3

Question 21.

Answer: <

Explanation:
3 × 3 = 9
4 × 3 = 12
9 < 12
So, 3 × 3 < 4 × 3

Lesson 4.4 Divide by 3 or 4

Explore and Grow

Put 12 counters into 3 equal groups. Draw to show your groups.
Use your equal groups to help you find the quotient.
12 ÷ 3 = ____
Answer: 4

Structure
Put 12 counters into 4 equal groups. Draw to show your groups. Write a division equation to match. What do you notice?
Answer: 3

Think and Grow: Divide by 3 or 4

Example
Find 18 ÷ 3

Answer: 6

Explanation:
Let the unknown number be x.
18 ÷ 3 = x
18/3 = x
x = 6
Thus 18 is 3 times 6.

Example
Find 32 ÷ 4.

Answer: 8

Explanation:
Let the unknown number be x.
32 ÷ 4 = x
32/4 = x
x = 8
Thus 32 is 4 times 8.
4 × 8 = 32

Show and Grow

Complete the model and find the quotient.
Question 1.
Find 28 ÷ 4.

28 ÷ 4 = _____
Answer: 7

Explanation:
Number of rows = 4
Number of counters = 28
Divide the number of counters by the number of rows
28/4 = 7
Thus there are 7 columns in each row.

Question 2.
Find 9 ÷ 3.

9 ÷ 3 = _____
Answer: 3

Explanation:

Number of rows = 3
Number of counters = 9
Divide the number of counters by the number of rows
9/3 = 3
Thus there are 3 columns in each row.

Apply and Grow: Practice

Complete the model and find the quotient.
Question 3.
Find 8 ÷ 4.

8 ÷ 4 = _____
Answer: 2

Explanation:

Number of rows = 4
Number of counters = 8
Divide the number of counters by the number of rows
8/4 = 2
Thus there are 2 columns in each row.

Question 4.
Find 24 ÷ 3.

24 ÷ 3 = _____
Answer: 8

Explanation:

Number of rows = 3
Number of counters = 24
Divide the number of counters by the number of rows
24/3 = 8
Thus there are 8 columns in each row.

Find the quotient
Question 5.
12 ÷ 3 = _____
Answer: 4

Explanation:
Divide the two numbers 12 and 3.
12/3 =4
Thus the quotient is 4

Question 6.
20 ÷ 4 = _____
Answer: 5

Explanation:
Divide the two numbers 20 and 4.
20/4 = 5
Thus the quotient is 5.

Question 7.
15 ÷ 3 = _____
Answer: 5

Explanation:
Divide the two numbers 15 and 3
15/3 = 5
Thus the quotient is 5.

Question 8.

Answer: 8

Explanation:
Divide the two numbers 32 and 4
32/4 = 8
Thus the quotient is 8.

Question 9.

Answer: 6

Explanation:
Divide the two numbers 3 and 18
18/3 = 6
Thus the quotient is 6.

Question 10.

Answer: 9

Explanation:
Divide the two numbers 36 and 4
36/4 = 9
Thus the quotient is 9.

Question 11.
Divide 9 by 3.
Answer: 3

Explanation:
Divide the two numbers 3 and 9
9/3 = 3
Thus the quotient is 3.

Question 12.
Divide 12 by 4.
Answer: 3

Explanation:
Divide the two numbers 12 and 4.
12/4 = 3
Thus the quotient is 3.

Question 13.
Divide 21 by 3.
Answer: 7

Explanation:
Divide the two numbers 21 by 3
21/3 = 7
Thus the quotient is 7.

Compare
Question 14.

Answer: >

Explanation:
Divide the two numbers.
27 ÷ 3 = 9
28 ÷ 4 = 7
9 > 7
27 ÷ 3 > 28 ÷ 4

Question 15.

Answer: >

Explanation:
Divide the two numbers
30 ÷ 3 =10
24 ÷ 4 = 6
10 > 6
30 ÷ 3 > 24 ÷ 4

Question 16.

Answer: <

Explanation:
Divide the two numbers
6 ÷ 3 = 2
16 ÷ 4 = 4
2 < 4
6 ÷ 3 < 16 ÷ 4

Question 17.
There are 36 water bottles in a package. The bottles are in 4 rows. How many water bottles are in each row?
Answer: 9

Explanation:
Given,
There are 36 water bottles in a package.
The bottles are in 4 rows.
36/4 = 9
Thus 9 water bottles are in each row.

Question 18.
DIG DEEPER!
Can you divide 20 students into 3 equal groups? Explain.
Answer: No
20 is not the multiple of 3. So, 20 students cannot be divided into 3 equal groups.

Think and Grow: Modeling Real Life

You arrange 36 chairs in 4 equal rows. You arrange 21 music stands in 3 equal rows. How many more chairs are in each row than music stands?

Division equations:
There are ______ more chairs in each row.

Answer:
Given,
You arrange 36 chairs in 4 equal rows.
36/4 = 9 chairs in each row
You arrange 21 music stands in 3 equal rows.
21/3 = 7 chairs in each row
Thus there are 2 more chairs in each row.

Show and Grow

Question 19.
You arrange 30 cups of fruit punch in 3 equal rows. You arrange 24 cups of lemonade in 4 equal rows. How many more cups of fruit punch are in each row than cups of lemonade?
Answer:
Given,
You arrange 30 cups of fruit punch in 3 equal rows.
30/3 = 10 cups of fruit punch
You arrange 24 cups of lemonade in 4 equal rows.
24/4 = 6 cups of lemonade
10 > 6
Thus 4 more cups of fruit punch are in each row than cups of lemonade.

Question 20.
You have a bag of 25 carrot sticks. You eat 5 of them and equally share the rest with 4 friends. How many carrot sticks does each friend get?

Answer: 5

Explanation:
Given that,
You have a bag of 25 carrot sticks. You eat 5 of them and equally share the rest with 4 friends.
25 – 5 = 20 carrot sticks
20/4 = 5 carrot sticks
Thus each friend gets 5 carrot sticks.

Question 21.
Your teacher has 18 yellow pencils and 18 red pencils. She puts 3 pencils on each desk in the class. How many desks are in the class?
Answer: 12

Explanation:
Given that,
Your teacher has 18 yellow pencils and 18 red pencils.
18 + 18 = 36 pencils
She puts 3 pencils on each desk in the class.
36/3 = 12
Thus there are 12 desks in the class.

Divide by 3 or 4 Homework & Practice 4.4

Complete the model and find the quotient
Question 1.
Find 27 ÷ 3

27 ÷ 3 = ______
Answer: 9

Explanation:
Number of rows = 3
Number of counters = 27
Divide the number of counters by the number of rows
27/3 = 9
Thus there are 9 counters in each row.

Question 2.
Find 20 ÷ 4.

20 ÷ 4 _____
Answer: 5

Explanation:

Number of rows = 4
Number of counters = 20
Divide the number of counters by the number of rows
20/4 = 5
Thus there are 5 counters in each row.

Find the quotient
Question 3.
6 ÷ 3 = _____
Answer: 2

Explanation:
Divide the two numbers 3 and 6.
6/3 = 2
Thus the quotient is 2.

Question 4.
28 ÷ 4 = _____
Answer: 7

Explanation:
Divide the two numbers 28 and 4.
28/4 = 7
Thus the quotient is 7.

Question 5.
18 ÷ 3 = _____
Answer: 6

Explanation:
Divide the two numbers 18 and 3.
18/3 = 6
Thus the quotient is 6.

Question 6.

Answer: 2

Explanation:
Divide the two numbers 4 and 8.
8/4 = 2
Thus the quotient is 2.

Question 7.

Answer: 8

Explanation:
Divide the two numbers 24 and 3
24/3 = 8
Thus the quotient is 8.

Question 8.

Answer: 4

Explanation:
Divide the two numbers 16 and 4.
16/4 = 4
Thus the quotient is 4.

Compare
Question 9.

Answer: <

Explanation:
Divide the two numbers.
9 ÷ 3 = 3
15 ÷ 3 = 5
3 < 5
So, 9 ÷ 3 < 15 ÷ 3

Question 10.

Answer: <

Explanation:
Divide the two numbers.
12 ÷ 3 = 4
12 ÷ 4 = 3
4 > 3
12 ÷ 3 > 12 ÷ 4

Question 11.

Answer: <

Explanation:
Divide the two numbers.
32 ÷ 4 = 8
36 ÷ 4 = 9
8 < 9
32 ÷ 4 < 36 ÷ 4

Question 12.
Number Sense
Tissue boxes are sold in packs of 3. A doctor’s office needs 21 boxes. How many packs should the office buy?
Answer: 7

Explanation:
Given that,
Tissue boxes are sold in packs of 3.
A doctor’s office needs 21 boxes.
21/3 = 7 packs
Therefore the office should buy 7 packs.

Question 13.
Structure
Write the division equation represented by the number line.

Answer: 32 ÷ 4 = 8

Explanation:
The count starts from 0.
The count jumps for every 4s.
There are 8 jumps.
Thus the division equation is 32 ÷ 4 = 8

Question 14.
YOU BE THE TEACHER
Your friend says she can use 3 × 6 = 18 to help find 6 ÷ 3. Is your friend correct? Explain.
Answer: Your friend is incorrect

Explanation:
Your friend says she can use 3 × 6 = 18 to help find 6 ÷ 3.
6 ÷ 3 = 2
The multiplication equation is different from the division equation.
By this, you can say that your friend is incorrect.

Question 15.
Modeling Real Life
A food vending machine has 40 snacks in rows of 4. A drink vending machine has 21 drinks in rows of 3. How many more rows of snacks are there than rows of drinks?
Answer:
Given,
A food vending machine has 40 snacks in rows of 4.
40/4 = 10
A drink vending machine has 21 drinks in rows of 3.
21/3 = 7
10 – 7 = 3
Thus 3 more rows of snacks are there than rows of drinks.

Question 16.
Modeling Real Life
A delivery person has 13 large packages and 14 small packages. He delivers 3 packages to each house. There are none left. How many houses does he deliver to?

Answer: 9

Explanation:
Given,
A delivery person has 13 large packages and 14 small packages.
13 + 14 = 27
He delivers 3 packages to each house. There are none left.
27/3 = 9
Thus he delivers 9 houses.

Review & Refresh

Find the product
Question 17.

Answer: 48

Explanation:
Multiply the two numbers 8 and 6.
8 × 6 = 48

Question 18.

Answer: 0

Explanation:
Multiply the two numbers 6 and 0.
Any number multiplied by 0 will be always 0.
6 × 0 = 0

Question 19.

Answer: 12

Explanation:
Multiply the two numbers 6 and 2.
6 × 2 = 12

Question 20.

Answer: 60

Explanation:
Multiply the two numbers 10 and 6.
10 × 6 = 60

Question 21.

Answer: 42

Explanation:
Multiply the two numbers 7 and 6.
7 × 6 = 42

Lesson 4.5 Divide by 6 or 7

Explore and Grow

Complete the statements and the models.

Answer: 42 ÷ 6 = 7

Reasoning
Without solving, which quotient is greater? Explain how you know.
Answer: The second figure is having a greater quotient.
42 ÷ 6 = 7
42 ÷ 7 = 6

Think and Grow: Divide by 6 or 7

Example
Find 48 ÷ 6.
Think: 6 times what number is 48?
6 × _____ = 48

Answer: 8

Explanation:
Number of rows = 6
Number of counters = 48
Divide the number of counters by the number of rows.
48/6 = 8
There are 8 columns.
6 × 8 = 48

Example
Find 49 ÷ 7.
Think: 7 times what number is 49?
7 × ____ = 49

Answer: 7

Explanation:
Number of rows = 7
Number of counters = 49
Divide the number of counters by the number of rows
49/7 = 7
There are 7 columns.
7 × 7 = 49

Show and Grow

Complete the model and find the quotient
Question 1.
Find 28 ÷ 7.

28 ÷ 7 = _____
Answer: 4

Explanation:
Number of rows = 7
Number of counters = 28
Divide the number of counters by the number of rows
28/7 = 4
There are 4 columns.

Question 2.
Find 54 ÷ 6.

54 ÷ 6 = _____
Answer: 9

Explanation:
Number of rows = 6
Number of counters = 54
Divide the number of counters by the number of rows
54/6 = 9
There are 9 columns.

Apply and Grow: Practice

Complete the model and find the quotient
Question 3.
Find 36 ÷ 6.

36 ÷ 6 = _____
Answer: 6

Explanation:
Number of rows = 6
Number of counters = 36
Divide the number of counters by the number of rows
36/6 = 6
There are 6 columns.

Question 4.
Find 14 ÷ 7.

14 ÷ 7 = _____
Answer: 2

Explanation:
Number of rows = 7
Number of counters = 14
Divide the number of counters by the number of rows
14/7 = 2
There are 2 columns.

Find the quotient
Question 5.
60 ÷ 6 = _____
Answer: 10

Explanation:
Divide the two numbers 60 and 6.
60/6 = 10
Thus the quotient is 10.

Question 6.
35 ÷ 7 = _____
Answer: 5

Exp7lanation:
Divide the two numbers 35 and 7.
35/7 = 5
Thus the quotient is 5.

Question 7.
24 ÷ 6 = _____
Answer: 4

Explanation:
Divide the two numbers 24 and 6.
24/6 = 4
Thus the quotient is 4.

Question 8.

Answer: 2

Explanation:
Divide the two numbers 12 and 6.
12/6 = 2
Thus the quotient is 2.

Question 9.

Answer: 6

Explanation:
Divide the two numbers 42 and 7.
42/7 = 6
Thus the quotient is 6.

Question 10.

Answer: 9

Explanation:
Divide the two numbers 63 and 7
63/7 = 9
Thus the quotient is 9.

Find the missing divisor
Question 11.
28 ÷ ____ = 7
Answer: 4

Explanation:
Let the missing divisor be a.
28 ÷ a = 7
28/a = 7
28 = 7a
a = 28/7
a = 4
Thus the missing divisor is 4.

Question 12.
30 ÷ ____ = 6
Answer: 5

Explanation:
Let the missing divisor be b.
30 ÷ b = 6
30/b = 6
30 = 6 × b
b = 30/6
b = 5
Thus the missing divisor is 5.

Question 13.
70 ÷ _____ = 7
Answer: 10

Explanation:
Let the missing divisor be c.
70 ÷ c = 7
70/c = 7
70 = 7 × c
c = 70/7
c = 10
Thus the missing divisor is 10.

Question 14.
You have 24 stones for the game mancala. There are 6 holes on the board. Each hole gets an equal number of stones. How many stones do you put in each hole?
Answer: 4

Explanation:
Given that,
You have 24 stones for the game mancala.
There are 6 holes on the board.
Each hole gets an equal number of stones.
24/6 = 4
Thus you put 4 stones in each hole.

Question 15.
Number Sense
Write the correct symbol to make each equation true

Answer:

Think and Grow: Modeling Real Life

You have 54 craft sticks. You use all of the sticks to make hexagons. How many hexagons can you make?

Division equation:
You can make _____ hexagons.

Answer:
Given,
You have 54 craft sticks. You use all of the sticks to make hexagons.
hexagon – 6
54/6 = 9
You can make 9 hexagons.

Show and Grow

Question 16.
You use 35 craft sticks to make 7 polygons. You use the same number of craft sticks for each polygon. How many craft sticks do you use for each polygon?
Answer: 5

Explanation:
Given,
You use 35 craft sticks to make 7 polygons. You use the same number of craft sticks for each polygon.
35/7 = 5
Thus you use 5 craft sticks for each polygon.

Question 17.
There are 42 students in gym class. The teacher divides the students into 7 teams. How many more students would be on each team if the teacher divides the students into 6 teams?
Answer:
Given that,
There are 42 students in gym class. The teacher divides the students into 7 teams.
42/7 = 6 students
If the teacher divides the students into 6 teams then,
42/6 = 7 students

Question 18.
You have a tray of 12 oatmeal bars. You keep 6 of them. How many bars can you give to each of your 6 friends?
Answer:
Given that,
You have a tray of 12 oatmeal bars. You keep 6 of them.
12/6 = 2
Thus you can give 2 bars to each of your 6 friends.

Divide by 6 or 7 Homework & Practice 4.5

Complete the model and find the quotient
Question 1.
Find 18 ÷ 6

18 ÷ 6 = _____
Answer: 3

Explanation:
Number of rows = 6
Number of counters = 18
Divide the number of counters by the number of rows
18/6 = 3
Thus there are 3 counters in each row

Question 2.
Find 35 ÷ 7

35 ÷ 7 = _____
Answer: 5

Explanation:
Number of rows = 7
Number of counters = 35
Divide the number of counters by the number of rows
35/7 = 5
Thus there are 5 counters in each row

Find the quotient
Question 3.
42 ÷ 6 = _____
Answer: 7

Explanation:
Divide the two numbers 42 and 6.
42/6 = 7
Thus the quotient is 7.

Question 4.
28 ÷ 7 = _____
Answer: 4

Explanation:
Divide the two numbers 28 and 7
28/7 = 4
Thus the quotient is 4.

Question 5.
54 ÷ 6 = _____
Answer: 9

Explanation:
Divide the two numbers 54 and 6.
54/6 = 9
Thus the quotient is 9.

Question 6.

Answer: 7

Explanation:
Divide the two numbers 49 and 7.
49/7 = 7
Thus the quotient is 7.

Question 7.

Answer: 10

Explanation:
Divide the two numbers 7 and 70
70/7 = 10
Thus the quotient is 10.

Question 8.

Answer: 5

Explanation:
Divide the two numbers 30 and 6.
30/6 = 5
Thus the quotient is 5.

Find the missing divisor.
Question 9.
36 ÷ ____ = 6
Answer: 9

Explanation:
Let the missing divisor be x.
36 ÷ x = 6
36/x = 6
36 = 6 × x
x = 36/6
x = 6
Thus the missing divisor is 6.

Question 10.
14 ÷ ____ = 7
Answer: 2

Explanation:
Let the missing divisor be y.
14 ÷ y = 7
14/y = 7
14 = 7 × y
y = 14/7
y = 2
Thus the missing divisor is 2.

Question 11.
60 ÷ _____ = 6
Answer: 10

Explanation:
Let the missing divisor be z.
60 ÷ z = 6
60/z = 6
60 = 6 × z
z = 60/6
z = 10
Thus the missing divisor is 10.

Question 12.
Number Sense
There are 7 continents. A scientist has 63 days to spend studying on all the continents. She wants to spend an equal number of days on each one. How many days can she spend on each continent?
Answer: 9

Explanation:
Given,
There are 7 continents. A scientist has 63 days to spend studying on all the continents.
She wants to spend an equal number of days on each one.
63/7 = 9 days
Thus she can spend 9 days on each continent.

Question 13.
Logic
I am an odd number. When you multiply me by 6, then divide the product by 3, the quotient is 10. What number am I?
Answer: 5

Explanation:
Let us consider 5 to be the odd number.
Now multiply by 6.
5 × 6 = 30
Now divide by 3.
30/3 = 10
So, the number is 5.

Question 14.
DIG DEEPER!
You deal 52 cards to 7 players. Does each player get the same number of cards? Explain.

Answer: No. Because 52 is not the multiple of 7.
Thus each player will not get the same number of cards.

Question 15.
Modeling Real Life
There are 70 students at a summer camp. A counselor divides the students into teams of 10. How many more teams would the counselor make if he divides the students into teams of 7?
Answer:
Given,
There are 70 students at a summer camp. A counselor divides the students into teams of 10.
If he divides into 7 teams then there will be 10 students in each team.
70/7 = 10

Question 16.
Modeling Real Life
There are 31 students in your class. Seven students are called to the nurse’s office to get their hearing checked. Your teacher divides the rest of the students into groups of 6. How many groups are there?
Answer:
Given that,
There are 31 students in your class. Seven students are called to the nurse’s office to get their hearing checked.
31 – 7 = 24
Your teacher divides the rest of the students into groups of 6.
24/6 = 4 groups
Thus there are 4 groups.

Review & Refresh

Find the product
Question 17.

Answer: 48

Explanation:
Multiply the two numbers 8 and 6.
8 × 6 = 48

Question 18.

Answer: 72

Explanation:
Multiply the two numbers 9 and 8.
9 × 8 = 72

Question 19.

Answer: 80

Explanation:
Multiply the two numbers 10 and 8.
10 × 8 = 80

Question 20.

Answer: 0

Explanation:
Multiply the two numbers 0 and 8.
Any number multiplied by 0 will be always 0.
Thus 8 × 0 = 0

Question 21.

Answer: 8

Explanation:
Multiply the two numbers 1 and 8.
Any number multiplied by 1 will be always the same number.
So, 1 × 8 = 8

Lesson 4.6 Divide by 8 or 9

Explore and Grow

Use repeated subtraction to find 48 ÷ 8.
Answer:
48 – 8 = 40
40 – 8 = 32
32 – 8 = 24
24 – 8 = 16
16 – 8 = 8
8 – 8 = 0
At sixth number we got 0.
So, 48/8 in repeated subtraction is 6.

Reasoning
How many times did you subtract 8 from 48? Does the quotient represent the number of groups or the size of the groups? Explain.
Answer: I subtracted 8 from 48 six times. Yes, the quotient represents the number of groups or size of the groups.

Think and Grow: Divide 8 or 9

Example
Find 40 ÷ 8.
Think: 8 times what number is 40?
8 × ____= 40

Answer: 5

Explanation:
Number of rows = 8
Number of counters = 40
Divide the number of counters by the number of rows
40/8 = 5
Thus there are 5 columns.
8 times 5 is 40.

Example
Find 54 ÷ 9.
Think: 9 times what number is 54?
9 × ____ = 54

Answer: 6

Explanation:
Number of rows = 9
Number of counters = 54
Divide the number of counters by the number of rows
54/9 = 6
Thus there are 6 columns.
9 times 6 is 54.

Show and Grow

Complete the model and find the quotient
Question 1.
24 ÷ 8 = ____

24 ÷ 8 = ____
Answer: 3

Explanation:
Number of rows = 8
Number of counters = 24
Divide the number of counters by the number of rows
24/8 = 3
There are 3 columns
8 times 3 is 24.

Question 2.
18 ÷ 9 = ____

18 ÷ 9 = ____
Answer: 2

Explanation:
Number of rows = 9
Number of counters = 18
Divide the number of counters by the number of rows
18/9 = 2
There are 2 columns
2 times 9 is 18.

Apply and Grow: Practice

Complete the model and find the quotient
Question 3.
Find 36 ÷ 9.

36 ÷ 9 = _____
Answer: 4

Explanation:
Number of rows = 9
Number of counters = 36
Divide the number of counters by the number of rows
36/9 = 4
There are 4 columns
4 times 9 is 36.

Question 4.
Find 32 ÷ 8.

32 ÷ 8 = ____
Answer: 4

Explanation:
Number of rows = 8
Number of counters = 32
Divide the number of counters by the number of rows
32/8 = 4
There are 4 columns
8 times 4 is 32.

Find the quotient
Question 5.
45 ÷ 9 = _____
Answer: 5

Explanation:
Divide the two numbers 45 and 9
45/9 = 5
Thus the quotient is 5.

Question 6.
56 ÷ 8 = _____
Answer: 7

Explanation:
Divide the two numbers 56 and 8.
56/8 = 7
Thus the quotient is 7.

Question 7.
90 ÷ 9 = ____
Answer: 10

Explanation:
Divide the two numbers 90 and 9.
90/9 = 10
Thus the quotient is 10.

Question 8.

Answer: 2

Explanation:
Divide the two numbers 9 and 18
18/9 = 2
Thus the quotient is 2.

Question 9.

Answer: 6

Explanation:
Divide the two numbers 8 and 48
48/8 = 6
Thus the quotient is 6.

Question 10.

Answer: 2

Explanation:
Divide the two numbers 16 and 8.
16/8 = 2
Thus the quotient is 2.

