Tag: Eureka Math Grade 5 Module 4

Engage NY Eureka Math 5th Grade Module 4 Lesson 5 Answer Key

Question 1.
A total of 2 yards of fabric is used to make 5 identical pillows. How much fabric is used for each pillow?
Answer:
2/5 yard of fabric

Explanation:

5 units = 2 yards
1 unit = 2/5 yard
Hence each pillow uses 2/5 yard of fabric

Question 2.
An ice cream shop uses 4 pints of ice cream to make 6 sundaes. How many pints of ice cream are used for each sundae?
Answer:
4/6 or 2/3 pint of ice cream is used

Explanation:
6 units = 4 pints
1 unit = 4/6 pint or 2/3 pint. Hence 4/6 or 2/3 pint of ice cream is used in each sundae.

Question 3.
An ice cream shop uses 6 bananas to make 4 identical sundaes. How many bananas are used in each sundae? Use a tape diagram to show your work.
Answer:
6/4 or 1 1/2 bananas.

Explanation:

4 units = 6 bananas
1 unit = 6 ÷ 4
= 6/4 bananas
= 1 1/2 bananas

Question 4.
Julian has to read 4 articles for school. He has 8 nights to read them. He decides to read the same number of articles each night.
a. How many articles will he have to read per night?
Answer:
4/8 or 1/2 of an article each night.

Explanation:
8 units = 4 articles
1 unit  = 4÷8
= 4/8 article
= 1/2 article
Hence julian must read 4/8 or 1/2 of an article each night.

b. What fraction of the reading assignment will he read each night?
Answer:
1/8

Explanation:
As julian is reading for each of 8 nights he reads 1/8 of his total assignment each night.

Question 5.
40 students shared 5 pizzas equally. How much pizza will each student receive? What fraction of the pizza did each student receive?
Answer:
5/40

Explanation:
40 units = 5 pizzas
1 unit    = 5/40 pizza
Therefore each student gets 5/40 of 1 pizza.

Question 6.
Lillian had 2 two-liter bottles of soda, which she distributed equally between 10 glasses.
a. How much soda was in each glass? Express your answer as a fraction of a liter.
Answer:
4/10 liters of soda.

Explanation:
10 units = 4 liters
1 unit    = 4 ÷ 10 liters
= 4/10 liters
Hence each glass will have 4/10 liter of soda.

b. Express your answer as a decimal number of liters.
Answer:
4/10 = 4 tenths = 0.4

Explanation:
Each glass will have 0.4 liter of soda.

c. Express your answer as a whole number of milliliters.
Answer:
400 ml of soda

Explanation:
1 liter = 1000 ml
0.4 * 1000 = 400
0.4 l = 400 ml
Hence each glass will have 400 ml of soda.

Question 7.
The Calef family likes to paddle along the Susquehanna River.
a. They paddled the same distance each day over the course of 3 days, traveling a total of 14 miles. How many miles did they travel each day? Show your thinking in a tape diagram.
Answer:
4 2/3 miles each day.

Explanation:

3 units = 14 miles
1 unit  = 14 ÷ 3
= 14/3 miles
= 4 2/3 miles
Therefor, the calef’s travel 4 2/3 miles each day.

b. If the Calefs went half their daily distance each day but extended their trip to twice as many days, how far would they travel?
Answer:
14 miles

Explanation:
Half the distance
4 2/3
|
2 1/3    2 1/3
Twice as many days:           Distance traveled
3 days * 2 = 6 days             = 6 days at 2 1/3 miles
= 6 * 21/3
= 2 1/3 + 2 1/3 + 2 1/3 + 2 1/3 + 2 1/3 +2 1/3
=12 6/3
= 12 +2
= 14
Hence the calf family would still travel 14 miles.

Eureka Math Grade 5 Module 4 Lesson 5 Exit Ticket Answer Key

A grasshopper covered a distance of 5 yards in 9 equal hops. How many yards did the grasshopper travel on each hop?
a. Draw a picture to support your work.
Answer:
9/5 = 1 4/5 yards

Explanation:
5 yards = 9 hops
1 yard  = 9/5
= 1 4/5 yard

b. How many yards did the grasshopper travel after hopping twice?
Answer:
2/5 yards

Explanation:
5 yards = 2 hops
= 2/5 yards

Eureka Math Grade 5 Module 4 Lesson 5 Homework Answer Key

Question 1.
When someone donated 14 gallons of paint to Rosendale Elementary School, the fifth grade decided to use it to paint murals. They split the gallons equally among the four classes.
a. How much paint did each class have to paint their mural?
Answer:
3 1/2 gallons for each class

Explanation:
14 gallons ÷ 4 classes
14/4
3 2/4
3 1/2 gal for each class

b. How much paint will three classes use? Show your thinking using words, numbers, or pictures.
Answer:
10 1/2 gallons

Explanation:

c. If 4 students share a 30-square-foot wall equally, how many square feet of the wall will be painted by each student?
Answer:
7 1/2 sq ft

Explanation:
30 sq ft ÷ 4 students
30 / 4= 7 2/4 = 7 1/2 sq ft

d. What fraction of the wall will each student paint?
Answer:
7.5/30

Question 2.
Craig bought a 3-foot-long baguette and then made 4 equally sized sandwiches with it.
a. What portion of the baguette was used for each sandwich? Draw a visual model to help you solve this problem.
Answer:
3/4 ft for each sandwich

Explanation:
3 feet ÷ 4 sandwiches
Hence 3/4 ft for each sandwich

b. How long, in feet, is one of Craig’s sandwiches?
Answer:
3/4 ft or 0.75 feet

c. How many inches long is one of Craig’s sandwiches?
Answer:
3/4 = 9 inches

Question 3.
Scott has 6 days to save enough money for a $45 concert ticket. If he saves the same amount each day, what is the minimum amount he must save each day in order to reach his goal? Express your answer in dollars.
Answer:
$7.50 each day

Explanation:
$45 ÷ 6 days = 45/6
= 7 3/6
= 7 1/2 each day

Engage NY Eureka Math 5th Grade Module 4 Lesson 11 Answer Key

Eureka Math Grade 5 Module 4 Lesson 11 Problem Set Answer Key

Question 1.
Kim and Courtney share a 16-ounce box of cereal. By the end of the week, Kim has eaten \(\frac{3}{8}\) of the box, and Courtney has eaten \(\frac{1}{4}\) of the box of cereal. What fraction of the box is left?
Answer:
3/8 box is left.

Explanation:
Kim = 3/8
Courtney = 1/4 = 2/8
3/8 + 2/8 = 5/8
8/8 – 5/8 = 3/8

Question 2.
Mathilde has 20 pints of green paint. She uses \(\frac{2}{5}\) of it to paint a landscape and \(\frac{3}{10}\) of it while painting a clover. She decides that, for her next painting, she will need 14 pints of green paint. How much more paint will she need to buy?
Answer:
Mathilde needs 8 more pints for the next painting.

Explanation:
Landscape 2/5 * 20 = (2 *20)/5 = 8 pints
Clover 3/10 * 20 = (3*20)/10 = 6 pints
Used 8+6 = 14 pints
Remaining 20 – 14 = 6 pints
Needs 14 -6 = 8 pints
Hence, Mathilde needs 8 more pints for the next painting.

Question 3.
Jack, Jill, and Bill each carried a 48-ounce bucket full of water down the hill. By the time they reached the bottom, Jack’s bucket was only \(\frac{3}{4}\) full, Jill’s was \(\frac{2}{3}\) full, and Bill’s was \(\frac{1}{6}\) full. How much water did they spill altogether on their way down the hill?
Answer:
Together they split 68 oz of water.

Explanation:
Jack 1/4 * 48 = 48/4 = 12 oz
Jill 1/3 * 48 = 48/3 = 16 oz
Bill 5/6 * 48 = 240/6 = 40 oz
Total = 12 + 16 +40 = 68 oz
Therefore, Together they split 68 oz of water.