Question 11.
Divide 54 by 9.
Answer: 6

Explanation:
Divide the two numbers 54 and 9
54/9 = 6
Thus the quotient is 6.

Question 12.
Divide 64 by 8.
Answer: 8

Explanation:
Divide the two numbers 64 and 8.
64/8 = 8
Thus the quotient is 8.

Question 13.
Divide 63 by 9
Answer: 7

Explanation:
Divide the two numbers 63 and 9
63/9 = 7
Thus the quotient is 7.

Compare
Question 14.

Answer: =

Explanation:
Divide the two numbers
81 ÷ 9 = 9
72 ÷ 8 = 9
9 = 9
So, 81 ÷ 9 = 72 ­÷ 8

Question 15.

Answer: >

Explanation:
Divide the two numbers
72 ÷ 9 = 8
40 ÷ 8 = 5
8 > 5
So, 72 ÷ 9 > 40 ÷ 8

Question 16.

Answer: <

Explanation:
Divide the two numbers
16 ÷ 8 = 2
27 ÷ 9 = 3
2 < 3
So, 16 ÷ 8 < 27 ÷ 9

Question 17.
A comic book has 63 pages. You read 9 pages each night. How many nights will it take to read the entire book?
Answer: 7

Explanation:
Given that,
A comic book has 63 pages. You read 9 pages each night.
63/9 = 7
Thus it will take 7 nights to read the entire book.

Question 18.
Logic
Find the missing number.

Answer: 8

Explanation:
8 times 8 is 64.
Thus the missing number is 8.

Think and Grow: Modeling Real Life

There are 9 innings in a baseball game. The table shows how many innings Newton played each season. How many games has Newton played in all?

Division equation:
Newton played ______ games in all.

Answer:
Given,
There are 9 innings in a baseball game.
The table shows how many innings Newton played each season.
Season 1: 81/9 = 9 games
Season 2: 63/9 = 7 games
9 + 7 = 16 games
Therefore Newton played 16 games in all.

Show and Grow

Question 19.
The third-grade and fourth-grade classes are going on a field trip. A van can carry 8 students. How many vans are needed in all?

Answer:
Given that,
The third-grade and fourth-grade classes are going on a field trip.
A van can carry 8 students.
Grade 3 – 48 students
Grade 4 – 56 students
third grade – 48/8 = 6 vans
fourth grade – 56/8 = 7 vans
6 + 7 = 13 vans
Thus 13 vans are needed in all.

Question 20.
Seventy-two ballet dancers are arranged into an array with 9 columns. How many dancers are in each column?
Answer: 8 dancers

Explanation:
Given that,
Seventy-two ballet dancers are arranged into an array with 9 columns.
72/9 = 8
Thus 8 dancers are in each column.

Question 21
You make 15 paper elephants and 17 paper lions. You give all of the animals away to 8 friends. Each friend gets the same number of animals. How many animals does each friend get?

Answer: 4

Explanation:
Given that,
You make 15 paper elephants and 17 paper lions.
15 + 17 = 32
You give all of the animals away to 8 friends.
Each friend gets the same number of animals.
32/8 = 4
Thus each friend gets 4 animals.

Divide by 8 or 9 Homework & Practice 4.6

Complete the model and find the quotient
Question 1.
Find 16 ÷ 8.

16 ÷ 8 = ____
Answer: 2

Explanation:
Number of rows = 8
Number of counters = 16
Divide the number of counters by the number of rows
Division equation is 16 ÷ 8 = 2
Thus the number of columns is 2.

Question 2.
Find 45 ÷ 9.

45 ÷ 9 = _____
Answer: 5

Explanation:
Number of rows = 9
Number of counters = 45
Divide the number of counters by the number of rows
Division equation is 45 ÷ 9 = 5
Thus the number of columns is 5.

Find the quotient
Question 3.
48 ÷ 8. = _____
Answer: 6

Explanation:
Divide the two numbers 48 and 8.
48/8 = 6
Thus the quotient is 6.

Question 4.
63 ÷ 9 = ______
Answer: 7

Explanation:
Divide the two numbers 63 and 9.
63/9 = 7
Thus the quotient is 7.

Question 5.
54 ÷ 9 = _____
Answer: 6

Explanation:
Divide the two numbers 54 and 9.
54/9 = 6
Thus the quotient is 6.

Question 6.

Answer: 4

Explanation:
Divide the two numbers 32 and 8.
32/8 = 4
Thus the quotient is 4.

Question 7.

Answer: 9

Explanation:
Divide the two numbers 72 and 8.
72/8 = 9
Thus the quotient is 9.

Question 8.

Answer: 2

Explanation:
Divide the two numbers 18 and 9.
18/9 = 2
Thus the quotient is 2.

Compare
Question 9.

Answer: =

Explanation:
Divide the two numbers
90/9 = 10
80/8 = 10
10 = 10
90 ÷ 9 = 80 ÷ 8

Question 10.

Answer:  <

Explanation:
Divide the two numbers
27/9 = 3
56/8 = 7
3 < 7
27 ÷ 9 < 56 ÷ 8

Question 11.

Answer: >

Explanation:
Divide the two numbers
72 ÷ 9 = 8
40 ÷ 8 = 5
8 > 5
72 ÷ 9 > 40 ÷ 8

Question 12.
A food truck owner needs 64 whole wheat pitas. The pitas come in packages of 8. How many packages should she buy?
Answer: 8

Explanation:
Given that,
A food truck owner needs 64 whole-wheat pitas. The pitas come in packages of 8.
64 ÷ 8 = 8
Thus she should buy 8 packages.

Question 13.
Patterns
Complete the division tables.

Answer:

Question 14.
Structure
Describe two different ways to find 54 ÷ 9.
Answer: 6
The different ways to find 54 ÷ 9 is a division equation and multiplication equation.
54/9 = 6
6 × 9 = 54

Question 15.
Modeling Real Life
A youth group leader is preparing for a remote-control car race. Batteries are sold in packs of 8. How many packs of batteries should he buy?

Answer:
Given,
A youth group leader is preparing for a remote-control car race.
Batteries are sold in packs of 8.
cars – 48
48 ÷ 8 = 6 batteries for cars
24 ÷ 8 = 3 batteries for remote

Question 16.
Modeling Real Life
Newton divides 32 treats equally between 8 friends. Descartes divides 27 treats equally between 9 friends. Whose friends get more treats? Explain.
Answer:
Given that,
Newton divides 32 treats equally between 8 friends.
32 ÷ 8 = 4
Descartes divides 27 treats equally between 9 friends.
27 ÷ 9 = 3
Thus Newton’s friends get more treats.

Review & Refresh

Find the missing factor.
Question 17.
____ × 4 = 0
Answer: 0

Explanation:
Let the missing factor be x.
x × 4 = 0
x = 0/4
x = 0
Thus the missing factor is 0.

Question 18.
1 × ____ = 2
Answer: 2

Explanation:
Let the missing factor be y.
1 × y = 2
y = 2/1
y = 2
Thus the missing factor is 2.

Question 19.
9 × ____ = 9
Answer: 1

Explanation:
Let the missing factor be z.
9 × z = 9
z = 9/9
z = 1
Thus the missing factor is 1.

Lesson 4.7 Divide by 0 or 1

Explore and Grow

Find the quotients

Answer:

Structure
What patterns do you notice? Use the patterns to find each quotient.
52 ÷ 52 = _____
0 ÷ 52 = _____
52 ÷ 1 = ______
Answer:
52 ÷ 52 = 1
Any number divided by the same number will be always 1.
0 ÷ 52 = 0
Any number divided by 0 will be always 0.
52 ÷ 1 = 52
Any number divided by 1 will be the same number.

Think and Grow: Divide by 0 or 1

Dividing a number by 1 or itself:
• Any number divided by1 is itself.
• Any number (except 0) divided by itself is 1.
Example
Find 7 ÷ 1.
Think: 1 time what number is 7?
1 × ____ = 7
Write: 7 × 1 = _____

Answer:
Any number divided by 1 will be the same number.
7 × 1 = 7

Example
Find 5 ÷ 5.
Think: 5 times what number is 5?
5 × ____ = 5
Write: 5 ÷ 5 = _____

Dividing with 0:
• 0 divided by any number (except 0) is 0.
• You cannot divide by 0.

Answer:
5 × 1 = 5
5 times 1 is 5.
5 ÷ 5 = 1

Example
Find 0 ÷ 8.
Think: 8 times what number is 0?
8 × ____ = 0
Write: 0 × 8 = _____

Answer:
0 times 8 is 0.
Any number multiplied by 0 is always 0.
0 × 8 = 0

Example
Find 9 ÷ 0.
Think: 0 times what number is 9?
There is no such number. So, you cannot divide by 0.

Show and Grow

Write the related multiplication fact. Then find the quotient.
Question 1.
2 ÷ 2 = _____
Answer: 1

Explanation:
The related multiplication fact for 2, 1 is
2 × 1 = 2
1 × 2 = 2
2 ÷ 2 = 1
Thus the quotient is 1.

Question 2.
0 ÷ 3 = _____
Answer: 0

Explanation:
The related multiplication fact for 0, 3 is
0 × 3 = 0
3 × 0 = 0
Thus the quotient is 0.

Question 3.
10 ÷ 1 =_____
Answer: 10

Explanation:
The related multiplication fact for 1, 10
1 × 10 = 10
10 × 1 = 10
10 ÷ 1 = 10
Thus the quotient is 10.

Question 4.
25 ÷ 25 = _____
Answer: 1

Explanation:
The related multiplication fact for 25, 1
1 × 25 = 25
25 × 1 = 25
25 ÷ 25 = 1
Thus the quotient is 1.

Apply and Grow: Practice

Write the related multiplication fact. Then find the quotient.
Question 5.
6 ÷ 1 = ______
Answer: 6

Explanation:
The related multiplication fact for 6,1
1 × 6 =6
6 × 1 = 6
6 ÷ 1 = 6
Thus the quotient is 6.

Question 6.
0 ÷ 2 = _____
Answer: 0

Explanation:
The related multiplication fact for 0,2
Any number divided by 0 will be always 0.
0 ÷ 2 = 0
Thus the quotient is 0.

Question 7.
9 ÷ 9 = ____
Answer: 1

Explanation:
The related multiplication fact for 1, 9
1 × 9 = 9
9 × 1 = 9
9 ÷ 9 = 1
Thus the quotient is 1.

Question 8.
8 ÷ 1 = _____
Answer: 8

Explanation:
The related multiplication fact for 1, 8
1 × 8 = 8
8 × 1 =8
8 ÷ 1 = 8
Thus the quotient is 8.

Find the quotient
Question 9.
5 ÷ 1 = _____
Answer: 5

Explanation:
Any number divided by 1 will be the same number.
5/1 = 5
Thus the quotient is 5

Question 10.
0 ÷ 7 = _____
Answer: 0

Explanation:
Any number divided by 0 will be always 0.
0/7 = 0
Thus the quotient is 0.

Question 11.
4 ÷ 4 = _____
Answer: 1

Explanation:
4/4 = 1
Thus the quotient is 1.

Question 12.

Answer: 15

Explanation:
Any number divided by 1 will be the same number.
15/1 = 1
Thus the quotient is 15.

Question 13.

Answer: 0

Explanation:
Any number divided by 0 will be always 0.
0/6 = 0
Thus the quotient is 0.

Question 14.

Answer: 1

Explanation:
24/24 = 1
Thus the quotient is 1.

Find the missing dividend or divisor.
Question 15.
2 ÷ ____ = 2
Answer: 1

Explanation:
Let the missing divisor be x.
2 ÷ x = 2
2/x = 2
2 = 2 × x
x = 2/2
x = 1
Thus the missing divisor is 1.

Question 16.
____ ÷ 12 = 0
Answer: 0

Explanation:
Let the missing divisor be y.
y ÷ 12 = 0
y/12 = 0
y = 0 × 12
y = 0
Thus the missing divisor is 0.

Question 17.
8 ÷ ____ = 1
Answer: 8

Explanation:
Let the missing divisor be z.
8 ÷ z = 1
8/z = 1
8 = 1 × z
z = 8
Thus the missing divisor is 8.

Compare
Question 18.

Answer: >

Explanation:
Divide the two numbers
4 ÷ 1 = 4
3 ÷ 1 = 3
4 > 3
So, 4 ÷ 1 > 3 ÷ 1

Question 19.

Answer: =

Explanation:
Any number divided by 0 will be always 0.
0 ÷ 6 = 0
0 ÷ 9 = 0
So, 0 ÷ 6 = 0 ÷ 9

Question 20.

Answer: <

Explanation:
Any number divided by 0 will be always 0.
0 ÷ 5 = 0
7 ÷ 1 = 7
0 < 7
0 ÷ 5 < 7 ÷ 1

Question 21.
There are 2 cheese blocks. Each mousetrap has 1 cheese block on it. How many mousetraps are there?

Answer: 2

Explanation:
Given that,
There are 2 cheese blocks. Each mousetrap has 1 cheese block on it.
2 ÷ 1 = 2
Thus there are 2 mousetraps.

Question 22.
Reasoning
Your friend says 14 ÷ 0 and 0 ÷ 14 both equal 0. Is your friend correct? Explain.
Answer: Incorrect

Explanation:
Your friend is incorrect because 0 divided by any number except 0 will be always 0.
0/14 = 0
but
14/0 =  infinity

Think and Grow: Modeling Real Life

A clown shares 10 balloons equally with 10 children. How many balloons does each child receive?

Division equation:
Each child receives a _____ balloon.

Answer: 1

Explanation:
Given that,
A clown shares 10 balloons equally with 10 children.
10/10 = 1
Therefore each child receives 1 balloon.

Show and Grow

Question 23.
You have 9 tokens. You need 1 token to play an arcade game. How many games can you play?
Answer: 9

Explanation:
Given that,
You have 9 tokens. You need 1 token to play an arcade game.
9/1 = 9
Thus you can play 9 games.

Question 24.
You have 9 quarters. You put 5 of them in your backpack. You divide the other quarters equally among 4 friends. How many quarters does each friend get?
Answer: 1

Explanation:
Given,
You have 9 quarters. You put 5 of them in your backpack.
9 – 5 = 4
You divide the other quarters equally among 4 friends.
4/4 = 1
Thus each friend gets 1 quarter.

Question 25.
You ask your friend the question below.
“What is 475 divided by475?”
Your friend immediately says 1. How does your friend solve the problem so quickly? Explain.
Answer:
475/475 = 1
Your friend solved the problem very quickly because he used the logic ” Any number divided by the same number will be always 1″.

Divide by 0 or 1 Homework & Practice 4.7

Write the related multiplication fact. Then find the quotient.
Question 1.
3 ÷ 1 = _____
Answer: 3

Explanation:
The related multiplication fact for 1,3
1 × 3 = 3
3 × 1 = 3
Divide the two numbers
3 ÷ 1 = 3
Thus the quotient is

Question 2.
0 ÷ 7 = _____
Answer: 0

Explanation:
The related multiplication fact for 0, 7
0 × 7 = 0
7 × 0 = 0
Divide the two numbers 0, 7
0/7 = 0
Thus the quotient is 0

Find the quotient.
Question 3.
8 ÷ 1 = _____
Answer: 8

Explanation:
The related multiplication fact for 1, 8
8 × 1 = 8
1 × 8 = 8
Divide the two numbers 8, 1
8/1 = 8
Thus the quotient is 8

Question 4.
0 ÷ 2 = _____
Answer: 0

Explanation:
The related multiplication fact for 0, 2
0 × 2 = 0
2 × 0 = 0
Divide the two numbers
0/2 = 0
Thus the quotient is 0

Question 5.
7 ÷ 7 = _____
Answer: 1

Explanation:
The related multiplication fact for 7, 1
1 × 7 = 7
7 × 1 = 7
Divide the two numbers
7/7 = 1
Thus the quotient is 1

Question 6.

Answer: 1

Explanation:
The related multiplication fact for 1, 12
12 × 1 = 12
1 × 12 = 12
Divide the two numbers
12/12 = 1
Thus the quotient is 1

Question 7.

Answer: 4

Explanation:
The related multiplication fact for 1, 4
1 × 4 = 4
4 × 1 = 4
Divide the two numbers
4/1 = 4
Thus the quotient is 4

Question 8.

Answer: 0

Explanation:
The related multiplication fact for 0, 10
0 × 10 = 0
10 × 0 = 0
Divide the two numbers
0/10 = 0
Thus the quotient is 0

Find the missing dividend or divisor
Question 9.
____ ÷ 3 = 0
Answer: 0

Explanation:
Let the missing dividend be x
x ÷ 3 = 0
x/3 = 0
x = 0 × 3
x = 0
Thus the missing dividend is 0.

Question 10.
10 ÷ ____ = 10
Answer: 1

Explanation:
Let the missing divisor be y.
10 ÷ y = 10
10/y = 10
10 = y × 10
y = 10/10
y = 1
Thus the missing divisor is 1.

Question 11.
____ ÷ 4 = 0
Answer: 0

Explanation:
Let the missing dividend be z.
z ÷ 4 = 0
z/4 = 0
z = 0 × 4
z = 0
Thus the missing dividend is 0.

Compare
Question 12.

Answer: =

Explanation:
Divide the two numbers
0 ÷ 7 = 0
0 ÷ 1 = 0
0 = 0
0 ÷ 7 = 0 ÷ 1

Question 13.

Answer: <

Explanation:
Divide the two numbers
0 ÷ 9 = 0
2 ÷ 1 = 2
0 < 2
0 ÷ 9 < 2 ­÷ 1

Question 14.

Answer: >

Explanation:
Divide the two numbers
6 ÷ 1 = 6
6 ÷ 6 = 1
6 > 1
6 ÷ 1 > 6 ÷ 6

Question 15.
Reasoning
How are the multiplication rules for 0 and 1 similar to the division rules for 0 and 1? How are they different?
Answer:
Multiplication and division are closely related, given that division is the inverse operation of multiplication. When we divide, we look to separate into equal groups, while multiplication involves joining equal groups.
multiplication rules for 0 and 1 are not similar to division rules for 0 and 1.
Any number multiplied by 0 will be zero.
But any number divided by 0 will be infinity.

Question 16.
Number Sense
Which has the greatest quotient?
6 ÷ 6
4 ÷ 1
0 ÷ 8
3 ÷ 1
Answer: 4 ÷ 1

Explanation:
6 ÷ 6 = 1
4 ÷ 1 = 4
0 ÷ 8 = 0
3 ÷ 1 = 3
Thus the correct answer is option b.

Question 17.
DIG DEEPER!
Use the numbers 0, 1, 5, and 10 to make the number sentence true.
____ ÷ _____ < _____ ÷ ______
Answer:
You need to write the equation by using the above numbers.
0 ÷ 1 < 5 ÷ 10

Question 18.
Modeling Real Life
There are 5 bird eggs. An equal number of eggs hatch each day for 5 days. How many eggs hatch each day?

Answer:
Given that,
There are 5 bird eggs. An equal number of eggs hatch each day for 5 days.
5/5 = 1
Therefore 1 egg hatch each day.

Question 19.
Modeling Real Life
A hotel orders twenty-four 48-inch televisions and twenty-six 60-inch televisions. The hotel puts 1 television in each room. How many rooms can get a new television?
Answer:
Given,
A hotel orders twenty-four 48-inch televisions and twenty-six 60-inch televisions.
The hotel puts 1 television in each room.
24 + 26 = 50
Thus 50 rooms can get a new television.

Review & Refresh

Find the product.
Question 20.
2 × 4 × 1 = _____
Answer: 8

Explanation:
First multiply 2 × 4
2 × 4 = 8
8 × 1 = 8
So, 2 × 4 × 1 = 8

Question 21.
2 × 3 × 5 = _____
Answer: 30

Explanation:
Multiply 2 and 3
2 × 3 = 6
6 × 5 = 30
So, 2 × 3 × 5 = 30

Question 22.
2 × 3 × 7 = _____
Answer: 42

Explanation:
Multiply 2 and 3
2 × 3 = 6
6 × 7 = 42
So, 2 × 3 × 7 = 42

Question 23.
5 × (2 × 9) = _____
Answer: 90

Explanation:
First, multiply the numbers in the bracket.
2 × 9 = 18
18 × 5 = 90

Question 24.
2 × (3 × 3) = _____
Answer: 18

Explanation:
First, multiply the numbers in the bracket.
3 × 3 = 9
9 × 2 = 18

Question 25.
2 × (8 × 1) = _____
Answer: 16

Explanation:
First, multiply the numbers in the bracket.
8 × 1 = 8
2 × 8 = 16

Lesson 4.8 Practice Division Strategies

Explore and Grow

Use and Strategies to find the quotient
36 ÷ 4 = _____
Answer: 9

Explanation:
You can find the quotient by using the number line.

Construct Arguments
What other strategies can you use to solve? Explain the strategy to your partner.
Answer:
You can also find the quotient by using the repeated subtraction.
36 – 4 = 32
32 – 4 = 28
28 – 4 = 24
24 – 4 = 20
20 – 4 = 16
16 – 4 = 12
12 – 4 = 8
8 – 4 = 4
4 – 4 = 0
Count the number of times subtraction repeated.
The subtraction repeated 9 times.
Thus the quotient is 9.

Think and Grow: Practice Division Strategies

Example
Find 45 ÷ 5.
One Way:
Use a multiplication fact. Draw an array to help.

Another Way:
Use a number line. Start at 45. Count back by 5s until you reach 0.

Show and Grow

Use any strategy to find the quotient.
Question 1.
30 ÷ 6 = _____
Answer: 5

Explanation:

Multiplication:
5 rows of 6 counters
5 × 6 = 30
30 counters
Division:
30 counters in 5 equal rows
30 ÷ 5 = 6
60 counters in each row.
Fact family for 5, 6 and 30:
5 × 6 = 30
6 × 5 = 30
30 ÷ 5 = 6
30 ÷ 6 = 5

Question 2.
56 ÷ 8 = _____
Answer: 7

Explanation:
Number of rows = 8
Number of counters = 56
Divide the number of rows by the number of counters.
56/8 = 7
Thus the quotient is 7.

Apply and Grow: Practice

Use any strategy to find the quotient.
Question 3.
40 ÷ 10 = _____
Answer: 4

Explanation:
You can find the quotient by using the repeated subtraction.
40 – 10 = 30
30 – 10 = 20
20 – 10 = 10
10 – 10 = 0
Thus the quotient is 4.

Question 4.
18 ÷ 3 = _____
Answer: 6

Explanation:
You can find the quotient by using the repeated subtraction.
18 – 3 = 15
15 – 3 = 12
12 – 3 = 9
9 – 3 = 6
6 – 3 = 3
3 – 3 = 0
Thus the quotient is 6.

Question 5.
49 ÷ 7 = ____
Answer: 7

Explanation:
You can find the quotient by using the repeated subtraction.
49 – 7 = 42
42 – 7 = 35
35 – 7 = 28
28 – 7 = 21
21 – 7 = 14
14 – 7 = 7
7 – 7 = 0
Thus the quotient is 7.

Question 6.
____ = 36 ÷ 9
Answer: 4

Explanation:
You can find the quotient by using the repeated subtraction.
36 – 9 = 27
27 – 9 = 18
18 – 9 = 9
9 – 9 = 0
Thus the quotient is 4.

Question 7.
____ = 4 ÷ 4
Answer: 1

Explanation:
You can find the quotient by using the repeated subtraction.
4 – 4 = 0
Thus the quotient is 1.

Question 8.
______ = 18 ÷ 2
Answer: 9

Explanation:
You can find the quotient by using the repeated subtraction.
18 – 2 = 16
16 – 2 = 14
14 – 2 = 12
12 – 2 = 10
10 – 2 = 8
8 – 2 = 6
6 – 2 = 4
4 – 2 = 2
2 – 2 = 0
Thus the quotient is 0.

Question 9.

Answer: 12

Explanation:
You can find the quotient by using the repeated subtraction.
12 – 1 = 11
11 – 1 = 10
10 – 1 = 9
9 – 1 = 8
8 – 1 = 7
7 – 1 = 6
6 – 1 = 5
5 – 1 = 4
4 – 1 = 3
3 – 1 = 2
2 – 1 = 1
1 – 1 = 0
Thus the quotient is 12.

Question 10.

Answer: 8

Explanation:
Divide the two numbers 5 and 40
40/5 = 8
Thus the quotient is 8.

Question 11.

Answer: 6

Explanation:
Divide the two numbers 8 and 48
48/8 = 6
Thus the quotient is 6.

Question 12.

Answer: 4

Explanation:
Divide the two numbers 6 and 24
24/6 = 4
Thus the quotient is 4.

Question 13.

Answer: 5

Explanation:
Divide the two numbers 4 and 20.
20/4 = 5
Thus the quotient is 5.

Question 14.

Answer: 3

Explanation:
Divide the two numbers 7 and 21
21/7 = 3
Thus the quotient is 3.

Question 15.

Answer: 10

Explanation:
Divide the two numbers 2 and 20.
20/2 = 10
Thus the quotient is 10.

Question 16.

Answer: 0

Explanation:
Divide the two numbers 0 and 7
0/7 = 0
Thus the quotient is 0.

Question 17.
Divide 54 by 6.
Answer: 9

Explanation:
Divide the two numbers 54 and 6.
54/6 = 9
Thus the quotient is 9.

Question 18.
Divide 27 by 9.
Answer: 3

Explanation:
Divide the two numbers 9 and 27.
27/9 = 3
Thus the quotient is 3.

Question 19.
Divide 70 by 10.
Answer: 7

Explanation:
Divide the two numbers 10 and 70
70/10 = 7
Thus the quotient is 7.

Question 20.
A construction worker wants to build a 32-foot-long wall in 8 hours. How many feet should he complete each hour so that it is built on time?

Answer: 4

Explanation:
Given that,
A construction worker wants to build a 32-foot-long wall in 8 hours.
32/4 = 4
Thus he should complete 4 feet each hour.

Question 21.
Writing
How can you use multiplication to help find 42 ÷ 7? Explain.
Answer:
42 = x × 7
x = 42/7
x = 6
So, 42 ÷ 7 = 6

Question 22.
YOU BE THE TEACHER
Your friend says she only needs to write two equations for the 4, 4, 16 fact family. Is your friend correct? Explain.
Answer:
4 × 4 = 16
16 ÷ 4 = 4
Yes, your friend is correct.

Think and Grow: Modeling Real Life

There are 72 oranges at a grocery store arranged into an array with 9 columns. There are 80 lemons arranged into an array with 8 columns. Which fruits as more rows?

Models:
Division equations:
The ______ have more rows.

Answer:
Given that,
There are 72 oranges at a grocery store arranged into an array with 9 columns.
72 ÷ 9 = 8
There are 80 lemons arranged into an array with 8 columns.
80 ÷ 8 = 10
Thus lemons have more rows.

Show and Grow

Question 23.
There are 63 peaches arranged into an array with 7 rows. There are 70 pears arranged into an array with 10 rows. Which fruit has more columns?

Answer:
Given,
There are 63 peaches arranged into an array with 7 rows.
63 ÷ 7 = 9
There are 70 pears arranged into an array with 10 rows.
70 ÷ 10 = 7
Thus peaches have more columns.

Question 24.
Newton has 20 quarters. He wants to trade all of them for bills. How many $1 bills would he get? How many $5 bills would he get?
Answer:
Given that,
Newton has 20 quarters. He wants to trade all of them for bills
20/5 = 4
Thus he will get four $5 bills.

Question 25.
A box of fruit snacks costs $5. Each box has 8 bags. Descartes spends $20 on fruit snacks. How many bags of fruit snacks does he get?
Answer:
Given that,
A box of fruit snacks costs $5. Each box has 8 bags.
$5 × 8 = $40
Descartes spends $20 on fruit snacks.
40 – 20 = $20
Thus Descartes get 4 bags of fruit snacks.

Practice Division Strategies Homework & Practice 4.8

Use any strategy to find the quotient
Question 1.
8 ÷ 1 = ____
Answer: 8

Explanation:
Divide the two numbers 8 and 1.
8/1 = 8
Thus the quotient is 8.

Question 2.
25 ÷ 5 = _____
Answer: 5

Explanation:
Divide the two numbers 5 and 25.
25/5 = 5
Thus the quotient is 5.

Question 3.
72 ÷ 8 = _____
Answer: 9

Explanation:
Divide the two numbers 8 and 72.
72/8 = 9
Thus the quotient is 9.

Question 4.
____ = 45 ÷ 9
Answer: 5

Explanation:
Divide the two numbers 9 and 45
45/9 = 5
Thus the quotient is 5.

Question 5.
____ = 0 ÷ 3.
Answer: 0

Explanation:
Divide the two numbers 0 and 3.
0 divided by any number is zero.
0/3 = 0
Thus the quotient is 0.

Question 6.
____ = 18 ÷ 2
Answer: 9

Explanation:
Divide the two numbers 18 and 2.
18/2 = 9
Thus the quotient is 9.

Question 7.

Answer: 3

Explanation:
Divide the two numbers 9 and 27.
27/9 = 3
Thus the quotient is 3.

Question 8.

Answer: 2

Explanation:
Divide the two numbers 14 and 7.
14/7 = 2
Thus the quotient is 2.

Question 9.

Answer: 10

Explanation:
Divide the two numbers 2 and 20.
20/2 = 10
Thus the quotient is 10.

Question 10.

Answer: 4

Explanation:
Divide the two numbers 3 and 12
12/3 = 4
Thus the quotient is 4.

Question 11.

Answer: 1

Explanation:
Divide the two numbers 16 and 16
16/16 = 1
Thus the quotient is 1.

Question 12.

Answer: 7

Explanation:
Divide the two numbers 10 and 70.
70/10 = 7
Thus the quotient is 7.

Question 13.

Answer: 6

Explanation:
Divide the two numbers 5 and 30.
30/5 = 6
Thus the quotient is 6.

Question 14.

Answer: 8

Explanation:
Divide the two numbers 8 and 64.
64/8 = 8
Thus the quotient is 8.

Question 15.
Divide 60 by 6.
Answer: 10

Explanation:
Divide the two numbers 6 and 60
60/6 = 10
Thus the quotient is 10.

Question 16.
Divide 9 by 3.
Answer: 3

Explanation:
Divide the two numbers 3 and 9.
9/3 = 3
Thus the quotient is 3.

Question 17.
Divide 63 by 9.
Answer: 7

Explanation:
Divide the two numbers 9 and 63.
63/9 = 7
Thus the quotient is 7.

Question 18.
DIG DEEPER!
Without dividing, how can you tell which quotient is smaller, 30 ÷ 5 or 30 ÷ 6? Explain.
Answer: The quotient of 30 ÷ 6  is smaller.

Explanation:
The largest divisor will have the smallest quotient.
30 ÷ 5 = 6
30 ÷ 6 = 5

Question 19.
Number Sense
Which expressions have a quotient of 7?

Answer:

Explanation:
70/10 = 7
64/8 = 8
35 ÷ 5 = 7
42 ÷ 7 = 6
21 ÷ 3 = 7
24 ÷ 8 = 3
7 ÷ 1 = 7

Question 20.
Reasoning
Use +, -, ×, or to complete the equations.

Answer:

Question 21.
Modeling Real Life
Newton has 60 dimes. He trades all of them for $1 bills. How many bills does he get?

Answer: 6

Explanation:
Newton has 60 dimes. He trades all of them for $1 bills.
Convert from dime to dollar.
10 dime = 1 dollar
60 dimes = $6

Question 22.
Modeling Real Life
Two girls are getting braids in their hair. The first girl wants a total of 30 beads with 3 beads on each braid. The second girl wants a total of 45 beads with 5 beads on each braid. Which girl has more braids?
Answer:
Given that,
Two girls are getting braids in their hair.
The first girl wants a total of 30 beads with 3 beads on each braid.
30/3 = 10
The second girl wants a total of 45 beads with 5 beads on each braid.
45/5 = 9
The first girl has more braids.

Review & Refresh

Find the sum.
Question 23.

Answer: 597

460
+137
597

Question 24.

Answer: 932
625
+297
932

Question 25.

Answer: 750
386
+ 364
750

Lesson 4.9 Problem Solving: Division

Explore and Grow

Use any strategy to solve.
There are 27 cups for a cup-stacking game. There are 3 players. Each player gets an equal number of cups. How many cups does each player get?

Answer:
Given,
There are 27 cups for a cup-stacking game.
There are 3 players.
27/3 = 9
Each player gets an equal number of cups.
Thus each player gets 9 cups.

Reasoning
Compare your strategy to your partner’s strategy. How are they the same? How are they different?

Think and Grow: Using the Problem-Solving Plan

Example
Newton buys a box of flower vases. The box has 2 rows with 4 vases in each row. The box costs $48. How much does each vase cost?
Understand the Problem
What do you need to find?
• You need to find how much each ______ costs.

Answer: You need to find each vase cost.

What do you know?
• The box has ______ rows of vases.
• Each row has ______ vases.
• The box costs _____.

Answer:
• The box has 2 rows of vases.
• Each row has 4 vases.
• The box costs $48.

Make a Plan

How will you solve?
• Multiply _____ by ______ to find how many _______ are in the box.
• Then divide _______ by the product.

Answer:
• Multiply 2 by 4 to find how many vases are in the box.
• Then divide cost by the product.

Solve

Each vase costs _______.

Answer:
2 × 4 = 8
48/8 = 6
Thus each vase cost $6.

Show and Grow

Question 1.
Descartes buys 3 packs of colored pencils and a backpack. He spends $33. The backpack costs $12. Each pack of colored pencils costs the same amount. How much is each pack of colored pencils?
Answer:
Given,
Descartes buys 3 packs of colored pencils and a backpack.
He spends $33. The backpack costs $12.
33 – 12 = $21
Each pack of colored pencils costs the same amount.
21/3 = $7
Thus each pack of colored pencils is $7.

Apply and Grow: Practice

Question 2.
You have 4 pages of homework and 2 chores to complete before you get free time. Each task takes 7 minutes to complete. You have60 minutes until dinner. What information do you know that will help you find how much free time you will have before dinner?
Answer:
Given that,
You have 4 pages of homework and 2 chores to complete before you get free time.
Each task takes 7 minutes to complete.
4 + 2 = 6
6 × 7 = 42 minutes
You have 60 minutes until dinner.
60 – 42 = 18 minutes
You will have 18 minutes of free time before dinner.

Question 3.
You are using dots to create a picture. You use 99 dots in all. Forty-six are blue. Thirty-five are purple. You use an equal number of yellow and green dots for the rest of the picture. How many green dots are in your picture?

Answer:
Given,
You are using dots to create a picture. You use 99 dots in all. Forty-six are blue.
Thirty-five are purple.
35 + 46 = 81
99 – 81 = 18
You use an equal number of yellow and green dots for the rest of the picture.
18/2 = 9
You use 9 yellow dots and 9 green dots.

Question 4.
You are making oatmeal for each of your 4 family members. You have 36 raisins and 20 blueberries. You want everyone to get an equal number of each. How many raisins and how many blueberries should you put in each bowl?


Answer:
Given that,
You are making oatmeal for each of your 4 family members.
You have 36 raisins and 20 blueberries.
36 + 20 = 56
You want everyone to get an equal number of each.
56/4 = 14
Therefore 14 raisins and blueberries should put in each bowl.

Think and Grow: Modeling Real Life

You have 2 boxes of crayons. One box has 24 crayons. The other box has 48 crayons. Eighteen of the crayons are broken. You put the crayons that are not broken, into 6 equal groups. How many crayons are in each group?

Understand the problem:
Make a plan:
Solve:
There are _____ crayons in each group.

Answer:
You have 2 boxes of crayons. One box has 24 crayons. The other box has 48 crayons.
24 + 48 = 72 crayons
Eighteen of the crayons are broken.
72 – 18 = 54 crayons
You put the crayons that are not broken, into 6 equal groups.
54/6 = 9 crayons.
Therefore there are 9 crayons in each group.

Show and Grow

Question 5.
You have 2 bags of beach glass. One bag has 17 pieces. The other bag has 18 pieces. You give 5 pieces to your friend. You sort the rest of the pieces into 3 equal groups. How many pieces are in each group?

Explain how you can check your answer.
Answer:
Given,
You have 2 bags of beach glass. One bag has 17 pieces. The other bag has 18 pieces.
17 + 18 = 35 pieces
You give 5 pieces to your friend.
35 – 5 = 30 pieces
You sort the rest of the pieces into 3 equal groups.
30/3 = 10
Thus there are 10 pieces in each group.

Problem Solving: Division Homework & Practice 4.9

Question 1.
A truck carries 4 chairs and a table. The table weighs 35 pounds. The total weight of the chairs and table is 63 pounds. How much does each chair weigh?
Answer: 7 pounds

Explanation:
Given that,
A truck carries 4 chairs and a table. The table weighs 35 pounds.
The total weight of the chairs and table is 63 pounds.
63 pounds – 35 pounds = 28 pounds
There are 4 chairs.
Divide 28 by 4 to find the weight of each chair.
28/4 = 7
Therefore each chair weighs 7 pounds.

Question 2.
You volunteer at a nursing home for 3 hours a day. You volunteered 6 hours last week and 12 hours this week. How many days did you volunteer?
Answer: 6 days

Explanation:
Given that,
You volunteer at a nursing home for 3 hours a day.
You volunteered 6 hours last week and 12 hours this week.
6 hours – 2 days
12 hours – 4 days
4 + 2 = 6 days
Thus you volunteer for 6 days.

Question 3.
Writing Write and solve your own word problem involving division.
Answer:
You work for 49 hours a week. How many hours do you work in a day?
Explanation:
You work for 49 hours a week.
Convert from weeks to days
1 week = 7 days
49/7 = 7 hours
Thus you work 7 hours a day.

Question 4.
Modeling Real Life
You have 2 trays of flavored ice cubes. One tray has 16 ice cubes. The other tray has 12 ice cubes. Eight of the ice cubes are not completely frozen yet. You divide the frozen ice cubes equally into 5 glasses. How many ice cubes are in each glass?
Answer:
Given that,
You have 2 trays of flavored ice cubes. One tray has 16 ice cubes.
16 × 2 = 32 ice cubes
The other tray has 12 ice cubes. Eight of the ice cubes are not completely frozen yet.
12 – 8 = 4
32 + 4 = 36 ice cubes
You divide the frozen ice cubes equally into 5 glasses.
36/5 = 7(approx)
Thus you divide 7 frozen ice cubes equally into 5 glasses.

Question 5.
Modeling Real Life
You have 2 bags of seashells. One bag has 13 seashells. The other bag has 25 seashells. You give6 seashells to your friend. You sort the rest of the seashells into 4 equal groups. How many seashells are in each group?

Answer:
Given that,
You have 2 bags of seashells. One bag has 13 seashells.
2 × 13 = 26 seashells
The other bag has 25 seashells. You give 6 seashells to your friend.
25 – 6 = 19
You sort the rest of the seashells into 4 equal groups.
26 + 19 = 45 seashells
45/4 = 11 (approx)
Thus there are 11 seashells in 4 equal groups.

Review & Refresh

Question 6.

Answer:
i. 5 sides
ii. 5 vertices
iii. pentagon

Explanation:
The above figure consists of 5 sides and 5 vertices. The polygon with 5 sides is called a pentagon.

Question 7.

Answer:
i. 4 sides
ii. 4 vertices
iii. Quadrilateral

Explanation:
The above figure consists of 4 sides and 4 vertices. The polygon with 4 sides is called a Quadrilateral.

Division Facts and Strategies Performance Task

You, your friend, and your cousin run for class president. Three teachers and 60 students are gathered in the gym for the election.
Question 1.
There is one teacher in each row. Each row has the same number of students. Find the number of people sitting in each row.

Answer:
Given that,
You, your friend, and your cousin run for class president.
Three teachers and 60 students are gathered in the gym for the election.
There is one teacher in each row. Each row has the same number of students.
60/3 = 20 students
Thus 20 people are sitting in each row.

Question 2.
Sixty students vote in the election. Thirty students vote for you. Twenty students vote for your friend. Five students vote for your cousin.
a.How many students still need to vote?

Answer:
Sixty students vote in the election. Thirty students vote for you.
60 – 30 = 30
Twenty students vote for your friend.
30 – 20 = 10
Five students vote for your cousin.
10 – 5 = 5
Thus still 5 students need to vote.

b.The remaining students all vote for your cousin. Complete the picture graph.

Answer:

Question 3.
As class president, you raise $95 to buy new toys for the school playground. Each ball costs $8 and each flying disc costs $6. You want to buy some balls and 3 flying discs. How many balls can you buy? How much money do you have left?
Answer:
Given that,
As class president, you raise $95 to buy new toys for the school playground.
Each ball costs $8 and each flying disc costs $6.
You want to buy some balls and 3 flying discs.
3 × $6 = $18
$95 – $18 = $77
We need to how many balls can you buy for $77.
72/8 = 9
77 – 72 = 5
Thus $5 left.

Division Facts and Strategies Activity

Four in a Row Blastoff!
Directions:
1. Players take turns rolling the die.
2. On your turn, choose and solve any division expression in the row of your roll. If you find the correct answer, place a counter on the space.
3. The first player to create 4 counters in a row, horizontally, vertically, or diagonally, wins! A spaceship blasts off! Cross out one spaceship and play again until all spaceships have blasted off!

Answer:
I choose 3, 9 ÷ 3 = 3
I choose 4, 16 ÷ 4 = 4
I choose 5, 25 ÷ 5 = 5
I choose 6, 36 ÷ 6 = 6

Division Facts and Strategies Chapter Practice

4.1 Use Arrays to Divide

Question 1.
There are 20 counters. The counters are in 4 equal rows. How many counters are in each row?
4 rows of ____
20 ÷ 4 = _____
Answer:
Given that,
There are 20 counters. The counters are in 4 equal rows.
20/4 = 5
Thus there are 4 rows of 5 counters
20 ÷ 4 = 5
Thus there are 5 counters in each row.

Question 2.
You have 32 counters. You arrange them with 8 counters in each row. How many rows of counters do you make?
____ rows of 8
32 ÷ 8 = _____
Answer:
Given,
You have 32 counters. You arrange them with 8 counters in each row.
32/8 = 4
4 rows of 8.
32 ÷ 8 = 4
Thus there are 4 rows of counters.

Question 3.
Precision
Label the parts of the division problem using quotient, dividend, and divisor

Answer:
The label for the above problem is
21 is dividend
3 is quotient
7 is divisor

4.2 Relate Multiplication and Division

Write the fact family for the numbers.
Question 4.
1, 5, 5
Answer:
The fact family for the numbers is
Multiplication Equation:
1 × 5 = 5
5 × 1 = 5
Division Equation:
5 ÷ 5 = 1
5 ÷ 1 = 5

Question 5.
2, 7, 14
Answer:
The fact family for the numbers is
Multiplication Equation:
2 × 7 = 14
7 × 2 = 14
Division Equation:
14 ÷ 2 = 7
14 ­÷ 7 = 2

Question 6.
9, 5, 45
Answer:
The fact family for the numbers is
Multiplication Equation:
9 × 5 = 45
5 × 9 = 45
Division Equation:
45 ÷ 5 = 9
45 ÷ 9 = 5

Question 7.
8, 6, 48
Answer:
The fact family for the numbers is
Multiplication Equation:
8 × 6 = 48
6 × 8 = 48
Division Equation:
48 ÷ 6 = 8
48 ÷ 8 = 6

4.3 Divide 2, 5, or 10

Write the related multiplication fact. The find the quotient.
Question 8.
Find 15 ÷ 5
5 × ____ = 15
15 ÷ 5 = ____
Answer:
Let the unknown number be x.
5 × x = 15
x = 15/5
x = 3
15 ÷ 5 = 3

Question 9.
Find 14 ÷ 2
2 × ____ = 14
14 ÷ 2 = ____
Answer:
Let the unknown number be x.
2 × x = 14
x = 14/2
x = 7
14 ÷ 2 = 7

Question 10.
Find 40 ÷ 10
10 × ____ = 40
40 ÷ 10 = ____
Answer:
Let the unknown number be x.
10 × x = 40
x = 40/10
x = 4
40 ÷ 10 = 4

Find the quotient.
Question 11.
60 ÷ 10 = _____
Answer: 6

Explanation:
Divide the two numbers 60 and 10.
60/10 = 6
Thus the quotient is 6.

Question 12.
20 ÷ 5 = _____
Answer: 4

Explanation:
Divide the two numbers 20 and 5.
20/5 = 4
Thus the quotient is 4.

Question 13.
20 ÷ 2 = _____
Answer: 10

Explanation:
Divide the two numbers 20 and 2.
20/2 = 10
Thus the quotient is 10.

Question 14.

Answer: 5

Explanation:
Divide the two numbers 25 and 5.
25/5 = 5
Thus the quotient is 5.

Question 15.

Answer: 9

Explanation:
Divide the two numbers 18 and 2.
18/2 = 9
Thus the quotient is 9.

Question 16.

Answer: 3

Explanation:
Divide the two numbers 30 and 10.
30/10 = 3
Thus the quotient is 3.

4.4 Divide by 3 or 4

Find the quotient.
Question 17.
18 ÷ 3 = _____
Answer: 6

Explanation:
Divide the two numbers 18 and 3.
18/3 = 6
Thus the quotient is 6.

Question 18.
40 ÷ 4 = ____
Answer: 10

Explanation:
Divide the two numbers 40 and 4.
40/4 = 10
Thus the quotient is 10.

Question 19.
24 ÷ 4 = _____
Answer: 6

Explanation:
Divide the two numbers 24 and 4.
24/4 = 6
Thus the quotient is 6.

Question 20.

Answer: 9

Explanation:
Divide the two numbers 3 and 27.
27/3 = 9
Thus the quotient is 9.

Question 21.

Answer: 3

Explanation:
Divide the two numbers 12 and 4.
12/4 = 3
Thus the quotient is 3.

Question 22.

Answer: 8

Explanation:
Divide the two numbers 24 and 3.
24/3 = 8
Thus the quotient is 8.

Question 23.
Structure
Write the division equation represented by the number line.

____ ÷ ____ = ____
Answer: 21 ÷ 3 = 7
Explanation:
The count starts from 0.
The count jumps for every 3s.
The division equation is 21 ÷ 3 = 7

4.5 Divide by 6 or 7

Find the quotient
Question 24.
42 ÷ 6 = _____
Answer: 7

Explanation:
Divide the two numbers 42 and 6.
42/6 = 7
Thus the quotient is 7.

Question 25.
54 ÷ 6 = _____
Answer: 9

Explanation:
Divide the two numbers 54 and 6.
54/6 = 9
Thus the quotient is 9.

Question 26.
28 ÷ 7 = ____
Answer: 4

Explanation:
Divide the two numbers 28 and 7.
28/7 = 4
Thus the quotient is 4.

Question 27.

Answer: 3

Explanation:
Divide the two numbers 21 and 7.
21/7 = 3
Thus the quotient is 3.

Question 28.

Answer: 6

Explanation:
Divide the two numbers 7 and 42.
42/7 = 6
Thus the quotient is 6.

Question 29

Answer: 5

Explanation:
Divide the two numbers 30 and 6.
30/6 = 5
Thus the quotient is 5.