Question 4.
Mrs. Diaz makes 5 dozen cookies for her class. One-ninth of her 27 students are absent the day she brings the cookies. If she shares the cookies equally among the students who are present, how many cookies will each student get?
Answer:
Each student will get 2 1/2 cookies.

Explanation:
Absent 1/9
Present 8/9
Present
8/9 of 27 = 24
50 dozen cookies = 5 *12 = 60 cookies
60/24 = 5/2 = 2 1/2.
Hence each student will get 2 1/2 cookies.

Question 5.
Create a story problem about a fish tank for the tape diagram below. Your story must include a fraction.

Answer:
26.

Explanation:
2/6 of 84 = 1/3 * 84 = 84/3 = 26

Eureka Math Grade 5 Module 4 Lesson 11 Exit Ticket Answer Key

Use a tape diagram to solve.
\(\frac{2}{3}\) of 5
Answer:
2/3 of 5 = 10/3

Explanation:
2/3 of 5 = 10/3 = 3 1/3

Eureka Math Grade 5 Module 4 Lesson 11 Homework Answer Key

Question 1.
Jenny’s mom says she has an hour before it’s bedtime. Jenny spends \(\frac{1}{3}\) of the hour texting a friend and \(\frac{1}{4}\) of the time brushing her teeth and putting on her pajamas. She spends the rest of the time reading her book. How many minutes did Jenny read?
Answer:
25 minutes

Explanation:
1/3 of 60 minutes is 20 minutes so she spends 20 minutes texting
1/4 of 60 minutes is 15 so she spent 15 minutes brushing her teeth and putting on pajamas
i.e 35 minutes total so far, so you need to subtract 35 from 60 to get the answer of 25

Question 2.
A-Plus Auto Body is painting designs on a customer’s car. They had 18 pints of blue paint on hand. They used \(\frac{1}{2}\) of it for the flames and \(\frac{1}{3}\) of it for the sparks. They need 7\(\frac{3}{4}\) pints of blue paint to paint the next design. How many more pints of blue paint will they need to buy?
Answer:
 pints more of blue paint.

Explanation:
Get the LCM of the denominators 2 and 3 i.e is 6
18 pints/6 units = 3
The flames: 1/2 or half of 6 unit above, that is 3 + 3 + 3 = 9 pints
The sparks 1/3 = 2/6 or 2 of 6 unit above, that is 3 + 3 = 6 pints
So, the remainder is 18-9-6 = 3 pints
They needed  pints of blue paint to paint the next design.
7 3/4 – 3 = ?
(7 +3/4) – 3
7 – 3 + 3/4
4 3/4
Thus, they  pints more of blue paint.

Question 3.
Giovanna, Frances, and their dad each carried a 10-pound bag of soil into the backyard. After putting soil in the first flower bed, Giovanna’s bag was \(\frac{5}{8}\) full, Frances’s bag was \(\frac{2}{5}\) full, and their dad’s was\(\frac{3}{4}\) full. How many pounds of soil did they put in the first flower bed altogether?
Answer:
12.25 pounds of soil in the flower bed.

Explanation:
5/8 = 25/40
2/5 = 16/40
3/4 = 30/40
And next
25 * 10/40 = 6.25 pounds
16 * 10/40 = 4 pounds
30 *10/40 = 7.5 pounds
These are the amount that was left in the bag.
10 – 6.25 = 3.75
10 -4 = 6
10 – 7.5 = 2.5
All together they put 12.25 (3.75 + 6 + 2.5) pounds of soil in the flower bed.

Question 4.
Mr. Chan made 252 cookies for the Annual Fifth Grade Class Bake Sale. They sold\(\frac{3}{4}\) of them, and \(\frac{3}{9}\) of the remaining cookies were given to PTA. members. Mr. Chan allowed the 12 student helpers to divide the cookies that were left equally. How many cookies will each student get?
Answer:
Each student gets 3.5 cookies.

Explanation:
The number of cookies left = (3*252)/4 =189
Number of cookies left after sold = 252 -189 = 63
3/9 of the remaining cookies were given to PTA members.
The number of cookies left after giving tp PTA members = (3*63)/9 = 21
Number of cookies left after giving to P.T.A members = 63 – 21 = 42
Each student get cookies = 42/12 = 3.5
Therefore the 3.5 cookies each student gets.

Question 5.
Using the tape diagram below, create a story problem about a farm. Your story must include a fraction.

Answer:
63

Explanation:
3/5 of 105 =63

Engage NY Eureka Math 5th Grade Module 4 Lesson 22 Answer Key

Eureka Math Grade 5 Module 4 Lesson 22 Problem Set Answer Key

Question 1.
Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.
a. \(\frac{1}{2}\) as long as 8 meters = ______ meter(s)

Answer:
4 meters.

Explanation:
Given that \(\frac{1}{2}\) as long as 8 meters which is \(\frac{1}{2}\) × 8 = 4 meters.

b. 8 times as long as \(\frac{1}{2}\) meter = _______ meter(s)

Answer:
4 meters.

Explanation:
Given that \(\frac{1}{2}\) meter is 8 times as long, so 8 × \(\frac{1}{2}\) which is 4 meters.

Question 2.
Draw a tape diagram to model each situation in Problem 1, and describe what happened to the number of meters when it was multiplied by the scaling factor.
a.
Answer:
The scaling factor is less than 1, so the number of meters decreases.

Explanation:
The scaling factor is less than 1, so the number of meters decreases.

b.
Answer:
The scaling factor is greater than 1, so the number of meters increased.

Explanation:
The scaling factor is greater than 1, so the number of meters increased.

Question 3.
Fill in the blank with a numerator or denominator to make the number sentence true.
a. 7 × \(\frac{}{4}\) < 7

Answer:
7 × \(\frac{}{4}\) < 7.

Explanation:
Given that 7 × \(\frac{}{4}\) < 7, so here in the numerator we will place a number that is less than 4. So we will place 3 in the numerator which will be 7 × \(\frac{3}{4}\) < 7.

b. \(\frac{7}{}\) × 15 > 15

Answer:
\(\frac{7}{2}\) × 15 > 15

Explanation:
Given that \(\frac{7}{2}\) × 15 > 15, so here in the denominator we will place a number that is less than 7. So we will place 2 in the denominator which will be \(\frac{7}{2}\) × 15 > 15.

c. 3 × \(\frac{}{5}\) = 3

Answer:
3 × \(\frac{5}{5}\) = 3

Explanation:
Given that 3 × \(\frac{}{5}\) = 3, so to justify the answer we will place 5 in the numerator which is 3 × \(\frac{5}{5}\) = 3.

Question 4.
Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.

a.

Answer:
\(\frac{5}{2}\).

Explanation:

Multiplying by a fraction greater than 1 will make the product larger than the other factor.

b.

Answer:
\(\frac{1}{2}\).

Explanation:

Multiplying by a fraction less than 1 will make the product less than the other factor.

Question 5.
Johnny says multiplication always makes numbers bigger. Explain to Johnny why this isn’t true. Give more than one example to help him understand.

Answer:
4 times 0.5 equals 2.

Explanation:
Given that Johnny says multiplication always makes numbers bigger which is not true because if we multiply any number by a decimal number, we will make it smaller. Because if we multiply a number by something less than one, we will get something less than itself. This also works if you multiply a number by a fraction. For example, 4 times 0.5 equals 2 because you are getting half of the original number which is 4.

Question 6.
A company uses a sketch to plan an advertisement on the side of a building. The lettering on the sketch is \(\frac{3}{4}\) inch tall. In the actual advertisement, the letters must be 34 times as tall. How tall will the letters be on the building?

Answer:
The letters on the building would be 25 \(\frac{1}{2}\) inch.