Find the missing divisor
Question 30.
18 ÷ ____ = 6
Answer: 3

Explanation:
Let the missing divisor be u.
18 ÷ u = 6
18/u = 6
18 = 6 × u
u = 18/6
u = 3
Thus the missing divisor is 3.

Question 31.
35 ÷ ____ = 7
Answer: 5

Explanation:
Let the missing divisor be v.
35 ÷ v = 7
35/v = 7
35 = 7 × v
v = 35/7
v = 5
Thus the missing divisor is 5.

Question 32.
36 ÷ ____ = 6
Answer: 6

Explanation:
Let the missing divisor be w.
36 ÷ w = 6
36/w = 6
36 = 6 × w
w = 36/6
w = 6
Thus the missing divisor is 6.

4.6 Divide by 8 or 9

Find the quotient
Question 33.
36 ÷ 9 = _____
Answer: 4

Explanation:
Divide the two numbers 36 and 9
36/9 = 4
Thus the quotient is 4.

Question 34.
64 ÷ 8 = ____
Answer: 8

Explanation:
Divide the two numbers 8 and 64
64/8 = 8
Thus the quotient is 8.

Question 35.
90 ÷ 9 = _____
Answer: 10

Explanation:
Divide the two numbers 90 and 9.
90/9 = 10
Thus the quotient is 10.

Question 36.

Answer: 4

Explanation:
Divide the two numbers 32 and 8.
32/8 = 4
Thus the quotient is 4.

Question 37.

Answer: 5

Explanation:
Divide the two numbers 45 and 9.
45/9 = 5
Thus the quotient is 5.

Question 38.

Answer: 7

Explanation:
Divide the two numbers 56 and 8
56/8 = 7
Thus the quotient is 7.

Compare
Question 39.

Answer: >

Explanation:
Divide the two numbers.
63 ÷ 9 = 7
48 ÷ 8 = 6
7 > 6
So, 63 ÷ 9 > 48 ÷ 8

Question 40.

Answer: =

Explanation:
Divide the two numbers
32 ÷ 8 = 4
36 ÷ 9 = 4
4 = 4
So, 32 ÷ 8 = 36 ÷ 9

Question 41.

Answer: <

Explanation:
Divide the two numbers
54 ÷ 9 = 6
80 ÷ 8 = 10
6 < 10
So, 54 ÷ 9 < 80 ÷ 10

Question 42.
A crayon box has 48 crayons. There are 8 crayons in each row. How many rows of crayons are there?

Answer: 6

Explanation:
Given,
A crayon box has 48 crayons. There are 8 crayons in each row.
48/8 = 6
Thus there are 6 rows of crayons.

4.7 Divide with 0 or 1

Find the quotient
Question 43.
13 ÷ 13 = _____
Answer: 1

Explanation:
Divide the two numbers 13 and 13.
13/13 = 1
Thus the quotient is 1.

Question 44.
0 ÷ 9 = _____
Answer: 0

Explanation:
Divide the two numbers 0 and 9
Any number divided by 0 will be always 0.
0/9 = 0
Thus the quotient is 0.

Question 45.
3 ÷ 1 = _____
Answer: 3

Explanation:
Divide the two numbers 3 and 1.
3/1 = 3
Thus the quotient is 3.

Question 46.

Answer: 2

Explanation:
Divide the two numbers 1 and 2.
2/1 = 2
Thus the quotient is 2.

Question 47.

Answer: 0

Explanation:
Divide the two numbers 0 and 5.
Any number divided by 0 will be always 0.
Thus the quotient is 0.

Question 48.

Answer: 1

Explanation:
Divide the two numbers 10 and 10.
10/10 = 1
Thus the quotient is 1.

Question 49.
Number Sense
Which has the greatest quotient?
15 ÷ 15
0 ÷ 10
6 ÷ 1
8 ÷ 1
Answer: 8 ÷ 1

Explanation:
Check all the quotient
15 ÷ 15 = 1
0 ÷ 10 = 0
6 ÷ 1 = 6
8 ÷ 1 = 8
Thus the correct answer is option D.

4.8 Practice Division Strategies

Use any Strategy to find the quotient
Question 50.
16 ÷ 4 = _____
Answer: 4

Explanation:
Divide the two numbers 4 and 16.
16/4 = 4
Thus the quotient is 4.

Question 51.
72 ÷ 9 = ____
Answer: 8

Explanation:
Divide the two numbers 9 and 72.
72/9 = 8
Thus the quotient is 8.

Question 52.
20 ÷ 10 = _____
Answer: 2

Explanation:
Divide the two numbers 20 and 10.
20/10 = 2
Thus the quotient is 2.

Question 53.
Divide 18 by 6.
Answer: 3

Explanation:
Divide the two numbers 18 and 6.
18/6 = 3
Thus the quotient is 3.

Question 54.
Divide 49 by 7.
Answer: 7

Explanation:
Divide the two numbers 49 and 7.
49/7 = 7
Thus the quotient is 7.

Question 55.
Divide 30 by 6.
Answer: 5

Explanation:
Divide the two numbers 30 and 6.
30/6 = 5
Thus the quotient is 5.

4.9 Problem Solving: Division

Question 56.
Modeling Real Life
A group of 13 servicemen and 11 servicewomen are being honored at an event. They stand in 3 equal rows. How many servicemen and servicewomen are in each row?

Answer: 9

Explanation:
Given,
A group of 13 servicemen and 11 servicewomen are being honored at an event.
13 + 14 = 27
They stand in 3 equal rows.
27/3 = 9
Thus there are 9 servicemen and servicewomen in each row.

Division Facts and Strategies Cumulative Practice

Question 1.
Which expression is the same as 6 × 3?
A. 3 × 6
B. 3 + 3 + 3 + 3 + 3 + 3
C. 6 + 6 + 6
D. 6 × 6 × 6
Answer: A. 3 × 6

Explanation:
Given the expression 6 × 3
By using the multiplication equation
we can say that 3 × 6 is the same as 6 × 3
Thus the correct answer is option A.

Question 2.
Use the clues to find the number.
• The number is more than 10.
• The number is less than 20.
• When the number is divided by 3, the quotient is even.
• When the number is divided by 4, the quotient is odd.
What is the number?
A. 15
B. 12
C. 24
D. 16
Answer: B. 12

Explanation:
Let the number be 12
12 ÷ 3 = 4 (even)
12 ÷ 4 = 3 (odd)
Thus the correct answer is option B.

Question 3.
Which expression is equal to 6 × 7?
A. (7 × 8) – 2
B. (5 × 7) + (1 × 7)
C. (5 × 1) + (5 × 2)
D. (5 × 1) × 7
Answer: B. (5 × 7) + (1 × 7)

Explanation:
A. (7 × 8) – 2
56 – 2 = 54
B. (5 × 7) + (1 × 7)
35 + 7 = 42
C. (5 × 1) + (5 × 2)
5 + 10 = 15
D. (5 × 1) × 7
5 × 7 = 35
6 × 7 = 42
Thus the correct answer is option B.

Question 4.
Which number makes the statement true?

A. 4
B. 8
C. 16
D. 2
Answer: A. 4

Explanation:
2 × 4 = x × 2
8 = 2x
x = 8/2
x = 4
Thus the correct answer is option A.

Question 5.
Which equation is true?

Answer: C

Explanation:
A. (5 × 4) × 1 = (5 × 4) + 1
20 ≠ 21
B. (5 × 4) + 1 = (5 × 4) × 1
21 ≠ 20
C. (5 × 4) × 1 = (5 × 4) × 1
20 = 20
D. (5 × 4) × 1 = 5 + (4 × 1)
20 ≠ 9
Thus the correct answer is option C.

Question 6.
You earn 10 points for each level you complete in a video game. When you have to restart a level, you lose 2 points. You complete 9 levels but have to restart 6 levels. How many points do you have?

A. 78 points
B. 102 points
C. 90 points
D. 42 points
Answer: 78 points

Explanation:
Given,
You earn 10 points for each level you complete in a video game.
When you have to restart a level, you lose 2 points.
You complete 9 levels but have to restart 6 levels.
9 × 10 = 90 points
6 × 2 = 12 points
90 – 12 = 78 points
Thus the correct answer is option A.

Question 7.
The table shows the numbers of items at the finish line of a race.

Part A How many medals are there?

Answer:
Medals:
Number of packages = 7
Number in each package = 9
7 × 9 = 63 medals

PartB Sixty students are running in the race. Is there enough of each item for all of the students? Explain.
Answer:
Given,
Sixty students are running in the race.
Water bottles:
Number of packages = 9
Number in each package = 8
9 × 8 = 72
Medals:
Number of packages = 7
Number in each package = 9
7 × 9 = 63 medals
Bananas:
Number of packages = 9
Number in each package = 6
9 × 6 = 54
Thus there are not enough bananas for all 60 students.

Question 8.
Which numbers are multiples of 2, 5, and 10?

Answer: 20

Explanation:
The fact family for 2, 5 and 10.
2 × 10 = 20
Thus the correct answer is option A.

Question 9.
Newton and Descartes share 18 toys equally. Which equation shows how many toys each has?
A. 18 ÷ 2 = 9
B. 18 – 2 = 16
C. 18 × 2 = 36
D. 18 ÷ 1 = 18
Answer: 18 ÷ 2 = 9

Explanation:
Given,
Newton and Descartes share 18 toys equally.
18/2 = 9
Thus the correct answer is option A.

Question 10.
Which multiplication fact can Newton use to check his answer?
72 ÷ 8 = 9

Answer: 9 × 8

Explanation:
72 ÷ 8 = 9
The multiplication fact for 9, 8 and 72 is
9 × 8 = 72
Thus the correct answer is option D.

Question 11.
Thirty dollars is divided evenly among 6 children. How much money (in dollars) does each child receive?

Answer:
Given,
Thirty dollars is divided evenly among 6 children
30/6 = 5
Thus each child receives 5 dollars.

Question 12.
Which expressions have a product of 16?

Answer: A. 4 × 4

Explanation:
The product of 16 is 4 × 4.
Thus the correct answer is option A.

Question 13.
Which equation shows the Multiplication Property of Zero?
A. 8 + 0 = 8
B. 8  – 0 = 8
C. 8 × 1 = 8
D. 8 × 0 = 0
Answer: D. 8 × 0 = 0

Explanation:
Any number multiplied by 0 is always 0.|
8 × 0 = 0
Thus the correct answer is option D.

Question 14.
One ticket to an amusement park costs $8. How much does it cost for a family of 4?


Answer: A. $32

Explanation:
Given,
One ticket to an amusement park costs $8.
8 × 4 = $32
Thus the correct answer is option A.

Question 15.
Which expression is represented by this number line?

A. 21 + 3
B. 3 × 7
C. 21 – 3
D. 7 + 3
Answer: B. 3 × 7

Explanation:
The count starts at 0.
It takes 3 jumps of 7.
3 × 7 = 21
Thus the correct answer is option B.

Question 16.
Which equations are in the fact family for 2, 10, and 20?

Answer: A, B, D, E

Explanation:
The fact family for 2, 10, 20 is:
2 × 10 = 20
10 × 2 = 20
20 ÷ 2 = 10
20 ÷ 10 = 2
Thus the correct answer is option A, B, D, E.

Division Facts and Strategies STEAM Performance Task

Dogs grow just like humans. They start as puppies, become adults, and then enter old age. But dogs age faster than humans. In general, to find the age of a small dog in dog years, multiply its age in human years by 5. To find the age of a large dog in dog years, multiply its age in human years by 7.

Question 1.
A small dog and a large dog are both 9 years old in human years. How old is each dog in dog years?
Answer:
Given,
A small dog and a large dog are both 9 years old in human years.
To find the age of a small dog in dog years, multiply its age in human years by 5.
5 × 9 = 45 years
Thus the age of a small dog is 45 years
To find the age of a large dog in dog years, multiply its age in human years by 7.
9 × 7 = 63 years
Thus the age of a large dog is 63 years.

Question 2.
The table shows the usual life spans of 6 dog breeds in dog years. Find each life span in human years. Organize the data in a bar graph.


Answer:

Question 3.
Write and answer a question about your graph.
Answer:
Draw the graph for the above table.

Question 4.
Cats also age faster than humans. The table shows the age of a cat for each human year.

a. A cat is 6 years old in human years. If the pattern in the table continues, how old is the cat in cat years?

Answer:
Given that,
A cat is 6 years old in human years.
By using the above table we can find the age of the cat in cat years.
6 years – 40 years

b. A cat is 10 years old in human years. How old is the cat in cat years?

Answer:
Given that,
A cat is 10 years old in human years.
By using the above table we can find the age of the cat in cat years.
1 year (human) = 4 years of cat
10 years = 56 years
Thus the age of cat in cat years is 56 years.

c. A small dog, a large dog, and a cat are each 6 years old (in human years). Order the animals by their ages (in animal years) from least to greatest.

Answer:
A small dog, a large dog, and a cat are each 6 years old (in human years).
Small dog in dog years, multiply its age in human years by 5.
6 × 5 = 30 years
To find the age of a large dog in dog years, multiply its age in human years by 7.
7 × 7 = 49 years
A cat is 6 years old in human years.
6 years – 40 years
Now arrange them from least to the greatest.
small dog, cat, and a large dog.

Question 5.
Use the Internet or another resource to answer each question.
a. What is another dog breed that is not listed in the table?

Answer: Bull Dog

b. About how long, how tall, and how heavy is one of these dogs?
Length: _____ inches
Height: _____ inches
Weight: ______ pounds

Answer:
The length, height, and weight of the bulldog is given below
length – 12 to 15 inches
height – 12 to 15 inches
weight – 40 to 43 pounds

c. What is one interesting fact about this dog breed?

Answer:
The interesting fact about bulldog is
1. These are independent
2. The dogs were bred for their wrinkles.

d. About how long would you expect this breed to live?
Answer: The life span of the bulldog is 8 to 10 years.

Conclusion:
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Big Ideas Math Answers Grade 3 Chapter 3 More Multiplication Facts and Strategies: See more ideas on multiplication in Big Ideas Math Book 3rd Grade Answer Key Chapter 3 More Multiplication Facts and Strategies. The students of the 3rd class can get the solutions for all the questions in different methods from Big Ideas Math Answers Chapter 3 More Multiplication Facts and Strategies. We have provided the solutions for all the questions in pdf format. Hence we suggest you download BIM 3rd Grade Answer Key Chapter 3 More Multiplication Facts and Strategies for free.

Big Ideas Math Book 3rd Grade Answer Key Chapter 3 More Multiplication Facts and Strategies

BIM Answer Key for Grade 3 Chapter 3 More Multiplication Facts and Strategies pdf links are available here. The topics covered in More Multiplication Facts and Strategies are multiply by 3, multiply by 4, multiply by 6, multiply by 7,  multiply by 8, multiply by 9. In addition to the exercise problems, you can also get the solutions for homework and practice problems. Tap the links to check out the solutions to all the questions from the below section.

Lesson 1 – Multiply by 3

• Lesson 3.1 Multiply by 3
• Multiply by 3 Homework & Practice 3.1

Lesson 2 Multiply by 4

• Lesson 3.2 Multiply by 4
• Multiply by 4 Homework & Practice 3.2

Lesson 3 Multiply by 6

• Lesson 3.3 Multiply by 6
• Multiply by 6 Homework & Practice 3.3

Lesson 4 Multiply by 7

• Lesson 3.4 Multiply by 7
• Multiply by 7 Homework & Practice 3.4

Lesson 5 Multiply by 8

• Lesson 3.5 Multiply by 8
• Multiply by 8 Homework & Practice 3.5

Lesson 6 Multiply by 9

• Lesson 3.6 Multiply by 9
• Multiply by 9 Homework & Practice 3.6

Lesson 7 Practice Multiplication Strategies

• Lesson 3.7 Practice Multiplication Strategies
• Practice Multiplication Strategies Homework & Practice 1.1

Lesson 8 Multiply Three Factors

• Lesson 3.8 Multiply Three Factors
• Multiply Three Factors Homework & Practice 3.8

Lesson 9 More Problem Solving: Multiplication

• Lesson 3.9 More Problem Solving: Multiplication
• More Problem Solving: Multiplication Homework & Practice 3.9

Performance Task

• More Multiplication Facts and Strategies Performance Task
• More Multiplication Facts and Strategies Activity
• More Multiplication Facts and Strategies Chapter Practice

Lesson 3.1 Multiply by 3

Explore and Grow

Use the number line to find the product.
4 × 3 = _____

Answer: 12

Repeated Reasoning
Explain how you can use the number line to find products greater than 20. Complete the table

Answer:

Think and Grow: Multiply by 3

Example
Find 5 × 3.

Answer:
Distribute 3 to 2 and 1.
5 × 3 = 5 × (2 + 1)
5 × 3 = (5 × 2) + (5 × 1)
5 × 3 = 10 + 5
5 × 3 = 15

Show and Grow

Find the product
Question 1.
6 × 3

Answer:
Distribute 3 to 2 and 1.
6 × 3 = 6 × (2 + 1)
6 × 3 = (6 × 2) + (6 × 1)
6 × 3 = 12 + 6
6 × 3 = 18

Question 2.
3 × 4

Answer:
Distribute 3 to 2 and 1.
3 × 4 = (2 + 1) × 4
3 × 4 = (2 × 4) + (1 × 4)
3 × 4 = 8 + 4
3 × 4 = 12

Question 3.
2 × 3

Answer:
Distribute 3 to 2 and 1.
2 × 3 = 2 × (2 + 1)
2 × 3 = (2 × 2) + (2 × 1)
2 × 3 = 4 + 2
2 × 3 = 6

Question 4.

Answer:
Distribute 3 to 2 and 1.
3 × 7 = (2 + 1) × 7
3 × 7 = (2 × 7) + (1 × 7)
3 × 7 = 14 + 7
3 × 7 = 21

Question 5.
3 × 8 = ____
Answer:
Distribute 3 to 2 and 1.
3 × 8 = (2 + 1) × 8
3 × 8 = (2 × 8) + (1 × 8)
3 × 8 = 16 + 8
3 × 8 = 24

Question 6.
3 × 1 = ____
Answer:
Distribute 3 to 2 and 1.
3 × 1 = (2 + 1) × 1
3 × 1 = (2 × 1) + (1 × 1)
3 × 1 = 2 + 1
3 × 1 = 3

Question 7.
3 × 3 = _____
Answer:
Distribute 3 to 2 and 1.
3 × 3 = (2 + 1) × 3
3 × 3 = (2 × 3) + (1 × 3)
3 × 3 = 6 + 3
3 × 3 = 9

Question 8.
3 × 5 = _____
Answer:
Distribute 3 to 2 and 1.
3 × 5 = (2 + 1) × 5
3 × 5 = (2 × 5) + (1 × 5)
3 × 5 = 10 + 5
3 × 5 = 15

Question 9.

Answer:
Multiply the two numbers 3 and 6.
3 × 6 = 18

Question 10.

Answer:
Multiply the two numbers 3 and 10.
Multiply 3 by 0 and 3 by 1
10 × 3 = 30

Question 11.

Answer:
Multiply the two numbers 3 and 4.
4 × 3 = 12

Question 12.

Answer:
Multiply the two numbers 3 and 9.
3 × 9 =27

Compare
Question 13.

Answer: >

Explanation:
8 × 3 = 24
3 × 6 = 18
24 is greater than 18
Thus 8 × 3 > 3 × 6

Question 14.

Answer: <

Explanation:
3 × 1 = 3
3 × 10 = 30
3 is less than 30.
3 × 1 < 3 × 10

Question 15.

Answer: =

Explanation:
Any number multiplied by 0 will be always 0.
3 × 0 = 0
0 × 3 = 0
Thus 3 × 0 = 0 × 3

Question 16.
A baseball game has 9 innings. Each team gets 3 outs every inning. How many outs does each team get in one game?
Answer:
Given that,
A baseball game has 9 innings. Each team gets 3 outs every inning.
9 × 3 = 27
Therefore each team gets 27 outs in one game.

Question 17.
YOU BE THE TEACHER
Your friend says 23 is a multiple of 3 because there is a 3 in the ones place. Is your friend correct? Explain.
Answer:
Given,
Your friend says 23 is a multiple of 3 because there is a 3 in the ones place.
No, my friend is not correct. Because 23 is a prime number it is not a multiple of 3.

Think and Grow: Modeling Real Life

Ten people want toride a camel. There are 3 camels. Twopeople can ride on each camel. Are there enough camels for all of the people to ride at the same time?

Multiplication equation:
There _____ enough camels for all of the people.

Answer:
Given,
Ten people want to ride a camel. There are 3 camels. Two people can ride on each camel.
3 × 2 = 6
There are not enough camels for all the 10 people.

Show and Grow

Question 18.
You want to give each of your 10 friends a sticker. You buy 4 sheets. Each sheet has 3 stickers. Do you have enough stickers?
Answer:
Given,
You want to give each of your 10 friends a sticker. You buy 4 sheets. Each sheet has 3 stickers.
1 sheet – 3 stickers
4 sheets – 4 × 3 stickers = 12 stickers
12 – 10 = 2 stickers
Yes, I have enough stickers.

Question 19.
DIG DEEPER!
You buy 2 heads of cauliflower and 5 ears of corn. How much money do you spend?

You buy 3 heads of broccoli and 1 head of cauliflower.How much money do you spend?

Answer:
The cost of 1 Broccoli is $3
The cost of 1 Cauliflower is $3
3 broccoli = 3 × $3 = $9
1 cauliflower = 1 × $3 = $3
9 + 3 = $12
Therefore I spent $12.

Multiply by 3 Homework & Practice 3.1

Find the product
Question 1.
3 × 3

Answer:
Distribute 3 to 2 and 1.
3 × 3 = 3 × (2 + 1)
3 × 3 = (3 × 2) + (3 × 1)
3 × 3 = 6 + 3
3 × 3 = 9

Question 2.
3 × 9

Answer:
Distribute 3 to 2 and 1.
3 × 9 = (2 + 1) × 9
3 × 9 = (2 × 9) + (1 × 9)
3 × 9 = 18 + 9
3 × 9 = 27

Question 3.
3 × 2 = ___
Answer:
Distribute 3 to 2 and 1.
3 × 2 = (2 + 1) × 2
3 × 2 = (2 × 2) + (1 × 2)
3 × 2 = 4 + 2
3 × 2 = 6

Question 4.
3 × 5 = ____
Answer:
Distribute 3 to 2 and 1.
3 × 5 = (2 + 1) × 5
3 × 5 = (2 × 5) + (1 × 5)
3 × 5 = 10 + 5
3 × 5 = 15

Question 5.
7 × 3 = _____
Answer:
Distribute 3 to 2 and 1.
7 × 3 = 7 × (2 + 1)
7 × 3 = (7 × 2) + (7 × 1)
7 × 3 = 14 + 7
7 × 3 = 21

Question 6.
0 × 3 = ____
Answer:
Any number multiplied by 0 will be always 0.
0 × 3 = 0

Question 7.

Answer:
Multiply the two numbers 3 and 4.
3 × 4 = 12

Question 8.

Answer:
multiply the two numbers 3 and 10.
3 × 10 = 30

Question 9.

Answer:
Multiply the two numbers 6 and 3.
6 × 3 = 18

Question 10.

Answer:
Multiply the two numbers 3 and 1.
3 × 1 = 3

Compare
Question 11.

Answer: <

Explanation:
0 × 3 = 0
3 × 3 = 9
0 is less than 9.
0 × 3 < 3 × 3

Question 12.

Answer: >

Explanation:
8 × 3 = 24
7 × 3 = 21
24 > 21
8 × 3 > 7 × 3

Question 13.

Answer: =

Explanation:
6 × 3 = 18
18 = 18

Question 14.
A Russian guitar, called a , has 3 strings. A music teacher is replacing the strings on 5 balalaikas. How many strings does the teacher need?

Answer:
Given that,
A Russian guitar, called a, has 3 strings. A music teacher is replacing the strings on 5 balalaikas.
3 × 5 = 15
Thus the teacher needs 15 strings.

Question 15.
Number Sense
Circle the multiples of 3.

Answer: The multiples of 3 are 12, 15, 21.

Question 16.
Modeling Real Life
You need 24 tennis balls. You buy 6 packs of 3 tennis balls. Do you have enough tennis balls?

Answer:
Given,
You need 24 tennis balls. You buy 6 packs of 3 tennis balls.
6 × 3 = 18
24 – 18 = 6 tennis balls
Thus I don’t have enough tennis balls.

Question 17.
DIG DEEPER!
Newton buys 3 packs of plates and 3 packs of cups. How much money does he spend?

Answer:
Given,
Newton buys 3 packs of plates and 3 packs of cups.
Cost of 1 plate = $4
Cost of 1 cup = $2
3 plates = 3 × $4 = $12
3 cups = 3 × $2 = $6
12 + 6 = 18
Thus Newton spend $18.

Review & Refresh

Question 18.
Which shapes show thirds?

Answer: The 2nd, 3rd, and 4th figures show thirds. Because the figures are divided into 3 parts.

Lesson 3.2 Multiply by 4

Explore and Grow

Use the tape diagram to find the product
3 × 4 = _____

Answer:

Repeated Reasoning
Explain how you can use a tape diagram to find the missing products in the table. Complete the table.

Answer:

Think and Grow: Multiply by 4

Example
Find 5 × 4.

Answer:
Rewrite 4 as 2 + 2.
5 × 4 = 5 × (2 + 2)
5 × 4 = (5 × 2) + (5 × 2)
5 × 4 = 10 + 10
5 × 4 = 20

Show and Grow

Find the product
Question 1.
6 × 4

Answer:
Rewrite 4 as 2 + 2.
6 × 4 = 6 × (2 + 2)
6 × 4 = (6 × 2) + (6 × 2)
6 × 4 = 12 + 12
6 × 4 = 24

Question 2.
4 × 8

Answer:
Rewrite 4 as 2 + 2.
4 × 8 = (2 + 2) × 8
4 × 8 = (2 × 8) + (2 × 8)
4 × 8 = 16 + 16
4 × 8 = 32

Apply and Grow:Practice

Find the product
Question 3.
4 × 4

Answer:
Rewrite 4 as 2 + 2.
4 × 4 = 4 × (2 + 2)
4 × 4 = (4 × 2) + (4 × 2)
4 × 4 = 8 + 8
4 × 4 = 16

Question 4.
4 × 2

Answer:
Rewrite 4 as 2 + 2.
4 × 2 = (2 + 2) × 2
4 × 2 = (2 × 2) + (2 × 2)
4 × 2 = 4 + 4
4 × 2 = 8

Question 5.
4 × 5 = ___
Answer:
Rewrite 4 as 2 + 2.
4 × 5 = (2 + 2) × 5
4 × 5 = (2 × 5) + (2 × 5)
4 × 5 = 10 + 10
4 × 5 = 20

Question 6.
4 × 7 = ___
Answer:
Rewrite 4 as 2 + 2.
4 × 7 = (2 + 2) × 7
4 × 7 = (2 × 7) + (2 × 7)
4 × 7 =  14 + 14
4 × 7 = 28

Question 7.
4 × 6 = ____
Answer:
Rewrite 4 as 2 + 2.
4 × 6 = (2 + 2) × 6
4 × 6 = (2 × 6) + (2 × 6)
4 × 6 = 12 + 12
4 × 6 = 24

Question 8.
4 × 1 = ____
Answer:
Rewrite 4 as 2 + 2.
4 × 1 = (2 + 2) × 1
4 × 1 = (2 × 1) + (2 × 1)
4 × 1 = 2 + 2
4 × 1 = 4

Question 9.

Answer:
Rewrite 4 as 2 + 2.
10 × 4 = 10 × (2 + 2)
10 × 4 = (10 × 2) + (10 × 2)
10 × 4 = 20 + 20
10 × 4 = 40

Question 10.

Answer:
Rewrite 4 as 2 + 2.
3 × 4 = 3 × (2 + 2)
3 × 4 = (3 × 2) + (3 × 2)
3 × 4 = 6 + 6
3 × 4 = 12

Question 11.

Answer:
Rewrite 4 as 2 + 2.
8 × 4 = 8 × (2 + 2)
8 × 4 = (8 × 2) + (8 × 2)
8 × 4 = 16 + 16
8 × 4 = 32

Question 12.

Answer:
Rewrite 4 as 2 + 2.
4 × 9 = (2 + 2) × 9
4 × 9 = (2 × 9) + (2 × 9)
4 × 9 = 18 + 18
4 × 9 = 36

Find the missing factor.
Question 13.
4 × ___ = 0
Answer: 0

Explanation:
Let the missing factor be x.
4 × x = 0
x = 0/4
x = 0
Thus the missing factor is 0.

Question 14.
___ × 4 = 40
Answer: 10

Explanation:
Let the missing factor be y.
y × 4 = 40
y = 40/4
y = 10
Thus the missing factor is 10.

Question 15.
4 = ____ × 4
Answer:
Let the missing factor be t.
4 = t × 4
t = 4/4
t = 1
Thus the missing factor is 1.

Question 16.
Number Sense
You exchange some dollar bills for quarters. How many quarters might you receive?

Answer:
Convert from dollars to quarters
1 dollar = 4 quarters
Multiples of 4 are 12, 16, 24, 36, 40.

Question 17.
Explain how you can use 2 × 3 to find 4 × 3.
Answer:
Rewrite 4 as 2 + 2.
4 × 3 = (2 + 2) × 3
4 × 3 = (2 × 3) + (2 × 3)
4 × 3 = 6 + 6
4 × 3 = 12

Think and Grow: Modeling Real Life

The graph shows the number of cars scheduled to get a new set of tires installed. How many new tires are installed on the busiest day?

What is the busiest day?
Multiplication equation:
______ new tires are installed on the busiest day.

Answer:
Monday = 6 × 1 = 6 new tires
Tuesday = 7 × 1 = 7 new tires
Wednesday = 3 × 1 = 3 new tires
Thursday = 8 × 1 = 8 new tires
Friday = 4 × 1 = 4 new tires
8 new tires are installed on the busiest day.

Show and Grow

Question 18.
Use the graph above. How many new tires are installed on the least busy day?
Answer:
Monday = 6 × 1 = 6 new tires
Tuesday = 7 × 1 = 7 new tires
Wednesday = 3 × 1 = 3 new tires
Thursday = 8 × 1 = 8 new tires
Friday = 4 × 1 = 4 new tires
3 new tires are installed on the least busy day.

Question 19.
DIGD EEPER!
Descartes is packing bags for party favors. Each bag needs 1 container of bubbles, 5 stickers, and 3 balloons. How many of each item does Descartes need to make 4 bags?

Answer:
Given that,
Descartes is packing bags for party favors.
Each bag needs 1 container of bubbles, 5 stickers, and 3 balloons.
4 bags = 1 bubble × 4 + 5 stickers × 4 + 3 balloons × 4
4 bags = 4 + 20 + 12 = 36
Thus Descartes need 4 bubbles, 20 stickers and 12 balloons.

Multiply by 4 Homework & Practice 3.2

Fing the product
Question 1.
3 × 4

Answer:
Rewrite 4 as 2 + 2.
3 × 4 = 3 × (2 + 2)
3 × 4 = (3 × 2) + (3 × 2)
3 × 4 = 6 + 6
3 × 4 = 12

Question 2.
4 × 9

Answer:
Rewrite 4 as 2 + 2.
4 × 9 = (2 + 2) × 9
4 × 9 = (2 × 9) + (2 × 9)
4 × 9 = 18 + 18
4 × 9 = 36

Question 3.
8 × 4 = ___
Answer:

Rewrite 4 as 2 + 2.
8 × 4 = 8 × (2 + 2)
8 × 4 = (8 × 2) + (8 × 2)
8 × 4 = 16 + 16
8 × 4 = 32

Question 4.
4 × 4 = ____
Answer:

Rewrite 4 as 2 + 2.
4 × 4 = 4 × (2 + 2)
4 × 4 = (4 × 2) + (4 × 2)
4 × 4 = 8 + 8
4 × 4 = 16

Question 5.
10 × 4 = _____
Answer:
Rewrite 4 as 2 + 2.
10 × 4 = 10 × (2 + 2)
10 × 4 = (10 × 2) + (10 × 2)
10 × 4 = 20 + 20
10 × 4 = 40

Question 6.
4 × 6 = _____
Answer:
Rewrite 4 as 2 + 2.
4 × 6 = (2 + 2) × 6
4 × 6 = (2 × 6) + (2 × 6)
4 × 6 = 12 + 12
4 × 6 = 24

Question 7.

Answer:
Rewrite 4 as 2 + 2.
4 × 5 = (2 + 2) × 5
4 × 5 = (2 × 5) + (2 × 5)
4 × 5 = 10 + 10
4 × 5 = 20

Question 8.

Answer:
Any number multiplied by 0 is always 0.
0 × 4 = 0

Question 9.

Answer:
Any number multiplied by 1 is always the same number.
1 × 4 = 4

Question 10.

Answer:
Rewrite 4 as 2 + 2.
2 × 4 = 2 × (2 + 2)
2 × 4 = (2 × 2) + (2 × 2)
2 × 4 = 4 + 4
2 × 4 = 8

Find the missing factor
Question 11.
10 × ____ = 40
Answer: 4

Explanation:
Let the missing factor be p.
10 × p = 40
p = 40/10 = 4
p = 4
Therefore the missing factor is 4.

Question 12.
____ × 1 = 4
Answer: 4

Explanation:
Let the missing factor be q.
q × 1 = 4
q = 4/1
q = 4
Therefore the missing factor is 4.

Question 13.
8 = ____ × 4
Answer: 2

Explanation:
Let the missing factor be r.
8 = r × 4
r = 8/4
r = 2
Therefore the missing factor is 2.

Question 14.
A string quartet has 4 musicians. Each musician’s instrument has 4 strings. How many total strings are there in a string quartet?
Answer: 16

Explanation:
Given that,
A string quartet has 4 musicians. Each musician’s instrument has 4 strings.
1 musician = 4 strings
4 musicians = 4 × 4 strings = 16 strings
Therefore there are 16 strings in a string quartet.

Question 15.
Which One Doesn’tBelong?
Which one does belong with the other three?

Answer:
(2 × 3) + (2 × 3) doesn’t belong to the other three expressions.
4 × 6, 6 × 4, (2 × 6) + (2 × 6) belong to other expressions. Because
4 × 6 = 24
6 × 4 = 24
(2 × 6) + (2 × 6) = 12 + 12 = 24

Question 16.
Modeling Real Life
The tally chart shows the number of tables a carpenter makes each day. Each table has 4 legs. How many legs does the carpenter make on the busiest day?

Answer:
Given,
The tally chart shows the number of tables a carpenter makes each day. Each table has 4 legs.
Monday – 5 + 5 = 10
Tuesday – 5 + 3 = 8
Wednesday – 4
Monday – 10 × 4 = 40
Tuesday – 8  × 4 = 32
Wednesday – 4 × 4 = 16
Thus the carpenter makes 40 legs on the busiest day.

Question 17.
DIG DEEPER!
Newton is packing lunches. Each lunch needs 1 sandwich, 2 celery sticks, 3 carrot sticks, and 4 strawberries. How many of each item does Newton need to make 4 lunches?
Answer:
Given,
Newton is packing lunches. Each lunch needs 1 sandwich, 2 celery sticks, 3 carrot sticks, and 4 strawberries.
1 lunch – 1 sandwich, 2 celery sticks, 3 carrot sticks, 4 strawberries
4 lunches – 1 sandwich × 4, 2 celery sticks × 4, 3 carrot sticks × 4, 4 strawberries × 4 = 4 + 8 + 12 + 16 = 40
Thus newton needs 4 sandwiches, 8 celery sticks, 12 carrot sticks, and 16 strawberries to make 4 lunches.

Review & Refresh

Write the number in expanded form and word form
Question 18.
837
____ + ____ + _____
_______________

Answer:
The expanded form of 837 is 800 + 30 + 7
The word form of 837 is Eight Hundred and Third Seven.

Question 19.
954
____ + ____ + ____
_______________

Answer:
The expanded form of 954 is 900 + 50 + 4
The word form of 954 is Nine Hundred and Fifty-Four.

Lesson 3.3 Multiply by 6

Explore and Grow
Question 1.
Use equal groups to find the product. Draw your model.
4 × 6 = _____
Answer:

6 + 6 + 6 + 6 = 24

Repeated Reasoning
Explain how you can use equal groups to multiply. Complete the table.

Answer:

Think and Grow: Multiply by 6

Example
Find 5 × 6.

Answer:
Rewrite 6 as 5 + 1.
5 × 6 = 5 × (5 + 1)
5 × 6 = (5 × 5) + (5 × 1)
5 × 6 = 25 + 5
5 × 6 = 30

Show and Grow

Find the product
Question 1.
3 × 6

Answer:
Distribute 6 as 3 + 3.
3 × 6 = 3 × (3 + 3)
3 × 6 = (3 × 3) + (3 × 3)
3 × 6 = 9 + 9
3 × 6 = 18

Question 2.
6 × 5

Answer:
Distribute 6 as 3 + 3.
6 × 5 = (3 + 3) × 5
6 × 5 = (3 × 5) + (3 × 5)
6 × 5 = 15 + 15
6 × 5 = 30

Apply and Grow: Practice

Find the product
Question 3.
6 × 7

Answer:

Distribute 6 as 3 + 3.
6 × 7 = (3 + 3) × 7
6 × 7 = (3 × 7) + (3 × 7)
6 × 7 = 21 + 21
6 × 7 = 42

Question 4.
4 × 6

Answer:
Distribute 6 as 3 + 3.
4 × 6 = 4 × (3 + 3)
4 × 6 = (4 × 3) + (4 × 3)
4 × 6 = 12 + 12
4 × 6 = 24

Question 5.
8 × 6 = ___
Answer:
Distribute 6 as 3 + 3.
8 × 6 = 8 × (3 + 3)
8 × 6 = (8 × 3) + (8 × 3)
8 × 6 = 24 + 24
8 × 6 = 48

Question 6.
7 × 6 = ____
Answer:
Distribute 6 as 3 + 3.
7 × 6 = 7 × (3 + 3)
7 × 6 = (7 × 3) + (7 × 3)
7 × 6 = 21 + 21
7 × 6 = 42

Question 7.
6 × 0 = ___
Answer: 0
Any number multiplied by 0 will be always 0.
6 × 0 = 0

Question 8.
6 × 4 = ____
Answer:
Distribute 6 as 3 + 3.
6 × 4 = (3 + 3) × 4
6 × 4 = (3 × 4) + (3 × 4)
6 × 4 = 12 + 12
6 × 4 = 24

Question 9.

Answer:
Distribute 6 as 3 + 3.
6 × 6 = 6 × (3 + 3)
6 × 6 = (6 × 3) + (6 × 3)
6 × 6 = 18 + 18
6 × 6 = 36

Question 10.

Answer: 6
Distribute 6 as 3 + 3.
6 × 1 = (3 + 3) × 1
6 × 1 = (3 × 1) + (3 × 1)
6 × 1 = 3 + 3
6 × 1 = 6

Question 11.

Answer: 12

Distribute 6 as 3 + 3.
2 × 6 = 2 × (3 + 3)
2 × 6 = (2 × 3) + (2 × 3)
2 × 6 = 6 + 6
2 × 6 = 12

Question 12.

Answer: 54
Distribute 6 as 3 + 3.
9 × 6 = 9 × (3 + 3)
9 × 6 = (9 × 3) + (9 × 3)
9 × 6 = 27 + 27
9 × 6 = 54

Compare
Question 13.

Answer: =

Explanation:
8 × 6 = 48
48 = 48

Question 14.

Answer: <

Explanation:
6 × 0 = 0
10 × 6 = 60
6 × 0 < 10 × 6

Question 15.

Answer: <

Explanation:
6 × 1 = 6
6 × 3 = 18
6 is less than 18.
6 × 1 < 6 × 3

Question 16.
There are 9 volleyball teams in a tournament. There are 6 players on each team. How many volleyball players are in the tournament?
Answer: 54

Explanation:
Given,
There are 9 volleyball teams in a tournament. There are 6 players on each team.
9 × 6 = 54
Thus there are 54 volleyball players in the tournament.

Question 17.
YOU BE THE TEACHER
Your friend says that all multiples of 3 are also multiples of 6. Is your friend correct? Explain.
Answer: No. Multiples of 3 are not the multiples of 6.

Think and Grow: Modeling Real Life

You have 5 apples. You cut each apple into8 slices. You have6 oranges and cut each orange into4 slices. Do you have more apple slices or orange slices?
Multiplication equations:


You have more _____ slices.

Answer:
Given,
You have 5 apples. You cut each apple into 8 slices. You have 6 oranges and cut each orange into 4 slices.
1 apple = 8 slices
5 apples = 5 × 8 slices = 40 slices
1 orange = 4 slices
6 oranges = 6 × 4 slices = 24 slices
40 slices is greater than 24 slices.
Therefore you have more apple slices.

Show and Grow

Question 18.
Your friend makes 6 bracelets each day for 7 days. Your cousin makes 10 bracelets each day for 3 days. Who makes fewer bracelets?

Answer:
Given,
Your friend makes 6 bracelets each day for 7 days.
Your cousin makes 10 bracelets each day for 3 days.
1 day = 6 bracelets
7 days = 7 × 6 bracelets = 42 bracelets
1 day = 10 bracelets
3 days = 3 × 10 bracelets = 30 bracelets
By this we can say that my cousin makes fewer bracelets.

Question 19.
You draw 6 octagons. How many sides do you draw?
Answer: A octagon contains 8 sides. Thus I need to draw 48 sides for all 6 octagon.

Question 20.
You draw 9 hexagons. How many sides do you draw?
Answer: A hexagon contains 6 sides. Thus I need to draw 54 sides for all 9 hexagons.

Multiply by 6 Homework & Practice 3.3

Find the product
Question 1.
2 × 6

Answer:
Distribute 6 as 3 + 3.
2 × 6 = 2 × (3 + 3)
2 × 6 = (2 × 3) + (2 × 3)
2 × 6 = 6 + 6
2 × 6 = 12

Question 2.
6 × 6

Answer:
Distribute 6 as 3 + 3.
6 × 6 = (3 + 3) × 6
6 × 6 = (3 × 6) + (3 × 6)
6 × 6 = 18 + 18
6 × 6 = 36

Question 3.
9 × 6 = ____
Answer:
Distribute 6 as 3 + 3.
9 × 6 = 9 × (3 + 3)
9 × 6 = (9 × 3) + (9 × 3)
9 × 6 = 27 + 27
9 × 6 = 54

Question 4.
5 × 6 = _____
Answer:
Distribute 6 as 3 + 3.
5 × 6 = 5 × (3 + 3)
5 × 6 = (5 × 3) + (5 × 3)
5 × 6 = 15 + 15
5 × 6 = 30

Question 5.
6 × 3 = ____
Answer:
Distribute 6 as 3 + 3.
6 × 3 = (3 + 3) × 3
6 × 3 = (3 × 3) + (3 × 3)
6 × 3 = 9 + 9
6 × 3 = 18

Question 6.
4 × 6 = ____
Answer:
Distribute 6 as 3 + 3.
4 × 6 = 4 × (3 + 3)
4 × 6 = (4 × 3) + (4 × 3)
4 × 6 = 12 + 12
4 × 6 = 24

Question 7.

Answer:
Distribute 6 as 3 + 3.
8 × 6 = 8 × (3 + 3)
8 × 6 = (8 × 3) + (8 × 3)
8 × 6 = 24 + 24
8 × 6 = 48

Question 8.

Answer:
Any number multiplied by 0 is always 0.
So, 6 × 0 = 0

Question 9.

Answer:
Any number multiplied by 1 is always the same number.
6 × 1 = 6

Question 10.

Answer:
Distribute 6 as 3 + 3.
10 × 6 = 10 × (3 + 3)
10 × 6 = (10 × 3) + (10 × 3)
10 × 6 = 30 + 30
10 × 6 = 60

Compare
Question 11.

Answer: <

Explanation:
4 × 6 = 24
6 × 6 = 36
24 < 36
Thus 4 × 6 < 6 × 6

Question 12.

Answer: >

Explanation:
6 × 5 = 30
4 × 5 = 20
30 > 20
Thus 6 × 5 > 4 × 5

Question 13.

Answer: =

Explanation:
6 × 7 = 42
42 = 42
Thus 42 = 6 × 7

Question 14.
There are 6 faces on a standard die. How many faces are on 5 dice?
Answer: 30 faces

Explanation:
Given that,
There are 6 faces on a standard die.
1 dice – 6 faces
5 dice – 5 × 6 faces = 30 faces
Thus 5 dice has 30 faces.

Question 15.
DIG DEEPER!
You have a muffin tin with 6 cups. You want to bake 36 muffins. How many times must you use the muffin tin?
Answer:
Given,
You have a muffin tin with 6 cups. You want to bake 36 muffins.
1 muffin tin – 6 cups
x – 36 muffins
36/6 = 6
Thus I must use 6 muffin tins.

Question 16.
Modeling Real Life
You practice the saxophone 1 hour in the morning and 2 hours at night each day. How many hours do you practice in 6 days?

Answer:
Given that,
You practice the saxophone for 1 hour in the morning and 2 hours at night each day.
1 day = 1 + 2 = 3 hours
6 days = 6 × 3 = 18 hours.
Thus you practice 18 hours in 6 days.

Question 17.
Modeling Real Life You want to make 6 pentagons using toothpicks. How many toothpicks do you need?
Answer:
We know that a pentagon contains 5 sides.
So to make the pentagon you need 5 toothpicks
6 pentagons = 6 × 5 = 30 toothpicks.
Thus you need 30 toothpicks to make 6 pentagons.

Review & Refresh

Question 18.
Find the total value.

Total value: _____
Answer:
2 dimes = $0.2
2 pennies = $0.02
1 Nickel = $0.05
1 Washington quarter = $0.25
1 cent = $0.01
Total Value = $0.2+ $0.02 + $0.05 + $0.25 + $0.01
= $0.53
Thus the total value is $0.53

Lesson 3.4 Multiply by 7

Explore and Grow
Question 1.
Use the number line to find the product
2 × 7 = ____

Answer:

Multiply 2 and 7.
7 + 7 = 14

Repeated Reasoning
Complete the table. Explain how you found the missing products.

Answer:

Think and Grow: Multiply by 7

Example
Find 3 × 7

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
3 × 7 = 3 × (5 + 2)
3 × 7 = (3 × 5) + (3 × 2)
3 × 7 = 15 + 6
3 × 7 = 21

Show and Grow

Find the product
Question 1.
4 × 7

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
4 × 7 = 4 × (5 + 2)
4 × 7 = (4 × 5) + (4 × 2)
4 × 7 = 20 + 8
4 × 7 = 28

Question 2.
7 × 9

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 9 = (5 + 2) × 9
7 × 9 = (5 × 9) + (2 × 9)
7 × 9 = 45 + 18
7 × 9 = 63

Apply and Grow: Practice

Find the product
Question 3.
7 × 7

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 7 = 7 × (5 + 2)
7 × 7 = (7 × 5) + (7 × 2)
7 × 7 = 35 + 14
7 × 7 = 49

Question 4.
7 × 6

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 6 = (5 + 2) × 6
7 × 6 = (5 × 6) + (2 × 6)
7 × 6 = 30 + 12
7 × 6 = 42

Question 5.
7 × 5 = ___
Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 5 = (5 + 2) × 5
7 × 5 = (5 × 5) + (2 × 5)
7 × 5 = 25 + 10
7 × 5 = 35

Question 6.
7 × 1 = ___
Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 1 = (5 + 2) × 1
7 × 1 = (5 × 2) + (2 × 1)
7 × 1 = 10 + 2
7 × 1 = 12

Question 7.
2 × 7 = ___
Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
2 × 7 = 2 × (5 + 2)
2 × 7 = (2 × 5) + (2 × 2)
2 × 7 = 10 + 4
2 × 7 = 14

Question 8.
3 × 7 = ____
Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
3 × 7 = 3 × (5 + 2)
3 × 7 = (3 × 5) + (3 × 2)
3 × 7 = 15 + 6
3 × 7 = 21

Question 9.