Explanation:
Given that a company uses a sketch to plan an advertisement on the side of a building and lettering on the sketch is \(\frac{3}{4}\) inch tall and the letters must be 34 times as tall. So to find the height of the building, we will multiply 34 × \(\frac{3}{4}\) inch and the height of the letters on the building which is 34 × \(\frac{3}{4}\) inch
= \(\frac{104}{4}\) inch
= \(\frac{51}{2}\) inch
= 25 \(\frac{1}{2}\) inch.
Therefore the letters on the building would be 25 \(\frac{1}{2}\) inch.

Question 7.
Jason is drawing the floor plan of his bedroom. He is drawing everything with dimensions that are \(\frac{1}{12}\) of the actual size. His bed measures 6 ft by 3 ft, and the room measures 14 ft by 16 ft. What are the dimensions of his bed and room in his drawing?

Answer:
The dimensions of his room in his drawing are 1 \(\frac{1}{3}\) by1 \(\frac{1}{6}\) ft,
The dimensions of his bed in his drawing are \(\frac{1}{2}\) ft by \(\frac{1}{4}\) ft.

Explanation:
Given that Jason is drawing the floor plan of his bedroom and he is drawing everything with dimensions that are \(\frac{1}{12}\) of the actual size and his bed measures 6 ft by 3 ft, and the room measures 14 ft by 16 ft. So the dimensions of his room in his drawing are \(\frac{1}{12}\) of 16 ft and \(\frac{1}{12}\) of 14 ft which is
= \(\frac{1}{12}\) × 16
= \(\frac{4}{3}\)
= 1 \(\frac{1}{3}\)
\(\frac{1}{12}\) of 14 ft
= \(\frac{1}{12}\) × 14 ft
= \(\frac{7}{6}\)
= 1 \(\frac{1}{6}\) ft
So the dimensions of his room in his drawing are 1 \(\frac{1}{3}\) by1 \(\frac{1}{6}\) ft.
For his bed in his drawing are \(\frac{1}{12}\) of 6 ft by \(\frac{1}{12}\) of 3 which is
= \(\frac{1}{12}\) × 6
= \(\frac{1}{2}\) ft
\(\frac{1}{12}\) of 3
= \(\frac{1}{12}\) × 3
= \(\frac{1}{4}\) ft.
So the dimensions of his bed in his drawing are \(\frac{1}{2}\) ft by \(\frac{1}{4}\) ft.

Eureka Math Grade 5 Module 4 Lesson 22 Exit Ticket Answer Key

Fill in the blank to make the number sentences true. Explain how you know.
a. \(\frac{}{3}\) × 11 ˃ 11

Answer:
\(\frac{4}{3}\) × 11 ˃ 11.

Explanation:
Given that \(\frac{}{3}\) × 11 ˃ 11, so here in the numerator we will place a number that is greater than 3. So we will place 4 in the numerator which will be \(\frac{4}{3}\) × 11 ˃ 11.

b. 5 × \(\frac{}{8}\) ˂ 5

Answer:
5 × \(\frac{5}{8}\) ˂ 5.

Explanation:
Given that 5 × \(\frac{}{8}\) ˂ 5, so here in the numerator we will place a number that is less than 8. So we will place 5 in the numerator which will be 5 × \(\frac{5}{8}\) ˂ 5.

c. 6 × \(\frac{2}{}\) = 6

Answer:
6 × \(\frac{2}{2}\) = 6

Explanation:
Given that 6 × \(\frac{2}{2}\) = 6, so to justify the answer we will place 2 in the numerator which is 6 × \(\frac{2}{2}\) = 6

Eureka Math Grade 5 Module 4 Lesson 22 Homework Answer Key

Question 1.
Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.
a. \(\frac{1}{3}\) as long as 6 meters = ______ meter(s)

Answer:
2 meters.

Explanation:
Given that \(\frac{1}{3}\) as long as 6 meters which is \(\frac{1}{3}\) × 6 = 2 meters.

b. 6 times as long as \(\frac{1}{3}\) meter = ______ meter(s)

Answer:
2 meters.

Explanation:
Given that \(\frac{1}{3}\) meter is 6 times as long, so 6 × \(\frac{1}{3}\) which is2 meters.

Question 2.
Draw a tape diagram to model each situation in Problem 1, and describe what happened to the number of meters when it was multiplied by the scaling factor.
a.

Answer:
The scaling factor is less than 1, so the number of meters decreases.

Explanation:
The scaling factor is less than 1, so the number of meters decreases.

b.

Answer:
The scaling factor is greater than 1, so the number of meters increased.

Explanation:
The scaling factor is greater than 1, so the number of meters increased.

Question 3.
Fill in the blank with a numerator or denominator to make the number sentence true.
a. 5 × \(\frac{}{3}\) ˃ 5

Answer:
5 × \(\frac{2}{3}\) ˃ 5.

Explanation:
Given that 5 × \(\frac{4}{3}\) ˃ 5, so here in the numerator, we will place a number that is greater than 3. So we will place 4 in the numerator which will be 5 × \(\frac{4}{3}\) ˃ 5.

b. \(\frac{6}{}\) × 12 ˂ 12

Answer:
\(\frac{6}{}\) × 12 ˂ 12.

Explanation:
Given that \(\frac{6}{7}\) × 12 ˂ 12, so here in the numerator, we will place a number that is greater than 6. So we will place 7 in the numerator which will be \(\frac{6}{7}\) × 12 ˂ 12.

c. 4 × \(\frac{}{5}\) = 4

Answer:
4 × \(\frac{5}{5}\) = 4

Explanation:
Given that 4 × \(\frac{5}{5}\) = 4, so to justify the answer we will place 5 in the numerator which is 4 × \(\frac{5}{5}\) = 4.

Question 4.
Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.

a.

Answer:
\(\frac{5}{4}\).

Explanation:
Multiplying by a fraction greater than 1 will make the product larger than the other factor.

b.

Answer:
\(\frac{1}{2}\).

Explanation:
Multiplying by a fraction less than 1 will make the product less than the other factor.

Question 5.
Write a number in the blank that will make the number sentence true.
a. 3 × _____ ˂ 1

Answer:
3 × \(\frac{1}{4}\) < 1.

Explanation:
To make the number sentence true we will place the number which is less than \(\frac{1}{3}\), so we will place \(\frac{1}{4}\) which will be less than 1. So the expression will be 3 × \(\frac{1}{4}\) < 1.

b. Explain how multiplying by a whole number can result in a product less than 1.

Answer:
When a positive whole number is multiplied by a fraction between 0 and 1, the product is less than the whole number. When a number greater than 1 is multiplied by a number greater than 1, the product is greater than both numbers.

Question 6.
In a sketch, a fountain is drawn \(\frac{1}{4}\) yard tall. The actual fountain will be 68 times as tall. How tall will the
fountain be?

Answer:
The actual height of the fountain is 17 yards.

Explanation:
Given that a fountain is drawn \(\frac{1}{4}\) yard tall and the actual fountain will be 68 times as tall. So the actual height of the fountain is \(\frac{1}{4}\) × 68 which is 17 yards.

Question 7.
In blueprints, an architect’s firm drew everything \(\frac{1}{24}\) of the actual size. The windows will actually measure 4 ft by 6 ft and doors measure 12 ft by 8 ft. What are the dimensions of the windows and the doors in the drawing?

Answer:
The dimensions of the windows are 2 in by 3 in.
The dimensions of the windows are 6 in by 4 in.

Explanation:
Given that an architect’s firm drew everything \(\frac{1}{24}\) of the actual size and the windows will actually measure 4 ft by 6 ft, so the dimensions of the length of the windows are \(\frac{1}{24}\) × 4 which is \(\frac{1}{6}\) ft, so in inch, it will be \(\frac{1}{6}\) × 12 which is 2 in. And the width of the windows is \(\frac{1}{24}\) × 6 which is \(\frac{1}{4}\), so in inch, it will be \(\frac{1}{4}\) × 12 which is 3 in. So the dimensions of the windows are 2 in by 3 in. Given that the measures of the door are 12 ft by 8 ft, so the dimensions of the length of the doors are \(\frac{1}{24}\) × 12 which is \(\frac{1}{2}\) ft, so in inch, it will be \(\frac{1}{2}\) × 12 which is 6 in. And the width of the windows is \(\frac{1}{24}\) × 8 which is \(\frac{1}{3}\), so in inch, it will be \(\frac{1}{3}\) × 12 which is 4 in.