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
10 × 7 = 10 × (5 + 2)
10 × 7 = (10 × 5) + (10 × 2)
10 × 7 = 50 + 20
10 × 7 = 70

Question 10.

Answer: 0
Any number multiplied by 0 is always 0.

Question 11.

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
8 × 7 = 8 × (5 + 2)
8 × 7 = (8 × 5) + (8 × 2)
8 × 7 = 40 + 16
8 × 7 = 56

Question 12.

Answer:
Rewrite 7 as 5 + 2.
Use Distributive Property.
7 × 9 = (5 + 2) × 9
7 × 9 = (5 × 9) + (2 × 9)
7 × 9 = 45 + 18
7 × 9 = 63

Find the missing factor
Question 13.
7 × ___ = 0
Answer: 0

Explanation:
Let the missing factor be x.
7 × x = 0
x = 0/7
x = 0
Thus the missing factor is 0.

Question 14.
___ × 7 = 35
Answer: 5

Explanation:
Let the missing factor be y.
y × 7 = 35
y = 35/7
y = 5
Thus the missing factor is 5.

Question 15.
70 = ___ × 7
Answer: 10

Explanation:
Let the missing factor be z.
70 = z × 7
z = 70/7
z = 10
Thus the missing factor is 10.

Question 16.
How many days are in 4 weeks?
Answer: 28 days

Explanation:
Convert from weeks to days.
1 week – 7 days
4 weeks – 4 × 7 = 28 days
Therefore there are 28 days in 4 weeks.

Question 17.
Number Sense
How can you use the Commutative Property of Multiplication to find 7 × 3?
Answer:
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
The Commutative Property of Multiplication of 7 × 3 is 3 × 7.

Think and Grow: Modeling Real Life

A child ticket costs $7. An adult ticket costs 4 times as much as the child ticket. Descartes has $40. Can he buy an adult ticket?
Multiplication equation:
Descartes _____ buy an adult ticket.

Answer:
Given,
A child ticket costs $7.
An adult ticket costs 4 times as much as the child ticket.
4 × $7 = $28
Descartes has $40.
$40 – $28 = $12
Therefore Descartes can buy an adult ticket.

Show and Grow

Question 18.
A small painting costs $5. A large painting costs 7 times as much as the small painting. Newton has $30.Can he buy a large painting?

Answer:
Given,
A small painting costs $5.
A large painting costs 7 times as much as a small painting.
7 × $5 = $35
Newton has $30.
$30 – $35 = -$5
Thus he cannot buy a large painting.

Question 19.
DIG DEEPER!
You study your spelling words for 5 minutes twice a day. How many minutes do you spend studying your spelling words in one week?
Answer:
Given,
You study your spelling words for 5 minutes twice a day.
1 day – 2 × 5 = 10 minutes
Convert from week to days.
1 week – 7 days
7 × 10 = 70 minutes

Question 20.
DIG DEEPER!
Your dentist tells you to brush your teeth for 3 minutes three times a day. How many minutes should you spend brushing your teeth in one week?

Answer:
Given,
Your dentist tells you to brush your teeth for 3 minutes three times a day.
3 minutes – 3 × 3 = 9 minutes a day.
Convert from week to day.
1 week – 7 days
7 × 9 minutes = 63 minutes a week.

Multiply by 7 Homework & Practice 3.4

Question 1.
5 × 7 =

Answer: 35

Explanation:
Rewrite 7 as 2 + 5.
5 × 7 = 5 × (2 + 5)
5 × 7 = (5 × 2) + (5 × 5)
5 × 7 = 10 + 25
5 × 7 = 35

Question 2.

Answer: 14

Explanation:
Rewrite 7 as 2 + 5.
7 × 2 = (2 + 5) × 2
7 × 2 = (2 × 2) + (5 × 2)
7 × 2 = 4 + 10
7 × 2 = 14

Question 3.
0 × 7 = ___
Answer: 0

Explanation: Any number multiplied by 0 will be always 0.

Question 4.
7 × 7 = ____
Answer: 49

Explanation:
Rewrite 7 as 2 + 5.
7 × 7 = (2 + 5) × 7
7 × 7 = (2 × 7) + (5 × 7)
7 × 7 = 14 + 35
7 × 7 = 49

Question 5.
10 × 7 = ____
Answer: 70

Explanation:
Rewrite 7 as 2 + 5.
10 × 7 = 10 × (2 + 5)
10 × 7 = (10 × 2) + (10 × 5)
10 × 7 = 20 + 50
10 × 7 = 70

Question 6.
8 × 7 = ____
Answer: 56

Explanation:
Rewrite 7 as 2 + 5.
8 × 7 = 8 × (2 + 5)
8 × 7 = (8 × 2) + (8 × 5)
8 × 7 = 16 + 40
8 × 7 = 56

Question 7.

Answer: 7

Explanation:
Rewrite 7 as 2 + 5.
7 × 1 = (2 + 5) × 1
7 × 1 = (2 × 1) + (5 × 1)
7 × 1 = 2 + 5
7 × 1 = 7

Question 8.

Answer: 63

Explanation:
Rewrite 7 as 2 + 5.
7 × 9 = (2 + 5) × 9
7 × 9 = (2 × 9) + (5 × 9)
7 × 9 = 18 + 45
7 × 9 = 63

Question 9.

Answer: 28

Explanation:
Rewrite 7 as 2 + 5.
4 × 7 = 4 × (2 + 5)
4 × 7 = (4 × 2) + (4 × 5)
4 × 7 = 8 + 20
4 × 7 = 28

Question 10.

Answer: 21

Explanation:
Rewrite 7 as 2 + 5.
3 × 7 = 3 × (2 + 5)
3 × 7 = (3 × 2) + (3 × 5)
3 × 7 = 6 + 15
3 × 7 = 21

Find the missing factor
Question 11.
7 × ____ = 7
Answer: 1

Explanation:
Let the missing factor be x.
7 × x = 7
x = 7/7
x = 1
Thus the missing factor is 1.

Question 12.
____ × 7 = 14
Answer: 2

Explanation:
Let the missing factor be y.
y × 7 = 14
y = 14/7
y = 2
Thus the missing factor is 2.

Question 13.
56 = ____ × 7
Answer: 8

Explanation:
Let the missing factor be t.
56 = t × 7
t = 56/7
t = 8
Thus the missing factor is 8.

Question 14.
You go to school for 5 days each week. You spend 7 hours at school each day. How many hours do you spend at school in one week?
Answer: 35

Explanation:
Given that,
You go to school for 5 days each week.
You spend 7 hours at school each day.
1 day – 7 hours
5 days – x
x = 5 × 7 hours
x = 35 hours
Thus you spend 35 hours at school in one week.

Question 15.
Number Sense
Circle the multiples of 7

Answer: Multiples of 7 are 21, 35, 56, 63

Question 16.
Structure
Find in two different ways 7 × 6
Answer: The two different ways to find 7 × 6 are
Multiply the two numbers 7 and 6
7 × 6 = 42
The other way to find the product 7 × 6 is by using the distributive property.
Rewrite 6 as 3 + 3.
7 × 6 = 7 × (3 + 3)
7 × 6 = (7 × 3) + (7 × 3)
7 × 6 = 21 + 21
7 × 6 = 42

Question 17.
Modeling Real Life
A pair of regular shoes costs $9. A pair of light-up shoes costs 7 times as much as the pair of regular shoes. Newton has $60. Can he buy a pair of light-up shoes?
Answer:
Given that,
A pair of regular shoes costs $9. A pair of light-up shoes costs 7 times as much as a pair of regular shoes.
9 × 7 = $63
Newton has $60.
$60 – $63 = -$3
By this, we can say that Newton cannot buy a pair of light-up shoes.

Question 18.
DIG DEEPER!
A veterinarian tells you to feed your dog 2 cups of food twice a day. How many cups of food should you feed your dog in one week?
Answer:
Given,
A veterinarian tells you to feed your dog 2 cups of food twice a day.
First, convert from week to day.
1 week = 7 days
7 × 2 cups = 14 cups
Thus you feed 14 cups in one week.

Review & Refresh

Question 19.
What is the best estimate of the length of a thumbtack?

Answer:
By seeing the figure we can estimate the length of a thumbtack as 2 centimeters.

Question 20.
What is the best estimate of the height of a trampoline?

Answer:
By seeing the figure we can estimate the height of a trampoline as 4 centimeters.

Lesson 3.5 Multiply by 8

Explore and Grow

Use the tape diagram to find the product
3 × 8 = ____

Answer: 24

Repeated Reasoning
Explain how you can use a different model to solve. Complete the table.

Answer: The tables for multiples of 8 are given below,

Think and Grow: Multiply by 8

Example
Find 5 × 8

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
5 × 8 = 5 × (4 + 4)
5 × 8 = (5 × 4) + (5 × 4)
5 × 8 = 20 + 20
5 × 8 = 40

Show and Grow

Find the product
Question 1.
4 × 8

Answer: 32

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
4 × 8 = 4 × (4 + 4)
4 × 8 = (4 × 4) + (4 × 4)
4 × 8 = 16 + 16
4 × 8 = 32

Question 2.
8 × 7

Answer: 56

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 7 = (4 + 4) × 7
8 × 7 = (4 × 7) + (4 × 7)
8 × 7 = 28 + 28
8 × 7 = 56

Find the product
Question 3.
8 × 8

Answer: 64

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 8 = (4 + 4) × 8
8 × 8 = (4 × 8) + (4 × 8)
8 × 8 = 32 + 32
8 × 8 = 64

Question 4.
3 × 8

Answer: 24

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
3 × 8 = 3 × (4 + 4)
3 × 8 = (3 × 4) + (3 × 4)
3 × 8 = 12 + 12
3 × 8 = 24

Question 5.
8 × 2 = ___
Answer: 16

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 2 = (4 + 4) × 2
8 × 2 = (4 × 2) + (4 × 2)
8 × 2 = 8 + 8
8 × 2 = 16

Question 6.
7 × 8 = ___
Answer: 56

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
7 × 8 = 7 × (4 + 4)
7 × 8 = (7 × 4) + (7 × 4)
7 × 8 = 28 + 28
7 × 8 = 56

Question 7.
8 × 6 = ____
Answer: 48

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 6 = (4 + 4) × 6
8 × 6 = (4 × 6) + (4 × 6)
8 × 6 = 24 + 24
8 × 6 = 48

Question 8.
10 × 8 = ____
Answer: 80

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
10 × 8 = 10 × (4 + 4)
10 × 8 = (10 × 4) + (10 × 4)
10 × 8 = 40 + 40
10 × 8 = 80

Compare
Question 9.

Answer: 0

Explanation:
Any number multiplied by 0 will be 0.
0 × 8 = 0 × (4 + 4)
0 × 8 = (0 × 4) + (0 × 4)
0 × 8 = 0 + 0
0 × 8 = 0

Question 10.

Answer: 72

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 9 = (4 + 4) × 9
8 × 9 = (4 × 9) + (4 × 9)
8 × 9 = 36 + 36
8 × 9 = 72

Question 11.

Answer: 40

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 5 = (4 + 4) × 5
8 × 5 = (4 × 5) + (4 × 5)
8 × 5 = 20 + 20
8 × 5 = 40

Question 12.

Answer: 8

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
1 × 8 = 1 × (4 + 4)
1 × 8 = (1 × 4) + (1 × 4)
1 × 8 = 4 + 4
1 × 8 = 8

Compare
Question 13.

Answer: =

Explanation:
8 × 8 = 64
64 = 64
So, 8 × 8 = 64

Question 14.

Answer: <

Explanation:
Any number multiplied by 0 will be 0.
Any number multiplied by 1 will be the same number.
8 × 0 = 0
8 × 1 = 8
0 < 8
So, 8 × 0 < 8 × 1

Question 15.

Answer: >

Explanation:
8 × 6 = 48
5 × 8 = 40
48 > 40
8 × 6 > 5 × 8

Question 16.
Which One Doesn’tBelong?
Which expression does not belong with the other three?

Answer:
4 × (4 + 3) = 4 × 7 = 28
3 × (1 + 7) = 3 × 8 = 24
3 × (3 + 5) = 3 × 8 = 24
3 × (4 + 4) = 3 × 8 = 24
Thus the first doesn’t belong with the other three.

Think and Grow: Modeling Real Life

A marching band has 7 rows with 8 musicians in each row. There is also a row of 6 people who carry flags. How many people are in the marching band in all?
Multiplication equation:
Addition equation:

There are _______ people in the marching band in all.

Answer:
A marching band has 7 rows with 8 musicians in each row.
1 row – 8 musicians
7 rows – 7 × 8 musicians = 56 musicians
There is also a row of 6 people who carry flags.
56 + 6 = 62 people
Therefore there are 62 people in the marching band in all.

Show and Grow

Question 17.
A table has 3 rows with 8 prizes in each row. There is also a row of 4 prizes on the floor. How many prizes are there in all?
Answer: 28 prizes

Explanation:
A table has 3 rows with 8 prizes in each row.
1 row – 8 prizes
3 rows – 8 × 3 = 24 prizes
There is also a row of 4 prizes on the floor
24 + 4 = 28 prizes
Thus there are 28 prizes in all.

Question 18.
DIG DEEPER!
One section of a parking lot has 2 rows of 8 cars. Another section of the parking lot has 8 rows of 6 cars. How many cars are in the parking lot in all?
Answer: 64 cars

Explanation:
Given that,
One section of a parking lot has 2 rows of 8 cars.
2 × 8 = 16 cars
Another section of the parking lot has 8 rows of 6 cars.
8 × 6 = 48 cars
16 + 48 = 64 cars
Thus 64 cars are in the parking lot in all.

Question 19.
DIG DEEPER!
One building has 8 rows of 5 windows. Another building has 9 rows of 8 windows. How many windows are on the two buildings in all?
Answer: 112 windows

Explanation:
Given that,
One building has 8 rows of 5 windows.
8 × 5 = 40 windows
Another building has 9 rows of 8 windows.
9 × 8 = 72 windows
40 windows + 72 windows = 112 windows
Therefore 112 windows are on the two buildings in all.

Multiply by 8 Homework & Practice 3.5

Question 1.
8 × 6

Answer: 48

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 6 = (4 + 4) × 6
8 × 6 = (4 × 6) + (4 × 6)
8 × 6 = 24 + 24
8 × 6 = 48

Question 2.
2 × 8

Answer: 16

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
2 × 8 = 2 × (4 + 4)
2 × 8 = (2 × 4) + (2 × 4)
2 × 8 = 8 + 8
2 × 8 = 16

Question 3.
8 × 0 = ____
Answer: 0

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 0 = (4 + 4) × 0
8 × 0 = (4 × 0) + (4 × 0)
8 × 0 = 0 + 0
8 × 0 = 0

Question 4.
4 × 8 = ____
Answer: 32

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
4 × 8 = 4 × (4 + 4)
4 × 8 = (4 × 4) + (4 × 4)
4 × 8 = 16 + 16
4 × 8 = 32

Question 5.
8 × 10 = ____
Answer: 80

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 10 = (4 + 4) × 10
8 × 10 = (4 × 10) + (4 × 10)
8 × 10 = 40 + 40
8 × 10 = 80

Question 6.
1 × 8 = ____
Answer: 8

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
1 × 8 = 1 × (4 + 4)
1 × 8 = (1 × 4) + (1 × 4)
1 × 8 = 4+ 4
1 × 8 = 8

Question 7.

Answer: 24

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 3 = (4 + 4) × 3
8 × 3 = (4 × 3) + (4 × 3)
8 × 3 = 12 + 12
8 × 3 = 24

Question 8.

Answer: 64

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 8 = (4 + 4) × 8
8 × 8 = (4 × 8) + (4 × 8)
8 × 8 = 32 + 32
8 × 8 = 64

Question 9.

Answer: 56

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
7 × 8 = 7 × (4 + 4)
7 × 8 = (7 × 4) + (7 × 4)
7 × 8 = 28 + 28
7 × 8 = 56

Question 10.

Answer: 72

Explanation:
Rewrite 8 as 4 + 4.
We can find the product by using the Distributive Property.
8 × 9 = (4 + 4) × 9
8 × 9 = (4 × 9) + (4 × 9)
8 × 9 = 36 + 36
8 × 9 = 72

Compare
Question 11.

Answer: >

Explanation:
8 × 3 = 24
8 × 2 = 16
24 > 16
So, 8 × 3 > 8 × 2

Question 12.

Answer: <

Explanation:
8 × 7 = 56
56 < 64
So, 8 × 7 < 64

Question 13.

Answer: =

Explanation:
8 × 1 = 8
1 × 8 = 8
8 = 8
So, 8 × 1 = 1 × 8

Question 14.
There are 8 batteries in a package. You buy 7 packages. How many batteries do you have?
Answer: 56 batteries

Explanation:
Given that,
There are 8 batteries in a package.
You buy 7 packages.
1 pack – 8 batteries
7 pack – 7 × 8 batteries
7 packs = 56 batteries
Therefore there are 56 batteries in all.

Question 15.
Patterns
Tell whether each statement is true or false. If false, explain.
The ones digit in multiples of 8 follows the pattern 8, 6, 4, 2, 0. _____
The product of an odd factor and 8 is always odd. ____

Answer:
The ones digit in multiples of 8 follows the pattern 8, 6, 4, 2, 0 is true. Because the multiples of 8 are 8, 16, 24, 32, 40.
Thus the statement is true.
The product of an odd factor and 8 is always odd is false. Because any odd number multiplied by an even number will be always an even number. Thus the statement is false.

Question 16.
Modeling Real Life
A trophy case has 4 shelves with 8 trophies on each shelf and 1 shelf with 3 trophies. How many trophies are there in all?

Answer: 35 trophies

Explanation:
Given,
A trophy case has 4 shelves with 8 trophies on each shelf and 1 shelf with 3 trophies.
1 shelf – 8 trophies
4 shelves – 4 × 8 trophies = 32 trophies
1 shelf – 3 trophies
32 + 3 = 35 trophies
Therefore there are 35 trophies in all.

Question 17.
DIG DEEPER!
In a science experiment, one group of students tests 2 rows of 8 magnets. A different group tests 1 row of 8 magnets. How many magnets do they test in all?
Answer: 24 magnets

Explanation:
Given that,
In a science experiment, one group of students tests 2 rows of 8 magnets.
2 × 8 = 16 magnets
A different group tests 1 row of 8 magnets.
1 × 8 = 8 magnets
16 + 8 = 24 magnets
Thus there are 24 magnets in all.

Review & Refresh

Show and write the time.

Question 18.
half past 3

Answer: 3:30

Explanation:

Half is nothing but 30 minutes.
So, half past 30 is 3:30

Question 19.
quarter to 11

Answer: 10:45

Explanation:

The quarter is nothing but 15. Quarter to 11 means 10:45.

Lesson 3.6 Multiply by 9

Explore and Grow

Write an equation to match the array

Cross out the last column. Write an equation to match the new array
____ × ____ = ____
Answer:

Now there are 4 rows of 9 columns.
So the equation to match the new arrays is 4 × 9 = 36

Repeated Reasoning
Explain how multiplying by 10 can help you multiple by 9. Complete the table.

Answer:
The multiples of 9 are given in the below table.

Think and Grow: Multiply by 9

Example
Find 6 × 9
One way: Use the Distributive Property. Rewrite 9 as 5 + 4

Distributive Property (with subtraction)

Answer: 54

Explanation:
Rewrite 9 as 5 + 4
6 × 9 = 6 × (5 + 4)
6 × 9 = (6 × 5) + (6 × 4)
6 × 9 = 30 + 24
6 × 9 = 54
Distribution property with subtraction
Rewrite 9 as 10 – 1
6 × 9 = 6 × (10 – 1)
6 × 9 = (6 × 10) – (6 × 1)
6 × 9 = 60 – 6
6 × 9 = 54

Show and Grow

Question 1.
Find 3 × 9

Answer: 27

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
3 × 9 = 3 × (10 – 1)
3 × 9 = (3 × 10) – (3 × 1)
3 × 9 = 30 – 3
3 × 9 = 27

Apply and Grow: Practice

Find the product
Question 2.

Answer: 36

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
4 × 9 = 4 × (10 – 1)
4 × 9 = (4 × 10) – (4 × 1)
4 × 9 = 40 – 4
4 × 9 = 36

Question 3.

Answer: 72

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 8 = (10 – 1) × 8
9 × 8 = (10 × 8) – (1 × 8)
9 × 8 = 80 – 8
9 × 8 = 72

Question 4.
9 × 7 = ___
Answer: 63

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 7 = (10 – 1) × 7
9 × 7 = (10 × 7) – (1 × 7)
9 × 7 = 70 – 7
9 × 7 = 63

Question 5.
9 × 1 = ___
Answer: 9

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 1 = (10 – 1) × 1
9 × 1 = (10 × 1) – (1 × 1)
9 × 1 = 10 – 1
9 × 1 = 9

Question 6.
2 × 9 = ____
Answer: 18

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
2 × 9 = 2 × (10 – 1)
2 × 9 = (2 × 10) – (2 × 1)
2 × 9 = 20 – 2
2 × 9 = 18

Question 7.
0 × 9 = ____
Answer: 0

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
0 × 9 = 0 × (10 – 1)
0 × 9 = (0 × 10) – (0 × 1)
0 × 9 = 0 – 0
0 × 9 = 0

Question 8.

Answer: 90

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 10 = (10 – 1) × 10
9 × 10 = (10 × 10) – (1 × 10)
9 × 10 = 100 – 10
9 × 10 = 90

Question 9.

Answer: 45

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 5 = (10 – 1) × 5
9 × 5 = (10 × 5) – (1 × 5)
9 × 5 = 50 – 5
9 × 5 = 45

Question 10.

Answer: 72

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
8 × 9 = 8 × (10 – 1)
8 × 9 = (8 × 10) – (8 × 1)
8 × 9 = 80 – 8
8 × 9 = 72

Question 11.

Answer: 81

Explanation:
Distribution property with subtraction
Rewrite 9 as 10 – 1
9 × 9 = 9 × (10 – 1)
9 × 9 = (9 × 10) – (9 × 1)
9 × 9 = 90 – 9
9 × 9 = 81

Find the missing factor
Question 12.
9 × ____ = 0
Answer: 0

Explanation:
Let the missing factor be p.
9 × p = 0
p = 0/9
p = 0
Thus the missing factor is 0.

Question 13.
___ × 9 = 45
Answer: 5

Explanation:
Let the missing factor be q.
q × 9 = 45
q = 45/9
q = 5
Thus the missing factor is 5.

Question 14.
9 × ____ = 36
Answer: 4

Explanation:
Let the missing factor be s.
9 × s = 36
s = 36/9
s = 4
Thus the missing factor is 4.

Question 15.
A softball team has 9 positions and 2 players for each position. How many players are on the team?

Answer: 18 players

Explanation:
Given that,
A softball team has 9 positions and 2 players for each position.
9 × 2 = 18 players
Thus there are 18 players on the team.

Question 16.
Number Sense
Which are not multiples of 9?

Answer: The numbers that are not the multiples of 9 are 50, 42, 10.

Think and Grow: Modeling Real Life

In geocaching, people search for a cache, or collection of objects, using a GPS device. You go geocaching for 9 days. You find 2 caches each day. Your goal is to find 20 caches. Do you reach your goal?
Multiplication equation:

You ______ reach your goal.

Answer: Yes

Explanation:
Given,
In geocaching, people search for a cache, or collection of objects, using a GPS device.
You go geocaching for 9 days.
You find 2 caches each day.
1 day – 2 caches
9 days – 9 × 2 caches = 18 caches
Your goal is to find 20 caches.
20 – 18 = 2 caches
Yes, you can reach your goal.

Show and Grow

Question 17.
You have 9 math problems for homework. You spend 4 minutes on each problem. Your goal is to finish your math homework in 40 minutes. Do you reach your goal?
Answer: Yes

Explanation:
Given,
You have 9 math problems for homework. You spend 4 minutes on each problem.
1 problem – 4 minutes
9 problems – 9 × 4 minutes = 36 minutes
Your goal is to finish your math homework in 40 minutes.
40 – 36 = 4 minutes
Yes, you reach your goal.

Question 18.
DIG DEEPER!
You exercise for 6 days. You exercise for 10 minutes each day. Your friend exercises for 8 days. Your friend exercises for 9 minutes each day. Who exercises the most minutes?
Answer: Your friend

Explanation:
Given,
You exercise for 6 days. You exercise for 10 minutes each day.
1 day – 10 minutes
6 days – 6 × 10 minutes = 60 minutes
Your friend exercises for 8 days. Your friend exercises for 9 minutes each day.
1 day – 9 minutes
8 days – 8 × 9  minutes = 72 minutes
Thus your friend exercises the most minutes.

Question 19.
DIG DEEPER!
Your school is collecting cans for a food drive. Seven students from your class each collect 9 cans. Eight students from your friend’s class each collect 8 cans. Which class collects the most cans?

Answer: Your friends class collects the most cans

Explanation:
Given,
Your school is collecting cans for a food drive. Seven students from your class each collect 9 cans.
1 student – 9 cans
7 students – 7 × 9 cans = 63 cans
Eight students from your friend’s class each collect 8 cans.
1 student – 8 cans
8 students – 8 × 8 cans = 64 cans
Thus Your friend’s class collects the most cans.

Multiply by 9 Homework & Practice 3.6

Find the product
Question 1.

Answer: 63

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction
7 × 9 = 7 × (10 – 1)
7 × 9 = (7 × 10) – (7 × 1)
7 × 9 = 70 – 7
7 × 9 = 63

Question 2.

Answer: 18

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
9 × 2 = (10 – 1) × 2
9 × 2 = (10 × 2) – (1 × 2)
9 × 2 = 20 – 2
9 × 2 = 18

Question 3.
1 × 9 = ____
Answer: 9

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
1 × 9 = 1 × (10 – 1)
1 × 9 = (1 × 10) – (1 × 1)
1 × 9 = 10 – 1
1 × 9 = 9

Question 4.
9 × 9 = _____
Answer: 81

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
9 × 9 = 9 × (10 – 1)
9 × 9 = (9 × 10) – (9 × 1)
9 × 9 = 90 – 9
9 × 9 = 81

Question 5.
10 × 9 = ____
Answer: 90

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
10 × 9 = 10 × (10 – 1)
10 × 9 = (10 × 10) – (10 × 1)
10 × 9 = 100 – 10
10 × 9 = 90

Question 6.
3 × 9 = _____
Answer: 27

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
3 × 9 = 3 × (10 – 1)
3 × 9 = (3 × 10) – (3 × 1)
3 × 9 = 30 – 3
3 × 9 = 27

Question 7.

Answer: 72

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
9 × 8 = (10 – 1) × 8
9 × 8 = (10 × 8) – (1 × 8)
9 × 8 = 80 – 8
9 × 8 = 72

Question 8.

Answer: 54

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
9 × 6 = (10 – 1) × 6
9 × 6 = (10 × 6) – (1 × 6)
9 × 6 = 60 – 6
9 × 6 = 54

Question 9.

Answer: 36

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
4 × 9 = 4 × (10 – 1)
4 × 9 = (4 × 10) – (4 × 1)
4 × 9 = 40 – 4
4 × 9 = 36

Question 10.

Answer: 0

Explanation:
Rewrite 9 as 10 – 1
We can find the product by using the distributive property with subtraction.
0 × 9 = 0 × (10 – 1)
0 × 9 = (0 × 10) – (0 × 1)
0 × 9 = 0
0 × 9 = 0

Find the missing factor
Question 11.
9 × ___ = 9
Answer: 1

Explanation:
Let the missing factor be a.
9 × a = 9
a = 9/9
a = 1
Therefore the missing factor is 1.

Question 12.
___ × 5 = 45
Answer: 9

Explanation:
Let the missing factor be r.
r × 5 = 45
r = 45/5
r = 9
Therefore the missing factor is 9.

Question 13.
90 = ___ × 10
Answer: 9

Explanation:
Let the missing factor be p.
90 = p × 10
p = 90/10
p = 9
Therefore the missing factor is 9.

Question 14.
You see 9 chipmunks on your walk to school. You see twice as many pigeons. How many pigeons do you see?
Answer: 18

Explanation:
Given that,
You see 9 chipmunks on your walk to school. You see twice as many pigeons.
Let the number of pigeons is x.
twice = 2x
2 × 9 = 18
Thus there are 18 pigeons.

Question 15.
Patterns
Use the table

What pattern do you notice in the ones digits? the tens digits?
What do you notice about the sum of the digits for each multiple of 9?
Answer:
The pattern in ones digit is 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.
The pattern in tens digit is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
I observe that the sum of digits for each multiple of 9 is 9.
18 = 1 + 8 = 9
27 = 2 + 7 = 9
36 = 3 + 6 = 9
45 = 4 + 5 = 9
54 = 5 + 4 = 9
63 = 6 + 3 = 9
72 = 7 + 2 = 9
81 = 8 + 1 = 9
90 = 9 + 0 = 9

Question 16.
YOU BE THE TEACHER
Your friend says the product of 7 × 9 is 69. Is your friend correct? Explain.
Answer: My friend is incorrect. Because the product of 7 × 9 is 63.

Question 17.
Modeling Real Life
You sell 8 orchids. You want to raise $70. Do you meet your goal?

Answer:
Given,
You sell 8 orchids.
The cost of 1 orchid – $9
8 orchids – 8 × $9 = $72
You want to raise $70.
$70 – $72 = -$2
No, I didn’t reach my goal.

DIG DEEPER!
Newton sells 9 lilies. Descartes sells 5 orchids. Who raises the most money?

Answer:
Given that,
Newton sells 9 lilies. Descartes sells 5 orchids.
Cost of lily – $6
9 × $6 = $54
Cost of Orchid – $9
5 × $9 = $45
Thus Newton raises more money.

Review & Refresh

Complete the equation.
Question 18.
4 × 5 = 5 × ____
Answer: 4

Explanation:
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
So, 4 × 5 = 5 × 4

Question 19.
8 × ____ = 7 × 8
Answer: 7

Explanation:
The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.
8 × 7 = 7 × 8

Lesson 3.7 Practice Multiplication Strategies

Explore and Grow

Show how to find the product
6 × 7 = ____
Answer: 42

Explanation:
Multiply the two numbers 6 and 7.
6 × 7 = 42

Reasoning
What other strategies can you use to solve?
Answer: The other strategy to find the product is by using the distributive property.
Rewrite 7 as 5 + 2
6 × 7 = 6 × (5 + 2)
6 × 7 = (6 × 5) + (6 × 2)
6 × 7 = 30 + 12
6 × 7 = 42

Think and Grow: Practice Multiplication Strategies

Example
Use any strategy to find 4 × 3.
One way: Use a number line. Skip count by 3s four times.

Another way: Use the Distributive Property

Answer:
Using Distributive Property
Rewrite 4 as 2 + 2.
4 × 3 = (2 + 2) × 3
4 × 3 = (2 × 3) + (2 × 3)
4 × 3 = 6 + 6
4 × 3 = 12

Show and Grow

Use any strategy to find the product
Question 1.
5 × 6 = ____
Answer: 30

Explanation:
Using Distributive Property
Rewrite 6 as 3 + 3.
5 × 6 = 5 × (3 + 3)
5 × 6 = (5 × 3) + (5 × 3)
5 × 6 = 15 + 15
5 × 6 = 30

Question 2.
3 × 8 = ____
Answer: 24

Explanation:
Using Distributive Property.
Rewrite 8 as 4 + 4.
3 × 8 = 3 × (4 + 4)
3 × 8 = (3 × 4) + (3 × 4)
3 × 8 = 12 + 12
3 × 8 = 24

Question 3.
7 × 8 = ____
Answer: 56

Explanation:
Using Distributive Property
Rewrite 8 as 4 + 4.
7 × 8 = 7 × (4 + 4)
7 × 8 = (7 × 4) + (7 × 4)
7 × 8 = 28 + 28
7 × 8 = 56

Question 4.
9 × 6 = ____
Answer: 54

Explanation:
Using Distributive Property
Rewrite 6 as 3 + 3.
9 × 6 = 9 × (3 + 3)
9 × 6 = (9 × 3) + (9 × 3)
9 × 6 = 27 + 27
9 × 6 = 54

Apply and Grow: Practice

Use any strategy to find the product
Question 5.
5 × 9 = _____
Answer: 45

Explanation:
Using Distributive Property
Rewrite 9 as 5 + 4.
5 × 9 = 5 × (5 + 4)
5 × 9 = (5 × 5) + (5 × 4)
5 × 9 = 25 + 20
5 × 9 = 45

Question 6.
5 × 7 = ____
Answer: 35

Explanation:
Using Distributive Property
Rewrite 7 as 5 + 2.
5 × 7 = 5 × (5 + 2)
5 × 7 = (5 × 5) + (5 × 2)
5 × 7 = 25 + 10
5 × 7 = 35

Question 7.
10 × 3 = ____
Answer: 30

Explanation:
Using Distributive Property
Rewrite 10 as 5 + 5.
10 × 3 = (5 + 5) × 3
10 × 3 = (5 × 3) + (5 × 3)
10 × 3 = 15 + 15
10 × 3 = 30

Question 8.
7 × 1 = ____
Answer: 7

Explanation:
Using Distributive Property
Rewrite 7 as 5 + 2.
7 × 1 = (5 + 2) × 1
7 × 1 = (5 × 1) + (2 ×1)
7 × 1 = 5 + 2
7 × 1 = 7

Question 9.
5 × 5 = ____
Answer: 25

Explanation:
Using Distributive Property
Rewrite 5 as 2 + 3
5 × 5 = 5 × (2 + 3)
5 × 5 = (5 × 2) + (5 × 3)
5 × 5 = 10 + 15
5 × 5 = 25

Question 10.
4 × 9 = ____
Answer: 36

Explanation:
Using Distributive Property
Rewrite 4 as 2 + 2.
4 × 9 = (2 + 2) × 9
4 × 9 = (2 × 9) + (2 × 9)
4 × 9 = 18 + 18
4 × 9 = 36

Question 11.

Answer: 48

Explanation:
Using Distributive Property.
Rewrite 8 as 4 + 4.
8 × 6 = (4 + 4) × 6
8 × 6 = (4 × 6) + (4 × 6)
8 × 6 = 24 + 24
8 × 6 = 48

Question 12.

Answer: 28

Explanation:
Using Distributive Property
Rewrite 4 as 2 + 2.
4 × 7 = (2 + 2) × 7
4 × 7 = (2 × 7) + (2 × 7)
4 × 7 = 14 + 14
4 × 7 = 28

Question 13.

Answer: 10

Explanation:
Using Distributive Property
Rewrite 5 as 2 + 3
5 × 2 = (2 + 3) × 2
5 × 2 = (2 × 2) + (2 × 3)
5 × 2 = 4 + 6
5 × 2 = 10

Name the strategy or property used to solve

Question 14.
9 × 9 = 9 × (10 – 1)
9 × 9 = (9 × 10) – (9 × 1)
9 × 9 = 90 – 9
9 × 9 = 81
Answer: Distributive property with subtraction
The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can subtract the numbers and then multiply, or you can multiply and then subtract.

Question 15.
2 × 4 = 8

Answer: Number line

Question 16.
DIG DEEPER!
Use known facts to find 6 × 12. Explain your strategy 6 × 12 = ____
Answer: 72

Explanation:
Rewrite 6 as 3 + 3.
6 × 12 = (3 + 3) × 12
6 × 12 = (3 × 12) + (3 × 12)
6 × 12 = 36 + 36
6 × 12 = 72

Think and Grow: Modeling Real Life

You want to make a dragon that is 25 feet long for a parade. You have 6 pieces of fabric that are each 5 feet long. Do you have enough fabric to make the dragon?


You _____ have enough fabric to make the dragon.

Answer:
Given,
You want to make a dragon that is 25 feet long for a parade.
You have 6 pieces of fabric that are each 5 feet long
6 × 5 = 30

Yes, you have enough fabric to make the dragon.

Show and Grow

Question 17.
A book is 70 pages long. You read 9 pages each day for one week. Do you finish the book in one week?
Answer: No

Explanation:
Given,
A book is 70 pages long. You read 9 pages each day for one week.
Convert week to day.
1 day – 9 pages
7 days – 7 × 9 pages = 63 pages
63 – 70 = -7
Thus you did not finish the book in one week.

Question 18.
DIG DEEPER!
You buy 4 packs of juice boxes. How many juice boxes do you buy in all?

Explain how you solved the problem.
Answer: 40 juice boxes

Explanation:
You buy 4 packs of juice boxes.
1 pack contains 5 grape, 3 apple, 2 berry
4 packs = 5 grapes × 4, 3 apple × 4, 2 berry × 4
= 20 grape, 12 apple, 8 berry
= 20 + 12 + 8 = 40
Thus you buy 40 juice boxes in all.

Practice Multiplication Strategies Homework & Practice 1.1

Use any strategy to find the product
Question 1.
0 × 6 = ____
Answer: 0

Explanation:
Any number multiplied by 0 will be always 0.

Question 2.
2 × 10 = ____
Answer: 20

Explanation:
You can find the product by using the distributive property.
Rewrite 10 as 5 + 5.
2 × 10 = 2 × (5 + 5)
2 × 10 = (2 × 5) + (2 × 5)
2 × 10 = 10 + 10
2 × 10 = 20

Question 3.
1 × 9 = ____
Answer: 9

Explanation:
You can find the product by using the distributive property.
Rewrite 9 as 6 + 3
1 × 9 = 1 × (6 + 3)
1 × 9 = (1 × 6) + (1 × 3)
1 × 9 = 6 + 3
1 × 9 = 9

Question 4.

Answer: 20

Explanation:
You can find the product by using the distributive property.
Rewrite 4 as 2 + 2.
4 × 5 = (2 + 2) × 5
4 × 5 = (2 × 5) + (2 × 5)
4 × 5 = 10 + 10
4 × 5 = 20

Question 5.

Answer: 72

Explanation:
You can find the product by using the distributive property.
Rewrite 9 as 6 + 3
8 × 9 = 8 × (6 + 3)
8 × 9 = (8 × 6) + (8 × 3)
8 × 9 = 48 + 24
8 × 9 = 72

Question 6.

Answer: 21

Explanation:
You can find the product by using the distributive property.
Rewrite 7 as 5 + 2.
7 × 3 = (5 + 2) × 3
7 × 3 = (5 × 3) + (2 × 3)
7 × 3 = 15 + 6
7 × 3 = 21

Name the strategy or property used to solve.
Question 7.
3 × 5 = ?

Answer: The strategy used for the above product is table diagram.

Question 8.

Answer: Distributive Property of Multiplication.

Explanation:
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Question 9.
Logic
Without multiplying, how can you tell which product will be greater,6 × 3 or 6 × 4? Explain.
Answer: We can say the greater product by comparing the multiples 4 is greater than 3. So, 6 × 3 is less than 6 × 4.

Question 10.
YOU BE THE TEACHER
Descartes uses the Distributive Property to solve 5 × 8. Is he correct? Explain.

Answer: No Descartes solution is incorrect.

Explanation:
Rewrite 8 as 10 – 2.
5 × 8 = 5 × (10 – 2)
5 × 8 = (5 × 10) – (5 × 2)
5 × 8 = 50 – 10
5 × 8 = 40

Question 11.
Modeling Real Life
You order 24 eggs from a farmer. The farmer has 8 chickens. Each chicken lays 3 eggs. Does the farmer have enough eggs for your order? Explain.

Answer:
Given that,
You order 24 eggs from a farmer.
The farmer has 8 chickens.
Each chicken lays 3 eggs.
8 × 3 eggs = 24 eggs
Yes, the farmer have enough eggs for your order.

Question 12.
DIG DEEPER!
You have 3 piles of sports cards. There are 3 baseball cards, 2 basketball cards, and 4 football cards in each pile. How many sports cards do you have in all?
Answer:
Given that,
You have 3 piles of sports cards.
There are 3 baseball cards, 2 basketball cards, and 4 football cards in each pile.
1 pile – 3 basketball cards, 2 basketball cards, and 4 football cards
3 piles – 9 basketball cards, 6 basketball cards, and 12 football cards
= 9 + 6 + 12 = 27 cards
Thus you have 27 sports cards in all.

Review & Refresh

Find the sum
Question 13.

Answer: 92

Explanation:
Add all the three numbers.
32
+13
+47
92

Question 14.

Answer: 84

Explanation:
Add all the three numbers.
46
+14
+24
84

Question 15.

Answer: 72

Explanation:
Add all the three numbers.
55
+10
+12
72

Question 16.

Answer: 63

Explanation:
Add all the three numbers.
21
+13
+29
63

Lesson 3.8 Multiply Three Factors

Explore and Grow

Model 2 arrays that each have 4 rows and 3 columns. Draw your model. Complete the equation for the arrays.
2 × ____ ×____ = _____
Answer: 2 × 4 × 3 = 24

Model 3 arrays that each have 2 rows and 4 columns. Draw your model. Complete the equation for the arrays.
3 × ___ × ____ = ____
Answer: 3 × 2 × 4 = 24

Structure
Compare the equations. How are they the same? How are they different?
Answer: The solutions for both equations are the same. But the arrays and rows and columns are different.

Think and Grow: Associative Property of Multiplication

Associative Property of Multiplication: Changing the grouping of factors does not change the product
Example
Find (5 × 2) × 3

Answer:
Associative Property of Multiplication
First find the factors in the bracket.
5 × 2 = 10
10 × 3 = 30
Commutative Property of Multiplication
5 × (2 × 3)
2 × 3 = 6
5 × 6 = 30

Example
Find 4 × (7 × 2)

Answer:
4 × (7 × 2) = 4 × (2 × 7)
4 × (2 × 7) = (4 × 2) × 7
(4 × 2) × 7 = 8 × 7 = 56
4 × (2 × 7) = 4 × 14 =56

Show and Grow

Find the product
Question 1.
(3 × 2) × 2 = _____
Answer: 12

Explanation:
First find the factors in the bracket.
(3 × 2) × 2
3 × 2 = 6
6 × 2 = 12

Question 2.
3 × (4 × 3) = ____
Answer: 36

Explanation:
First find the factors in the bracket.
3 × (4 × 3)
(4 × 3) = 12
3 × 12 = 36

Apply and Grow: Practice

Find the product
Question 3.
(3 × 2) × 7 = ____
Answer: 42

Explanation:
First find the factors in the bracket.
3 × 2 = 6
6 × 7 = 42

Question 4.
5 × (4 × 2) = _____
Answer: 40

Explanation:
First find the factors in the bracket.
4 × 2 = 8
5 × 8 = 40

Question 5.
(3 × 6) × 2 = ____
Answer: 36

Explanation:
First find the factors in the bracket.
3 × 6 = 18
18 × 2 = 36

Question 6.
3 × (5 × 3) = ____
Answer: 45

Explanation:
First find the factors in the bracket.
5 × 3 = 15
3 × 15 = 45

Question 7.
(4 × 10) × 2 = ____
Answer: 80

Explanation:
First find the factors in the bracket.
4 × 10 = 40
40 × 2 = 80

Question 8.
6 × (0 × 7) = ____
Answer: 0

Explanation:
First find the factors in the bracket.
0 × 7 = 0
6 × 0 = 0

Tell whether the equation is true or false. Explain.

Question 9.

Answer: True

Explanation:
First find the factors in the bracket.
5 × 3 = 15
15 × 4 = 60
5 × 4 = 20
3 × 20 = 60
Thus the above statement is true.

Question 10.

Answer: False

Explanation:
First find the factors in the bracket.
2 × 6 = 12
4 × 12 = 48
8 × 4 = 32
48 ≠ 32
Thus the above statement is false.

Question 11.
A water ride has 4 log boats. Each boat has 2 sections with 2 seats in each section. How many seats does the water ride have?

Answer:
Given that,
A water ride has 4 log boats. Each boat has 2 sections with 2 seats in each section.
1 section – 2 seats
2 sections – 2 × 2 seats = 4 seats
4 × 4 seats = 16 seats
Therefore the water ride have 16 seats.

Question 12.
DIG DEEPER!
Complete the square so that the product of the numbers in each row and each column equals 24.

Answer:

Think and Grow: Modeling Real Life

There are 26 students in your class. Your teacher brings in 4 boxes of muffins. Each box has 4 packages with 2 muffins in each package. Are there enough muffins for the class?
Multiplication equation:
There ______ enough muffins for the class.

Answer:
Given,
There are 26 students in your class.
Your teacher brings in 4 boxes of muffins.
Each box has 4 packages with 2 muffins in each package.
1 package – 2 muffins
4 packages – 2 × 4 packages = 8 packages
4 × 8 packages = 32 packages
32 – 26 = 6
Thus there are enough muffins for the class.

Show and Grow

Question 13.
Newton needs to send out 50 letters. He buys 4 sheets of stamps. Each sheet has 2 rows with 6 stamps in each row. Does Newton have enough stamps to send out all the letters?
Answer:
Given that,
Newton needs to send out 50 letters.
He buys 4 sheets of stamps.
Each sheet has 2 rows with 6 stamps in each row.
2 × 6 = 12 stamps
4 × 12 stamps = 48 stamps
48 – 50 = -2
Newton does not have enough stamps to send out all the letters.

Question 14.
DIG DEEPER!
There are 60 people in line to ride the tram at a zoo. There are 5 benches on each tram car. Two people fit on each bench. The tram is 5 cars long. How many people will have to wait for the next tram?

Answer:
Given that,
There are 60 people in line to ride the tram at a zoo.
There are 5 benches on each tram car.
Two people fit on each bench.
5 × 2 = 10 people fit on 5 benches
The tram is 5 cars long
5 × 10 = 50 people
50 – 60 = -10 people
Thus 10 people will have to wait for the next time.

Multiply Three Factors Homework & Practice 3.8

Find the product
Question 1.
(2 × 4) × 1 = _____
Answer: 8

Explanation:
First multiply the factors in the bracket.
2 × 4 = 8
8 × 1 = 8
Thus (2 × 4) × 1 = 8

Question 2.
2 × (3 × 3) = ____
Answer: 18

Explanation:
First multiply the factors in the bracket.
3 × 3 = 9
2 × 9 = 18
Thus 2 × (3 × 3) = 18

Question 3.
(4 × 2) × 9 = _____
Answer: 72

Explanation:
First multiply the factors in the bracket.
4 × 2 = 8
8 × 9 = 72
Thus (4 × 2) × 9 = 72

Question 4.
2 × (8 × 5) = _____
Answer: 80

Explanation:
First multiply the factors in the bracket.
8 × 5 = 40
2 × 40 = 80
So, 2 × (8 × 5) = 80

Tell whether the equation is true or false. Explain
Question 5.