Engage NY Eureka Math 5th Grade Module 4 Lesson 9 Answer Key

Eureka Math Grade 5 Module 4 Lesson 9 Problem Set Answer Key

Question 1.
Convert. Show your work using a tape diagram or an equation. The first one is done for you.
a. \(\frac{1}{2}\) yard = 1\(\frac{1}{2}\) feet
\(\frac{1}{2}\) yard = \(\frac{1}{2}\) × 1 yard
= \(\frac{1}{2}\) × 3 feet
= \(\frac{3}{2}\) feet
= 1\(\frac{1}{2}\) feet

b. \(\frac{1}{3}\) foot = ________ inches
\(\frac{1}{3}\) foot = \(\frac{1}{3}\) × 1 foot
= \(\frac{1}{3}\) × 12 inches
=

Answer:
4 inches

Explanation:
1/3 foot = 1/3 * 1 foot
= 1/3 * 12 inches
= 12/3
= 4 inches

c. \(\frac{5}{6}\) year = ________ months
Answer:
10 months

Explanation:
5/6 year = 5/6 * 1 year
= 5/6 * 12 months
= 60/6 months
= 10 months

d. \(\frac{4}{5}\) meter = ________ centimeters
Answer:
80 centimeters

Explanation:
4/5 m = 4/5 *1m
= 4/5 * 100 cm
= 400/5
= 80 cm

e. \(\frac{2}{3}\) hour = ________ minutes
Answer:
40 minutes

Explanation:
2/3 hr = 2/3 * 1 hr
= 2/3 * 60
= 120/3 min
= 40 min

f. \(\frac{3}{4}\) yard = ________ inches
Answer:
27 inches

Explanation:
3/4 yard = 3/4 * 1 yd
= 3/4 * 36 inches
= 108/4 inches
= 27 inches

Question 2.
Mrs. Lang told her class that the class’s pet hamster is \(\frac{1}{4}\) ft in length. How long is the hamster in inches?
Answer:
The hamster is 3 inches long

Explanation:
1/4 ft = 1/4 * 1 ft
= 1/4 *12 inc
= 3 inc

Question 3.
At the market, Mr. Paul bought \(\frac{7}{8}\) lb of cashews and \(\frac{3}{4}\) lb of walnuts. How many ounces of cashews did Mr. Paul buy?
Answer:
14 ounces of cashews.

Explanation:
7/8 lb = 7/8 *1 lb
= 7/8 * 16 oz
= 112 oz/8
= 14 oz
Hence Mr paul bought 14 ounces of cashews.

b. How many ounces of walnuts did Mr. Paul buy?
Answer:
12 ounces of walnuts.

Explanation:
3/4 lb = 3/4 * 1 lb
= 3/4 * 16 oz
= 48/4 oz
= 12 oz.
Hence Mr paul bought 12 ounces of walnuts.

c. How many more ounces of cashews than walnuts did Mr. Paul buy?
Answer:
2 ounces.

Explanation:
14 oz – 12 oz = 2 oz
Mr.paul bought 2 ounces more cashews than walnuts.

d. If Mrs. Toombs bought 1\(\frac{1}{2}\) pounds of pistachios, who bought more nuts, Mr. Paul or Mrs. Toombs? How many ounces more?
Answer:
2 ounces more

Explanation:
Mr paul = 14 oz + 12 oz = 26 oz
Mrs. Toombs = 1 1/2 lb = 3/2 lb = 3/2 * 1 lb
= 3/2 * 16 oz
= 48/2
= 24 oz
So 26 oz – 24 oz = 2oz.
Hence Mr. paul bought more nuts than Mrs. Toombs. He bought 2 ounces more than she did.

Question 4.
A jewelry maker purchased 20 inches of gold chain. She used \(\frac{3}{8}\) of the chain for a bracelet. How many inches of gold chain did she have left?
Answer:
She had 12 1/2 inches left.

Explanation:
8 units = 20
1 unit = 20/8
= 2 4/8
5 units = 2 4/8 + 2 4/8 + 2 4/8 + 2 4/8 + 2 4/8
= 10 20/8
= 12 4/8
= 12 1/2

Eureka Math Grade 5 Module 4 Lesson 9 Exit Ticket Answer Key

Question 1.
Express 36 minutes as a fraction of an hour: 36 minutes = _______ hour
Answer:
3/5

Explanation:
1 hr =60minutes
take 36min /60 min=18/30
=9/15=3/5

Question 2.
Solve.
a. \(\frac{2}{3}\) feet = _______ inches
Answer:
2 inches

Explanation:
2/3 feet = 2/3 * 12 inches
= (2*12)/12
= 24/12
= 2 inches

b. \(\frac{2}{5}\) m = _______ cm
Answer:
40 cm

Explanation:
2/5 m = 2/5 * 100 cm
= (2*100)/5
= 40 cm

c. \(\frac{5}{6}\) year = _______ months
Answer:
10 months

Explanation:
1 year = 12 months
5/6 year = 5/6 * 12
= (5*12)/6
= 10

Eureka Math Grade 5 Module 4 Lesson 9 Homework Answer Key

Question 1.
Convert. Show your work using a tape diagram or an equation. The first one is done for you.
a. \(\frac{1}{4}\) yard = 9 inches
\(\frac{1}{4}\) yard = \(\frac{1}{4}\) × 1 yard
= \(\frac{1}{4}\) × 36 inches
= \(\frac{36}{4}\) inches
= 9 inches

b. \(\frac{1}{6}\) foot = ________ inches
\(\frac{1}{6}\) foot = \(\frac{1}{6}\) × 1 foot
= \(\frac{1}{6}\) × 12 inches

Answer:
2 inches

Explanation:
1/6 * 12 =2 inches

c. \(\frac{3}{4}\) year = ________ months
Answer:
9 inches

Explanation:
3/4 year = 3/4 * 12 months
= (3*12)/4
= 9 inches

d. \(\frac{3}{5}\) meter = ________ centimeters
Answer:
60 centimeters

Explanation:
3/5 m = 3/5 * 100
= (3*100)/5
= 60 centimeters

e. \(\frac{5}{12}\) hour = ________ minutes
Answer:
25 minutes

Explanation:
5/12 hr = 5/12 * 60 minutes
= (5*60)/12
= 25 minutes

f. \(\frac{2}{3}\) yard = ________ inches
Answer:
24 inches

Explanation:
1 yard = 36 inches
2/3 yard = 2/3 * 36 inches
= (2*36)/3
= 24 inches

Question 2.
Michelle measured the length of her forearm. It was \(\frac{3}{4}\) of a foot. How long is her forearm in inches?
Answer:
The length of Michelle’s forearm is 9 inches

Explanation:
1 ft = 12 in
length of Michelle’s forearm was 3/4 of a foot
Now convert to inches
3/4 ft = 3/4 * 12
= 9 inc
Therefore the length of Michelle’s forearm is 9 inches.

Question 3.
At the market, Ms. Winn bought \(\frac{3}{4}\) lb of grapes and \(\frac{5}{8}\) lb of cherries.
a. How many ounces of grapes did Ms. Winn buy?
Answer:
12 ounces of grapes

Explanation:
3/4 lb = 3/4 * ounces
= 3/4 * 1 lb
=  3/4 * 16 ounces
= 12 ounces

b. How many ounces of cherries did Ms. Winn buy?
Answer:
10 ounces of cherries

Explanation:
5/8 lb = 5/8 * 1 lb
= 5/8 * 16 ounces
= 10 ounces

c. How many more ounces of grapes than cherries did Ms. Winn buy?
Answer:
There are 12 ounces of grapes and 10 ounces of cherries. Hence by doing the difference for both we can get more ounces of grapes than cherries.
So 12 -10 = 2 ounces. Hence 2 more ounces of grapes than cherries.

d. If Mr. Phillips bought 1\(\frac{3}{4}\) pounds of raspberries, who bought more fruit, Ms. Winn or Mr. Phillips? How many ounces more?
Answer:
Explanation:
1 3/4 pounds = 7/4 pounds
1 pound = 16 oz
7/4 pounds = 7/4 * 16
= 21
Ms.Winn bought 22 ounces of fruits and Mr. Phillips bought 21 ounces of fruit. Therefore, 1 ounce more fruits are there.

Question 4.
A gardener has 10 pounds of soil. He used \(\frac{5}{8}\) of the soil for his garden. How many pounds of soil did he use in the garden? How many pounds did he have left?
Answer:
3 3/4

Explanation:
5/8 *10
50/8
6 2/8
6 1/4
10 -6 1/4
Hence 3 3/4 pounds have left.

Engage NY Eureka Math 5th Grade Module 4 Lesson 13 Answer Key

Eureka Math Grade 5 Module 4 Lesson 13 Problem Set Answer Key

Solve. Draw a rectangular fraction model to show your thinking. Then, write a multiplication sentence. The first one has been done for you.

a. Half of \(\frac{1}{4}\) pan of brownies = \(\frac{1}{4}\) pan of brownies.
\(\frac{1}{2}\) × \(\frac{1}{4}\) = \(\frac{1}{8}\)

b. Half of \(\frac{1}{3}\) pan of brownies = _____ pan of brownies.

Answer:
\(\frac{1}{6}\) pan of brownies.

Explanation:
Given that there is half of \(\frac{1}{3}\) pan of brownies which is \(\frac{1}{2}\) × \(\frac{1}{3}\) = \(\frac{1}{6}\) pan of brownies.

c. A fourth of \(\frac{1}{3}\) pan of brownies = _____ pan of brownies.

Answer:
\(\frac{1}{12}\) pan of brownies.

Explanation:
Given that there is half of \(\frac{1}{3}\) pan of brownies which is \(\frac{1}{4}\) × \(\frac{1}{3}\) = \(\frac{1}{12}\) pan of brownies.

d. \(\frac{1}{4}\) of \(\frac{1}{4}\)

Answer:
\(\frac{1}{16}\).

Explanation:
Given that \(\frac{1}{4}\) of \(\frac{1}{4}\) which is \(\frac{1}{4}\) × \(\frac{1}{4}\) = \(\frac{1}{16}\).

e. \(\frac{1}{2}\) of \(\frac{1}{6}\)

Answer:
\(\frac{1}{12}\).

Explanation:
Given that \(\frac{1}{2}\) of \(\frac{1}{6}\) which is \(\frac{1}{2}\) × \(\frac{1}{6}\) = \(\frac{1}{12}\).

Question 2.
Draw rectangular fraction models of 3 × \(\frac{1}{4}\) and \(\frac{1}{3}\) × \(\frac{1}{4}\). Compare multiplying a number by 3 and by 1 third.

Answer:
\(\frac{3}{4}\) > \(\frac{1}{12}\).

Explanation:
Given the equations are 3 × \(\frac{1}{4}\) which is \(\frac{3}{4}\) and \(\frac{1}{3}\) × \(\frac{1}{4}\) which is \(\frac{1}{12}\). And \(\frac{3}{4}\) > \(\frac{1}{12}\).
 

Question 3.
\(\frac{1}{2}\) of Ila’s workspace is covered in paper. \(\frac{1}{3}\) of the paper is covered in yellow sticky notes. What fraction of Ila’s workspace is covered in yellow sticky notes? Draw a picture to support your answer.

Answer:
\(\frac{1}{6}\)

Explanation:
Given that \(\frac{1}{2}\) of Ila’s workspace is covered in paper and \(\frac{1}{3}\) of the paper is covered in yellow sticky notes, so the fraction of Ila’s workspace is covered in yellow sticky notes is \(\frac{1}{2}\) × \(\frac{1}{3}\) which is \(\frac{1}{6}\).

Question 4.
A marching band is rehearsing in rectangular formation. \(\frac{1}{5}\) of the marching band members play percussion instruments. \(\frac{1}{2}\) of the percussionists play the snare drum. What fraction of all the band members play the snare drum?

Answer:
The fraction of all the band members who play the snare drum is \(\frac{1}{10}\).

Explanation:
Given that a \(\frac{1}{5}\) of the marching band members play percussion instruments and \(\frac{1}{2}\) of the percussionists play the snare drum, so the fraction of all the band members play the snare drum is \(\frac{1}{2}\) of \(\frac{1}{5}\) which is \(\frac{1}{2}\) × \(\frac{1}{5}\) = \(\frac{1}{10}\).

Question 5.
Marie is designing a bedspread for her grandson’s new bedroom. \(\frac{2}{3}\) of the bedspread is covered in race cars, and the rest is striped. \(\frac{1}{4}\) of the stripes are red. What fraction of the bedspread is covered in red stripes?

Answer:
The fraction of the bedspread is covered in red stripes is \(\frac{1}{12}\).

Explanation:
Given that \(\frac{2}{3}\) of the bedspread is covered in race cars, and the rest is stripped and \(\frac{1}{4}\) of the stripes are red. The striped bedspread would be 1 – \(\frac{2}{3}\) which is \(\frac{1}{3}\).
So the fraction of the bedspread is covered in red stripes is \(\frac{1}{3}\) × \(\frac{1}{4}\) which is \(\frac{1}{12}\).

Eureka Math Grade 5 Module 4 Lesson 13 Exit Ticket Answer Key

Question 1.
Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.

\(\frac{1}{3}\) × \(\frac{1}{3}\) =

Answer:
\(\frac{1}{9}\).

Explanation:
Given that \(\frac{1}{3}\) × \(\frac{1}{3}\) which is \(\frac{1}{9}\).

Question 2.
Ms. Sheppard cuts \(\frac{1}{2}\) of a piece of construction paper. She uses \(\frac{1}{6}\) of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?

Answer:
The fraction of the sheet of paper does she use to make the flower is \(\frac{1}{12}\).

Explanation:
Given that Ms. Sheppard cuts \(\frac{1}{2}\) of a piece of construction paper and she uses \(\frac{1}{6}\) of the piece to make a flower, so the fraction of the sheet of paper does she use to make the flower is \(\frac{1}{2}\) × \(\frac{1}{6}\) which is \(\frac{1}{12}\).

Eureka Math Grade 5 Module 4 Lesson 13 Homework Answer Key

Solve. Draw a rectangular fraction model to show your thinking.

a. Half of \(\frac{1}{2}\) cake = _____ cake.

Answer:
\(\frac{1}{4}\).

Explanation:
Given that half of \(\frac{1}{2}\) cake which is \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{1}{4}\).

b. One-third of \(\frac{1}{2}\) cake = _____ cake.

Answer:
\(\frac{1}{6}\).

Explanation:
Given that One-third of \(\frac{1}{2}\) cake which is \(\frac{1}{3}\) × \(\frac{1}{2}\) = \(\frac{1}{6}\).

c. \(\frac{1}{4}\) of \(\frac{1}{2}\)

Answer:
\(\frac{1}{8}\).

Explanation:
Given that latex]\frac{1}{4}[/latex] of \(\frac{1}{2}\) which is latex]\frac{1}{4}[/latex] × \(\frac{1}{2}\) = \(\frac{1}{8}\).

d. \(\frac{1}{2}\) × \(\frac{1}{5}\)

Answer:
\(\frac{1}{10}\).

Explanation:
Given that latex]\frac{1}{2}[/latex] of \(\frac{1}{5}\) which is latex]\frac{1}{2}[/latex] × \(\frac{1}{5}\) = \(\frac{1}{10}\).

e. \(\frac{1}{3}\) × \(\frac{1}{3}\)

Answer:
\(\frac{1}{9}\).