Answer: False

Explanation:
Any number multiplied by 0 will be always 0.
0 × 3 = 0
7 × 0 = 0
7 × 3 = 21
Thus the equation 7 × (0 × 3) = 7 ×3 is false.

Question 6.

Answer: True

Explanation:
6 × 5 = 30
2 × 30 = 60
6 × 2 = 12
12 × 5 = 60
Thus the equation 2 × (6 × 5) = (6 × 2) × 5 is false.

Question 7.
A sudoku puzzle is made of 9 large squares. Each large square is made of an array with 3 rows and 3 columns of small squares. How many small squares are there?

Answer: 81 small squares

Explanation:
Given that,
A sudoku puzzle is made of 9 large squares.
Each large square is made of an array with 3 rows and 3 columns of small squares.
3 × 3 = 9 small squares in each large square
9 × 9 = 81 small squares in sudoko puzzle.

Question 8.
DIG DEEPER!
Use the number of cards to complete the equations.

Answer:
Solve the equations by using the number of cards.

Question 9.
YOU BE THE TEACHER
Your friend says that (2 × 1) × 7 is equal to 2 × (1 × 7). Is your friend correct? Explain.
Answer:
Given,
Your friend says that (2 × 1) × 7 is equal to 2 × (1 × 7).
(2 × 1) × 7 = 2 × 7 = 14
2 × (1 × 7) = 2 × 7 = 14
Thus your friend is correct.

Question 10.
Writing
How do you know 2 × 9 × 5 is the same as 10 × 9?
Answer:
2 × 9 × 5 = 18 × 5 = 90
10 × 9 = 90
Thus the expression is correct.

Question 11.
Modeling Real Life
There are 64 soccer players. Some coaches bring 7 boxes of protein bars. Each box has 5 packages with 2 protein bars in each package. Are there enough protein bars for each soccer player to get one?

Answer:
Given that,
There are 64 soccer players.
Some coaches bring 7 boxes of protein bars.
Each box has 5 packages with 2 protein bars in each package.
1 package – 2 protein bars
5 packages – 2 × 5 = 10 protein bars
7 × 10 = 70 protein bars
70 – 64 = 6
Thus each soccer player get enough protein bars.

Review & Refresh

Question 12.
A training academy certifies 12 fire fighting Dalmations. They divide the Dalmations among different cities with 3 Dalmatians in each city. How many cities receive firefighting Dalmations?
____ ÷ _____ = _____
Answer:
Given that,
A training academy certifies 12 fire fighting Dalmations. They divide the Dalmations among different cities with 3 Dalmatians in each city.
12 ÷ 3 = 4
Therefore 4 cities receive firefighting Dalmations.

Lesson 3.9 More Problem Solving: Multiplication

Explore and Grow

Model the story. A baseball league gives 8 new baseballs to each team. There are 8 teams. How many baseballs does the league need?

The baseball league needs ______ baseballs.
Answer:
Given,
A baseball league gives 8 new baseballs to each team.
There are 8 teams.
8 × 8 baseballs = 64 baseballs
Thus, the baseball league needs 64 baseballs.

Reasoning
Explain how you can use a different strategy to solve.
Answer:
We can solve by using the distributive property.
8 can be written as (10 – 1)
8 × 8 = 8 × (10 – 2)
8 × 8 = (8 × 10) – (8 × 2)
8 × 8 = 80 – 16
8 × 8 = 64

Think and Grow: Using the Problem-Solving Plan

Example
You want to make 8 dream catchers. You have 30 feathers. You tie 3 feathers to each dream catcher. How many feathers do you have left?

Understand the Problem

What do you know?
• You want to make ______ dream
• You have ______ feathers in all
• You tie _____ feathers to each dream catcher.

Answer:
Fill the blanks with the help of the above question.
• You want to make 8 dream
• You have 30 feathers in all
• You tie 3 feathers to each dream catcher.

What do you need to find?
• You need to find how many ______ are left after catchers. you make dream catchers.

Answer:
By seeing the above question we can fill the blanks.
• You need to find how many feathers are left after catchers. you make dream catchers.

Make a Plan

How will you solve?
• Multiply _____ by ______ to find how many ______ you used to make 8 dream catchers.
• Subtract the product from ______.

Answer:
Fill in the blanks by using the above question.
• Multiply 8 by 3 to find how many feathers you used to make 8 dream catchers.
• Subtract the product from total number of feathers.

Solve
8 × 3 = ______
30 – ___ = _____
You have _____ feathers left.

Answer:
8 × 3 = 24
30 – 24 = 6
Thus, you have 6 feathers left.

Show and Grow

Question 1.
You want to make 6 cheese sandwiches. You have 8 slices of cheese in all. You put 2 slices on each sandwich. How many more slices of cheese do you need?

Answer:
Given that,
You want to make 6 cheese sandwiches.
Each sandwich needs 2 slices.
6 × 2 = 12 slices
You have 8 slices of cheese in all. You put 2 slices on each sandwich.
12 – 8 = 4 slices
Therefore you need 4 slices of cheese.

Apply and Grow: Practice

Question 2.
You have 60 fluid ounces of water and 6 water bottles. You pour 8 fluid ounces of water into each bottle. What information do you know that will help you find how much water you have left?
Answer:
Given,
You have 60 fluid ounces of water and 6 water bottles. You pour 8 fluid ounces of water into each bottle.
To find how much water you have left we need to subtract total fluid ounces and amount of fluid ounces in 6 water bottles.
6 × 8 fluid ounces = 48 fluid ounces
60 – 48 = 12 fluid ounces
Thus 12 fluid ounces of water is left.

Question 3.
A sheet of stamps has 2 rows with 5 stamps in each row. You buy 3 sheets of stamps. How many stamps do you buy?

Answer:
Given that,
A sheet of stamps has 2 rows with 5 stamps in each row.
2 × 5 = 10 stamps in each row.
You buy 3 sheets of stamps.
10 × 3 = 30 stamps
Thus you buy 30 stamps.

Question 4.
Your cousin works two jobs. She walks dogs 4 days each week for 2 hours each day. She babysits 2 days each week for 5 hours each day. How many hours does your cousin work in one week?
Answer:
Given that,
Your cousin works two jobs. She walks dogs 4 days each week for 2 hours each day.
4 × 2 = 8 hours each week
She babysits 2 days each week for 5 hours each day.
2 × 5 hours = 10 hours
8 + 10 = 18 hours in one week
Thus your cousin 18 hours in one week.

Question 5.
Four arcade tokens cost $1. You buy $5 in tokens. You play 6 games that cost 3 tokens each. How many tokens do you have left?

Answer:
Given that,
Four arcade tokens cost $1. You buy $5 in tokens.
1 × 4 = 4 tokens
5 × 4 = 20 tokens
You play 6 games that cost 3 tokens each.
6 × 3 = 18 tokens
20 – 18 tokens = 2 tokens
Thus 2 tokens are leftover.

Think and Grow: Modeling Real Life

A basketball team scores 6 three-pointers, 9 two-pointers, and 7 free throws in the first quarter. How many points does the team score in all?

Understand the problem:
Make a plan:
Solve:
The team scores ____ points in all.

Answer:
Given that,
A basketball team scores 6 three-pointers, 9 two-pointers, and 7 free throws in the first quarter.
6 × 3 points = 18 points
9 × 2 points = 18 points
7 × 1 point = 7 point
18 + 18 + 7 = 43 points
Thus the team scores 43 points in all.

Show and Grow

Question 6.
Descartes buys 4 shirts, 3 pairs of shorts, and 2 pairs of pants. How much does he spend in all?

Answer:
Given that,
Descartes buys 4 shirts, 3 pairs of shorts, and 2 pairs of pants.
4 shirts – 4 × $5 = $20
3 shorts – 3 × $7 = $21
2 pants – 2 × $10 = $20
20 + 21 + 20 = $61
Thus Descartes spend $61 in all.

Question 7.
DIG DEEPER!
City workers set up 100 chairs for a concert in a park. Section A has 4 rows with 9 chairs in each row. Section B has 3 rows with 8 chairs in each row. Section C has 8 equal rows. How many chairs are in each of section C’s rows?

Answer: 40

Explanation:
Given that,
City workers set up 100 chairs for a concert in a park.
Section A has 4 rows with 9 chairs in each row.
4 × 9 = 36 chairs
Section B has 3 rows with 8 chairs in each row.
3 × 8 = 24 chairs
Section C has 8 equal rows.
100 – 36 – 24 = 40 chairs
Thus there are 40 chairs in Section C.

More Problem Solving: Multiplication Homework & Practice 3.9

Question 1.
You and 3 of your friends each spend $9 on a present. How much does the present cost?

Answer: $36

Explanation:
Given,
You and 3 of your friends each spend $9 on a present.
1 – $9
4 – 4 × $9 = $36
Thus the cost of the present is $36.

Question 2.
A landlord is replacing windows in an apartment complex. There are 6 apartments. Each apartment has 8 windows. Seven windows do not need replacing. How many windows does the landlord need to replace?

Answer: 41 windows

Explanation:
Given,
A landlord is replacing windows in an apartment complex.
There are 6 apartments. Each apartment has 8 windows.
6 × 8 = 48 windows
Seven windows do not need replacing.
48 – 7 = 41
Therefore the landlord needs to replace 41 windows.

Question 3.
Women’s boxing consists of four 2-minute rounds. There is a 1-minute rest interval between each round. What information do you know that will help you find how long a boxing match lasts?
Answer: I need that information about the time that last four 2-minute rounds and 1-minute rest interval.

Explanation:
Given,
Women’s boxing consists of four 2-minute rounds.
4 × 2 = 8 minutes
There is a 1-minute rest interval between each round.
4 × 1 = 4 minutes
8 + 4 = 12 minutes
Thus the boxing match lasts for 12 minutes.

Question 4.
Writing
Write and solve your own word problem that involves multiplication.
Answer:
Find the product of 3 × 5
We can find the product by using the distributive property.
Rewrite 5 as 2 + 3.
3 × 5 = 3 × (2 + 3)
3 × 5 = (3 × 2) + (3 × 3)
3 × 5 = 6 + 9
3 × 5 = 15

Question 5.
Modeling Real Life
You play a trivia game with your friends. Team A answers 3 hard questions and 6 easy questions. Team B answers 5 hard questions and 2 easy questions. Which team is winning? by how many points?

Answer:
Given,
You play a trivia game with your friends. Team A answers 3 hard questions and 6 easy questions.
Hard – 5 points
Easy – 2 points
3 hard question = 3 × 5 = 15 points
6 easy questions = 6 × 2 = 12 points
15 + 12 = 27 points
Team B answers 5 hard questions and 2 easy questions.
5 hard question = 5 × 5 = 25 points
2 easy questions = 2 × 2 = 4 points
25 + 4 = 29 points
Thus Team B is winning the points by 2 points.

Review & Refresh

Question 6.

Answer:
i. 5 sides
ii. 5 vertices
iii. pentagon

Explanation:
By seeing the above figure we can say that the shape of the image is a pentagon with 5 sides and 5 vertices.

Question 7.

Answer:
i. 4 sides
ii. 4 vertices
iii. Quadrilateral

Explanation:
The figure has 4 sides and 4 vertices so the shape is a quadrilateral.

More Multiplication Facts and Strategies Performance Task

Question 1.
You and your friend make origami animals.
a.You have two packages of paper. One package has 8 colors with 6 sheets of each color. Another package has 3 white sheets and 9 times as many colored sheets as white sheets. How many sheets of paper do you have in all?

Answer:
Given,
You have two packages of paper. One package has 8 colors with 6 sheets of each color.
8 × 6 = 48 colors in 6 sheets
Another package has 3 white sheets and 9 times as many colored sheets as white sheets.
9 × 3 = 27 sheets
= 27 + 6 = 33 sheets

b.You and your friend each want to make 5 origami animals every day for one week. Do you have enough paper? Explain.

Answer:
Given,
You and your friend each want to make 5 origami animals every day for one week.
5 + 5 = 10 origami animals every day for one week.
10 × 7 = 70 origami animals
Yes, you have enough paper.
c.You make a jumping frog. The first step is to fold the paper into fourths that are shaped like triangles. Draw lines to show how you would fold your paper.

d. It takes 12 steps to make a crane. Your friend makes 8 paper cranes. How many steps does your friend do in all? Explain.

Answer:
Given,
It takes 12 steps to make a crane. Your friend makes 8 paper cranes.
12 × 8 = 96 steps
Your friend does 96 steps in all.

More Multiplication Facts and Strategies Activity

Product Lineup
Directions:
1. Players take turns flipping two number cards.
2. On your turn, multiply the two numbers and place a counter on the product.
3. If you flip two of the same number, take another turn.
4. The first player to create two lines of 5 in a row, horizontally, vertically, or diagonally, wins!

Answer:
Multiply 5 by row, horizontally and vertically.
5 × 27 = 135
5 × 64 = 320
5 × 3 = 15

More Multiplication Facts and Strategies Chapter Practice

3.1 Multiply by 3

Draw the model to find the product
Question 1.
3 × 8
Answer:

Question 2.
3 × 4
Answer:

Find the product
Question 3.

Answer: 15

Explanation:
Multiply the two numbers 3 and 5.
3 × 5 = 15

Question 4.

Answer: 0

Explanation:
Multiply the two numbers 0 and 3.
Any number multiplied by 0 will be always 0.
So, 0 × 3 = 0

Question 5.

Answer: 3

Explanation:
Multiply the two numbers 1 and 3.
Any number multiplied by 1 will be always the same number.
1 × 3 = 3

Question 6.

Answer: 18

Explanation:
Multiply the two numbers 3 and 6.
3 × 6 = 18

3.2 Multiply by 4

Find the product
Question 7.

Answer: 32

Explanation:
Multiply the two numbers 4 and 8.
4 × 8 = 32

Question 8.

Answer: 40

Explanation:
Multiply the two numbers 10 and 4.
10 × 4 = 40

Question 9.

Answer: 28

Explanation:
Multiply the two numbers 7 and 4.
7 × 4 = 28

Question 10.

Answer: 16

Explanation:
Multiply the two numbers 4 and 4.
4 × 4 = 16

Find the missing factor
Question 11.
1 × ___ = 4
Answer: 4

Explanation:
Let the missing factor be a.
1 × a = 4
a = 4/1
a = 4
Thus the missing factor is 4.

Question 12.
____ × 4 = 0
Answer: 0

Explanation:
Let the missing factor be b.
b × 4 = 0
b = 0/4
b = 0
Thus the missing factor is 0.

Question 13.
20 = ____ × 4
Answer: 5

Explanation:
Let the missing factor be c.
20 = c × 4
c = 20/4
c = 5
Thus the missing factor is 5.

Question 14.
Number Sense
How can you use 2 × 5 to find 4 × 5?
Answer:
Rewrite 4 as 2 + 2.
4 × 5 = (2 + 2) × 5
4 × 5 = (2 × 5) + (2 × 5)
4 × 5 = 10 + 10
4 × 5 = 20

3.3 Multiply by 6

Find the product
Question 15.

Answer: 30

Explanation:
Multiply the two numbers 6 and 5.
6 × 5 = 30

Question 16.

Answer: 12

Explanation:
Multiply the two numbers 6 and 2.
6 × 2 = 12

Question 17.

Answer: 54

Explanation:
Multiply the two numbers 9 and 6.
9 × 6 = 54

Question 18

Answer: 18

Explanation:
Multiply the two numbers 3 and 6.
3 × 6 = 18

Compare
Question 19.

Answer: <

Explanation:
Compare both expressions
7 × 6 = 42
6 × 8 = 48
42 is less than 48.
7 × 6 < 6 × 8

Question 20.

Answer: >

Explanation:
Compare both expressions
6 × 9 = 54
4 × 6 = 24
54 is greater than 24.
6 × 9 > 4 × 6

Question 21.

Answer: =

Explanation:
Compare both expressions
6 × 6 = 36
36 = 6 × 6

3.4 Multiply by 7

Find the product
Question 22.

Answer: 0

Explanation:
Multiply the two numbers 0 and 7.
Any number multiplied by 0 is always 0.
0 × 7 = 0

Question 23.

Answer: 49

Explanation:
Multiply the two numbers 7 and 7.
7 × 7 = 49

Question 24.

Answer: 70

Explanation:
Multiply the two numbers 10 and 7.
10 × 7 = 70

Question 25.

Answer: 14

Explanation:
Multiply the two numbers 7 and 2.
7 × 2 = 14

Question 26.

Answer: 7

Explanation:
Multiply the two numbers 7 and 1.
Any number multiplied by 1 is always the same number.
7 × 1 = 7

Question 27.

Answer: 63

Explanation:
Multiply the two numbers 7 and 9.
7 × 9 = 63

Question 28.

Answer: 28

Explanation:
Multiply the two numbers 4 and 7.
4 × 7 = 28

Question 29.

Answer: 56

Explanation:
Multiply the two numbers 8 and 7.
8 × 7 = 56

3.5 Multiply by 8

Find the product
Question 30.

Answer: 48

Explanation:
Multiply the two numbers 8 and 6.
8 × 6 = 48

Question 31.

Answer: 72

Explanation:
Multiply the two numbers 9 and 8.
9 × 8 = 72

Question 32.

Answer: 32

Explanation:
Multiply the two numbers 4 and 8.
4 × 8 = 32

Question 33.

Answer: 40

Explanation:
Multiply the two numbers 8 and 5.
8 × 5 = 40

Question 34.
Precision
There are 8 fluid ounces in 1 cup. How many fluid ounces are in 3 cups?

Answer: 24 fluid ounces

Explanation:
Given,
There are 8 fluid ounces in 1 cup.
1 cup – 8 fluid ounces
3 cups – 3 × 8 fluid ounces = 24 fluid ounces
Therefore there are 24 fluid ounces in 3 cups.

3.6 Multiply by 9

Find the product
Question 35.

Answer: 90

Explanation:
Multiply the two numbers 10 and 9.
10 × 9 = 90

Question 36.

Answer: 36

Explanation:
Multiply the two numbers 9 and 4.
9 × 4 = 36

Question 37.

Answer: 54

Explanation:
Multiply the two numbers 9 and 6.
9 × 6 = 54

Question 38.

Answer: 18

Explanation:
Multiply the two numbers 3 and 6.
3 × 6 = 18
Thus the product of 3 and 6 is 18.

Question 39.
Reasoning
An artist needs 80 flower petals for a craft. She picks 9 flowers that each have 8 petals. Does she have enough flower petals for her craft? Explain.

Answer:
Given,
An artist needs 80 flower petals for a craft.
She picks 9 flowers that each have 8 petals.
9 × 8 = 72 flower petals.
80 – 72 = 8  flower petals
Therefore, She has enough flower petals for her craft.

3.7 Practice Multiplication Strategies

Use any strategy to find the product
Question 40.
2 × 7 = ____
Answer: 14

Explanation:
We can find the product by using the distributive property.
Rewrite 7 as 5 + 2.
2 × 7 = 2 × (5 + 2)
2 × 7 = (2 × 5) + (2 × 2)
2 × 7 = 10 + 4
So, 2 × 7 = 14

Question 41.
6 × 6 = ____
Answer: 36

Explanation:
We can find the product by using the distributive property.
Rewrite 6 as 3 + 3
6 × 6 = 6 × (3 + 3)
6 × 6 = (6 × 3) + (6 × 3)
6 × 6 = 18 + 18
Thus 6 × 6 = 36

Question 42.
5 × 1 = _____
Answer: 5

Explanation:
We can find the product by using the distributive property.
Rewrite 5 as 2 + 3
5 × 1 = (2 + 3) × 1
5 × 1 = (2 × 1) + (3 × 1)
5 × 1 = 2 + 3
Thus 5 × 1 = 5

Question 43.
8 × 10 = ____
Answer: 80

Explanation:
We can find the product by using the distributive property.
Rewrite 10 as 5 + 5
8 × 10 = 8 × (5 + 5)
8 × 10 = (8 ×5) + (8 × 5)
8 × 10 = 40 + 40
So, 8 × 10 = 80

Question 44.
4 × 0 = ____
Answer: 0

Explanation:
We can find the product by using the distributive property.
Any number multiplied by 0 will be always 0.
So, 4 × 0 = 0

Question 45.
10 × 10 = ____
Answer: 100

Explanation:
We can find the product by using the distributive property.
Rewrite 10 as 5 + 5
10 × 10 = 10 × (5 + 5)
10 × 10 = (10 ×5) + (10 × 5)
10 × 10 = 50 + 50
Thus 10 × 10 = 100

Question 46.
Modeling Real Life
Newton has 4 bundles of balloons. There is 1 blue balloon, 2 purple balloons, and 1 green balloon in each bundle. How many balloons does he have in all?

Answer: 16 balloons

Explanation:
Given that,
Newton has 4 bundles of balloons.
There is 1 blue balloon, 2 purple balloons, and 1 green balloon in each bundle.
4 bundles = 1 blue balloon × 4 + 2 purple balloons × 4 + 1 green balloon × 4
= 4 blue ballon + 8 purple balloon + 4 green balloon
= 16 balloons
Thus there are 16 balloons in all.

3.8 Multiply Three Factors

Find the product
Question 47.
(4 × 2) × 2 = _____
Answer: 16

Explanation:
Given the expression as (4 × 2) × 2
First, multiply the factors in the bracket.
4 × 2 = 8
8 × 2 = 16
Thus (4 × 2) × 2 = 16

Question 48.
3 × (3 × 3) = ____
Answer: 27

Explanation:
Given the expression as 3 × (3 × 3)
First, multiply the factors in the bracket.
3 × 3 = 9
3 × 9 = 27
Thus 3 × (3 × 3) = 27

Question 49.
(3 × 3) × 6 = ____
Answer: 54

Explanation:
Given the expression as (3 × 3) × 6
First, multiply the factors in the bracket.
3 × 3 = 9
9 × 6 = 54
Thus (3 × 3) × 6 = 54

Question 50.
2 × (8 × 4) = _____
Answer: 64

Explanation:
Given the expression as 2 × (8 × 4)
First, multiply the factors in the bracket.
8 × 4 =32
2 × 32 = 64
Thus 2 × (8 × 4) = 64

Question 51.
(2 × 0) × 4 = _____
Answer: 0

Explanation:
Given the expression as (2 × 0) × 4
First, multiply the factors in the bracket.
2 × 0 = 0
0 × 4 = 0
Thus (2 × 0) × 4 = 0

Question 52.
0 × (8 × 5) = ____
Answer: 0

Explanation:
Given the expression as 0 × (8 × 5)
First, multiply the factors in the bracket.
8 × 5 = 40
0 × 40 = 0
Thus 0 × (8 × 5) = 0

3.9 More Problem Solving: Multiplication

Question 53.
You find 2 four-leaf clovers and 9 three-leaf clovers. What is the total number of leaves on the clovers you find?

Answer:
Given that,
You find 2 four-leaf clovers and 9 three-leaf clovers
2 four-leaf clovers = 4 + 4 = 8 leaves
9 three-leaf clovers = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 =27 leaves
8 + 27 = 35
Thus the total number of leaves on the cloves are 35.

Question 54.
A bakery sells croissants for $2 each. A tray contains 2 rows of 4 croissants. You buy 2 trays. How many croissants do you buy?

Answer: 16 croissants

Explanation:
Given that,
A bakery sells croissants for $2 each.
A tray contains 2 rows of 4 croissants.
2 × 4 = 8
You buy 2 trays.
8 × 2 = 16 croissants
Cost of croissants = 16 × $2 = $32
Thus I can buy 16 croissants.

Final Words:

I hope the solutions provided in Big Ideas Math Answers Grade 3 Chapter 3 More Multiplication Facts and Strategies are beneficial for all the students to overcome the difficulties. If you have any quieries regarding the topics grade 3 students can post the comments in the below comment section. Stay with us to get the solutions for all 3rd Std Bigideas Math Answers for all the chapters.