Explanation:
Given that latex]\frac{1}{3}[/latex] of \(\frac{1}{3}\) which is latex]\frac{1}{3}[/latex] × \(\frac{1}{3}\) = \(\frac{1}{9}\).

f. \(\frac{1}{4}\) × \(\frac{1}{3}\)

Answer:
\(\frac{1}{12}\).

Explanation:
Given that latex]\frac{1}{4}[/latex] of \(\frac{1}{3}\) which is latex]\frac{1}{4}[/latex] × \(\frac{1}{3}\) = \(\frac{1}{12}\).

Question 2.
Noah mows \(\frac{1}{2}\) of his property and leaves the rest wild. He decides to use \(\frac{1}{5}\) of the wild area for a vegetable garden. What fraction of the property is used for the garden? Draw a picture to support your answer.

Answer:
The fraction of the property is used for the garden is \(\frac{1}{10}\).

Explanation:
Given that Noah mows \(\frac{1}{2}\) of his property and leaves the rest wild and he decides to use \(\frac{1}{5}\) of the wild area for a vegetable garden, so the fraction of the property is used for the garden is \(\frac{1}{2}\) × \(\frac{1}{5}\) which is \(\frac{1}{2}\) × \(\frac{1}{5}\) = \(\frac{1}{10}\).

Question 3.
Fawn plants \(\frac{2}{3}\) of the garden with vegetables. Her son plants the remainder of the garden. He decides to use \(\frac{1}{2}\) of his space to plant flowers, and in the rest, he plants herbs. What fraction of the entire garden is planted in flowers? Draw a picture to support your answer.

Answer:
The fraction of the entire garden is planted in flowers is \(\frac{1}{6}\).

Explanation:
Given that fawn plants \(\frac{2}{3}\) of the garden with vegetables and her son plants the remainder of the garden and he decides to use \(\frac{1}{2}\) of his space to plant flowers, and in the rest, he plants herbs. So her son gets \(\frac{2}{3}\) × \(\frac{1}{2}\) which is \(\frac{1}{3}\). So the fraction of the entire garden is planted in flowers is \(\frac{1}{2}\) × \(\frac{1}{3}\) which is \(\frac{1}{6}\).

Question 4.
Diego eats \(\frac{1}{5}\) of a loaf of bread each day. On Tuesday, Diego eats \(\frac{1}{4}\) of the day’s portion before lunch. What fraction of the whole loaf does Diego eat before lunch on Tuesday? Draw a rectangular fraction model to support your thinking.

Answer:
The fraction of the whole loaf does Diego eat before lunch on Tuesday is \(\frac{1}{20}\).

Explanation:
Given that Diego eats \(\frac{1}{5}\) of a loaf of bread each day and on tuesday, Diego eats \(\frac{1}{4}\) of the day’s portion before lunch. So the fraction of the whole loaf does Diego eat before lunch on Tuesday is \(\frac{1}{5}\) × \(\frac{1}{4}\) which is \(\frac{1}{20}\).

Engage NY Eureka Math 5th Grade Module 4 Lesson 21 Answer Key

Eureka Math Grade 5 Module 4 Lesson 21 Sprint Answer Key

A
Multiply Decimals

Answer:

Question 1.
3 × 2 =

Answer:
3 × 2 = 6.

Explanation:
By multiplication 3 by 2, we will get the result as 6

Question 2.
3 × 0.2 =

Answer:
3 × 0.2 = 0.6.

Explanation:
By multiplication 3 by 0.2, we will get the result as 0.6.

Question 3.
3 × 0.02 =

Answer:
3 × 0.02 = 0.06.

Explanation:
By multiplication 3 by 0.02, we will get the result as 0.06.

Question 4.
3 × 3 =

Answer:
3 × 3 = 9.

Explanation:
By multiplication 3 by 3, we will get the result as 9.

Question 5.
3 × 0.3 =

Answer:
3 × 0.3 = 0.9.

Explanation:
By multiplication 3 by 0.3, we will get the result as 0.9.

Question 6.
3 × 0.03 =

Answer:
3 × 0.03 = 0.09.

Explanation:
By multiplication 3 by 0.03, we will get the result as 0.09.

Question 7.
2 × 4 =

Answer:
2 × 4 = 8.

Explanation:
By multiplication 2 by 4, we will get the result as 8.

Question 8.
2 × 0.4 =

Answer:
2 × 0.4 = 0.8.

Explanation:
By multiplication 2 by 0.4, we will get the result as 0.8.

Question 9.
2 × 0.04 =

Answer:
2 × 0.04 = 0.08.

Explanation:
By multiplication 2 by 0.04, we will get the result as 0.08.

Question 10.
5 × 3 =

Answer:
5 × 3 = 15.

Explanation:
By multiplication 5 by 3, we will get the result as 15.

Question 11.
5 × 0.3 =

Answer:
5 × 0.3 = 1.5.

Explanation:
By multiplication 5 by 0.3, we will get the result as 1.5.

Question 12.
5 × 0.03 =

Answer:
5 × 0.03 = 0.15.

Explanation:
By multiplication 5 by 0.03, we will get the result as 0.15.

Question 13.
7 × 2 =

Answer:
7 × 2 = 14.

Explanation:
By multiplication 7 by 2, we will get the result as 14.

Question 14.
7 × 0.2 =

Answer:
7 × 0.2 = 1.4.

Explanation:
By multiplication 7 by 0.2, we will get the result as 1.4.

Question 15.
7 × 0.02 =

Answer:
7 × 0.02 = 0.14.

Explanation:
By multiplication 7 by 0.02, we will get the result as 0.14.

Question 16.
4 × 3 =

Answer:
4 × 3 = 12.

Explanation:
By multiplication 4 by 3, we will get the result as 12.

Question 17.
4 × 0.3 =

Answer:
4 × 0.3 = 1.2.

Explanation:
By multiplication 4 by 0.3, we will get the result as 1.2.

Question 18.
0.4 × 3 =

Answer:
0.4 × 3 = 1.2.

Explanation:
By multiplication 0.4 by 3, we will get the result as 1.2.

Question 19.
0.4 × 0.3 =

Answer:
0.4 × 0.3 = 0.12.

Explanation:
By multiplication 0.4 by 0.3, we will get the result as 0.12.

Question 20.
0.4 × 0.03 =

Answer:
0.4 × 0.03 = 0.012.

Explanation:
By multiplication 5 by 3, we will get the result as 0.012.

Question 21.
0.3 × 0.04 =

Answer:
0.3 × 0.04 = 0.012.

Explanation:
By multiplication 0.3 by 0.04, we will get the result as 0.012.

Question 22.
6 × 2 =

Answer:
6 × 2 = 12.

Explanation:
By multiplication 6 by 2, we will get the result as 12.

Question 23.
0.6 × 2 =

Answer:
0.6 × 2 = 1.2.

Explanation:
By multiplication 0.6 by 2, we will get the result as 1.2.

Question 24.
0.6 × 0.2 =

Answer:
0.6 × 0.2 = 0.12.

Explanation:
By multiplication 0.6 by 0.2, we will get the result as 0.12.

Question 25.
0.6 × 0.02 =

Answer:
0.6 × 0.02 = 0.012.

Explanation:
By multiplication 0.6 by 0.02, we will get the result as 0.012.

Question 26.
0.2 × 0.06 =

Answer:
0.2 × 0.06 = 0.012.

Explanation:
By multiplication 0.2 by 0.06, we will get the result as 0.012.

Question 27.
5 × 7 =

Answer:
5 × 7 = 35.

Explanation:
By multiplication 5 by 7, we will get the result as 35.

Question 28.
0.5 × 7 =

Answer:
0.5 × 7 = 3.5.

Explanation:
By multiplication 0.5 by 7, we will get the result as 3.5.

Question 29.
0.5 × 0.7 =

Answer:
0.5 × 0.7 = 0.35.

Explanation:
By multiplication 0.5 by 0.7, we will get the result as 0.35.

Question 30.
0.5 × 0.07 =

Answer:
0.5 × 0.07 = 0.035.

Explanation:
By multiplication 0.5 by 0.07, we will get the result as 0.035.

Question 31.
0.7 × 0.05 =

Answer:
0.7 × 0.05 = 0.035.

Explanation:
By multiplication 0.7 by 0.05, we will get the result as 0.035.

Question 32.
2 × 8 =

Answer:
2 × 8 = 16.

Explanation:
By multiplication 2 by 8, we will get the result as 16.

Question 33.
9 × 0.2 =

Answer:
9 × 0.2 = 1.8.

Explanation:
By multiplication 9 by 0.2, we will get the result as 1.8.

Question 34.
3 × 7 =

Answer:
3 × 7 = 21.

Explanation:
By multiplication 3 by 7, we will get the result as 21.

Question 35.
8 × 0.03 =

Answer:
8 × 0.03 = 0.24.

Explanation:
By multiplication 8 by 0.03, we will get the result as 0.24.

Question 36.
4 × 6 =

Answer:
4 × 6 = 24.

Explanation:
By multiplication 4 by 6, we will get the result as 24.

Question 37.
0.6 × 7 =

Answer:
0.6 × 7 = 4.2.

Explanation:
By multiplication 0.6 by 7, we will get the result as 4.2.

Question 38.
0.7 × 0.7 =

Answer:
0.7 × 0.7 = 0.49.

Explanation:
By multiplication 0.7 by 0.7, we will get the result as 0.49.

Question 39.
0.8 × 0.06 =

Answer:
0.8 × 0.06 = 0.048.

Explanation:
By multiplication 0.8 by 0.06, we will get the result as 0.048.

Question 40.
0.09 × 0.6 =

Answer:
0.09 × 0.6 = 0.054.

Explanation:
By multiplication 0.09 by 0.6, we will get the result as 0.054.

Question 41.
6 × 0.8 =

Answer:
6 × 0.8 = 4.8.

Explanation:
By multiplication 6 by 0.8, we will get the result as 4.8.

Question 42.
0.7 × 0.9 =

Answer:
0.7 × 0.9 = 0.63.

Explanation:
By multiplication 0.7 by 0.9, we will get the result as 0.63.

Question 43.
0.08 × 0.8 =

Answer:
0.08 × 0.8 = 0.064.

Explanation:
By multiplication 0.08 by 0.8, we will get the result as 0.064.

Question 44.
0.9 × 0.08 =

Answer:
0.9 × 0.08 = 0.072.

Explanation:
By multiplication 0.9 by 0.08, we will get the result as 0.072.

B
Multiply Decimals

Question 1.
4 × 2 =

Answer:
4 × 2 = 8.

Explanation:
By multiplication 4 by 2, we will get the result as 8.

Question 2.
4 × 0.2 =

Answer:
4 × 0.2 = 0.8.

Explanation:
By multiplication 4 by 0.2, we will get the result as 0.8.

Question 3.
4 × 0.02 =

Answer:
4 × 0.02 = 0.08.

Explanation:
By multiplication 4 by 2, we will get the result as 0.08.

Question 4.
2 × 3 =

Answer:
2 × 3 = 6.

Explanation:
By multiplication 2 by 3, we will get the result as 6.

Question 5.
2 × 0.3 =

Answer:
2 × 0.3 = 0.6.

Explanation:
By multiplication 2 by 0.3, we will get the result as 0.6.

Question 6.
2 × 0.03 =

Answer:
2 × 0.03 = 0.06.

Explanation:
By multiplication 2 by 0.03, we will get the result as 0.06.

Question 7.
3 × 3 =

Answer:
3 × 3 = 9.

Explanation:
By multiplication 3 by 3, we will get the result as 9.

Question 8.
3 × 0.3 =

Answer:
3 × 0.3 = 0.9.

Explanation:
By multiplication 3 by 0.3, we will get the result as 0.9.

Question 9.
3 × 0.03 =

Answer:
3 × 0.03 = 0.09.

Explanation:
By multiplication 3 by 0.03, we will get the result as 0.09.

Question 10.
4 × 3 =

Answer:
4 × 3 = 12.

Explanation:
By multiplication 4 by 3, we will get the result as 12.

Question 11.
4 × 0.3 =

Answer:
4 × 3 = 12.

Explanation:
By multiplication 4 by 3, we will get the result as 12.

Question 12.
4 × 0.03 =

Answer:
4 × 0.03 = 0.12.

Explanation:
By multiplication 4 by 0.03, we will get the result as 012.

Question 13.
9 × 2 =

Answer:
9 × 2 = 18.

Explanation:
By multiplication 9 by 2, we will get the result as 18.

Question 14.
9 × 0.2 =

Answer:
9 × 0.2 = 1.8.

Explanation:
By multiplication 9 by 0.2, we will get the result as 1.8.

Question 15.
9 × 0.02 =

Answer:
9 × 0.02 = 0.18.

Explanation:
By multiplication 9 by 0.02, we will get the result as 0.18.

Question 16.
5 × 3 =

Answer:
5 × 3 = 15.

Explanation:
By multiplication 5 by 3, we will get the result as 15.

Question 17.
5 × 0.3 =

Answer:
5 × 0.3 = 1.5.

Explanation:
By multiplication 5 by 0.3, we will get the result as 1.5.

Question 18.
0.5 × 3 =

Answer:
0.5 × 3 = 1.5.

Explanation:
By multiplication 0.5 by 3, we will get the result as 1.5.

Question 19.
0.5 × 0.3 =

Answer:
0.5 × 0.3 = 0.15.

Explanation:
By multiplication 0.5 by 0.3, we will get the result as 0.15.

Question 20.
0.5 × 0.03 =

Answer:
0.5 × 0.03 = 0.015.

Explanation:
By multiplication 0.5 by 0.03, we will get the result as 0.015.

Question 21.
0.3 × 0.05 =

Answer:
0.3 × 0.05 = 0.015.

Explanation:
By multiplication 0.3 by 0.05, we will get the result as 0.015.

Question 22.
8 × 2 =

Answer:
8 × 2 = 16.

Explanation:
By multiplication 8 by 2, we will get the result as 16.

Question 23.
0.8 × 2 =

Answer:
0.8 × 2 = 1.6.

Explanation:
By multiplication 0.8 by 2, we will get the result as 1.6.

Question 24.
0.8 × 0.2 =

Answer:
0.8 × 0.2 = 0.16.

Explanation:
By multiplication 0.8 by 0.2, we will get the result as 0.16.

Question 25.
0.8 × 0.02 =

Answer:
0.8 × 0.02 = 0.016.

Explanation:
By multiplication 0.8 by 0.02, we will get the result as 0.016.

Question 26.
0.2 × 0.08 =

Answer:
0.2 × 0.08 = 0.016.

Explanation:
By multiplication 0.2 by 0.08, we will get the result as 0.016.

Question 27.
5 × 9 =

Answer:
5 × 9 = 45.

Explanation:
By multiplication 5 by 9, we will get the result as 45.

Question 28.
0.5 × 9 =

Answer:
0.5 × 9 = 4.5.

Explanation:
By multiplication 0.5 by 9, we will get the result as 4.5.

Question 29.
0.5 × 0.9 =

Answer:
0.5 × 0.9 = 0.45.

Explanation:
By multiplication 0.5 by 0.9, we will get the result as 0.45.

Question 30.
0.5 × 0.09 =

Answer:
0.5 × 0.09 = 0.045.

Explanation:
By multiplication 0.5 by 0.09, we will get the result as 0.045.

Question 31.
0.9 × 0.05 =

Answer:
0.9 × 0.05 = 0.045.

Explanation:
By multiplication 0.9 by 0.05, we will get the result as 0.045Question 32.

Question: 32.
2 × 6 =

Answer:
2 × 6 = 12.

Explanation:
By multiplication 2 by 6, we will get the result as 12.

Question 33.
7 × 0.2 =

Answer:
7 × 0.2 = 1.4.

Explanation:
By multiplication 7 by 0.2, we will get the result as 1.4.

Question 34.
3 × 8 =

Answer:
3 × 8 = 24.

Explanation:
By multiplication 3 by 8, we will get the result as 24.

Question 35.
9 × 0.03 =

Answer:
9 × 0.03 = 0.27.

Explanation:
By multiplication 9 by 0.03, we will get the result as 0.27.

Question 36.
4 × 8 =

Answer:
4 × 8 = 32.

Explanation:
By multiplication 4 by 8, we will get the result as 32.

Question 37.
0.7 × 6 =

Answer:
0.7 × 6 = 4.2.

Explanation:
By multiplication 0.7 by 6, we will get the result as 4.2.

Question 38.
0.6 × 0.6 =

Answer:
0.6 × 0.6 = 0.36.

Explanation:
By multiplication 0.6 by 0.6, we will get the result as 0.36.

Question 39.
0.6 × 0.08 =

Answer:
0.6 × 0.08 = 0.048.

Explanation:
By multiplication 0.6 by 0.08, we will get the result as 0.048.

Question 40.
0.06 × 0.9 =

Answer:
0.06 × 0.9 = 0.054.

Explanation:
By multiplication 0.06 by 0.9, we will get the result as 0.054.

Question 41.
8 × 0.6 =

Answer:
8 × 0.6 = 4.8.

Explanation:
By multiplication 8 by 0.6, we will get the result as 4.8.

Question 42.
0.9 × 0.7 =

Answer:
0.9 × 0.7 = 0.63.

Explanation:
By multiplication 0.9 by 0.7, we will get the result as 0.63.

Question 43.
0.07 × 0.7 =

Answer:
0.07 × 0.7 = 0.049.

Explanation:
By multiplication 0.07 by 0.7, we will get the result as 0.049.

Question 44.
0.8 × 0.09 =

Answer:
0.8 × 0.09 = 0.072.

Explanation:
By multiplication 0.8 by 0.09, we will get the result as 0.072.

Eureka Math Grade 5 Module 4 Lesson 21 Problem Set Answer Key

Fill in the blanks. The first one has been done for you.

a. \(\frac{1}{4}\) × 1 = \(\frac{1}{4}\) × \(\frac{3}{3}\) = \(\frac{3}{12}\)

b. \(\frac{3}{4}\) × 1 = \(\frac{3}{4}\) × – = \(\frac{21}{28}\)

Answer:
\(\frac{3}{4}\) × 1 = \(\frac{3}{4}\) × \(\frac{7}{7}\)  = \(\frac{21}{28}\)

Explanation:
To justify the answer we will place \(\frac{7}{7}\).

c. \(\frac{7}{4}\) × 1 = \(\frac{7}{4}\) × – = \(\frac{35}{20}\)

Answer:
\(\frac{7}{4}\) × 1 = \(\frac{7}{4}\) × \(\frac{5}{5}\) = \(\frac{35}{20}\)

Explanation:
To justify the answer we will place \(\frac{5}{5}\).

d. Use words to compare the size of the product to the size of the first factor.

Answer:
Each time, the first factor is being multiplied by a fraction equal to 1, so the product is equal to the first factor.

Question 2.
Express each fraction as an equivalent decimal.
a. \(\frac{1}{4}\) × \(\frac{25}{25}\) =

Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = 0.025.

Explanation:
Given that \(\frac{1}{4}\) × \(\frac{25}{25}\) which is \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.

b. \(\frac{3}{4}\) × \(\frac{25}{25}\) =

Answer:
\(\frac{3}{4}\) × \(\frac{25}{25}\) = 0.75.

Explanation:
Given that \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) and the equivalent decimal of \(\frac{75}{100}\) is 0.75.

c. \(\frac{1}{5}\) × – =

Answer:
\(\frac{1}{5}\) × \(\frac{20}{20}\) = 0.20.

Explanation:
Given \(\frac{1}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{1}{5}\) × \(\frac{20}{20}\) = \(\frac{20}{100}\)  and the equivalent decimal of \(\frac{20}{100}\) is 0.20.

d. \(\frac{4}{5}\) × – =

Answer:
\(\frac{4}{5}\) × \(\frac{20}{20}\) = 0.80.

Explanation:
Given \(\frac{4}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{4}{5}\) × \(\frac{20}{20}\) = \(\frac{80}{100}\)  and the equivalent decimal of \(\frac{80}{100}\) is 0.80.

e. \(\frac{1}{20}\)

Answer:
\(\frac{1}{20}\) × \(\frac{5}{5}\) = 0.05.

Explanation:
Given \(\frac{1}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{1}{20}\) × \(\frac{5}{5}\) = \(\frac{5}{100}\)  and the equivalent decimal of \(\frac{5}{100}\) is 0.05.

f. \(\frac{27}{20}\)

Answer:
\(\frac{27}{20}\) × \(\frac{5}{5}\) = 1.35.

Explanation:
Given \(\frac{27}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{27}{20}\) × \(\frac{5}{5}\) = \(\frac{135}{100}\)  and the equivalent decimal of \(\frac{135}{100}\) is 1.35.

g. \(\frac{7}{4}\)

Answer:
\(\frac{7}{4}\) × \(\frac{25}{25}\) = 1.75.

Explanation:
Given \(\frac{7}{4}\) and we need to place \(\frac{25}{25}\) which is \(\frac{7}{4}\) × \(\frac{25}{225}\) = \(\frac{175}{100}\)  and the equivalent decimal of \(\frac{175}{100}\) is 1.75.

h. \(\frac{8}{5}\)

Answer:
\(\frac{8}{5}\) × \(\frac{20}{20}\) = 1.60.

Explanation:
Given \(\frac{1}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{8}{5}\) × \(\frac{20}{20}\) = \(\frac{160}{100}\)  and the equivalent decimal of \(\frac{160}{100}\) is 1.60.

i. \(\frac{24}{25}\)

Answer:
\(\frac{24}{25}\) × \(\frac{4}{4}\) = 0.96.

Explanation:
Given \(\frac{24}{25}\) and we need to place \(\frac{4}{4}\) which is \(\frac{24}{25}\) × \(\frac{4}{4}\) = \(\frac{96}{100}\)  and the equivalent decimal of \(\frac{96}{100}\) is 0.96.

j. \(\frac{93}{50}\)

Answer:
\(\frac{93}{50}\) × \(\frac{2}{2}\) = 1.86.

Explanation:
Given \(\frac{93}{50}\) and we need to place \(\frac{2}{2}\) which is \(\frac{93}{50}\) × \(\frac{2}{2}\) = \(\frac{186}{100}\)  and the equivalent decimal of \(\frac{186}{100}\) is 1.86.

k. 2\(\frac{6}{25}\)

Answer:
2\(\frac{6}{25}\) × \(\frac{4}{4}\) = 2.24.

Explanation:
Given 2\(\frac{6}{25}\) which is \(\frac{56}{25}\) and we need to place \(\frac{4}{4}\) which is \(\frac{56}{25}\) × \(\frac{4}{4}\) = \(\frac{224}{100}\)  and the equivalent decimal of \(\frac{224}{100}\) is 2.24.

l. 3\(\frac{31}{50}\)

Answer:
3\(\frac{31}{50}\) × \(\frac{2}{2}\) = 3.62.

Explanation:
Given 3\(\frac{31}{50}\) which is \(\frac{181}{50}\) and we need to place \(\frac{2}{2}\) which is \(\frac{181}{50}\) × \(\frac{2}{2}\) = \(\frac{362}{100}\)  and the equivalent decimal of \(\frac{362}{100}\) is 3.62.

Question 3.
Jack said that if you take a number and multiply it by a fraction, the product will always be smaller than what you started with. Is he correct? Why or why not? Explain your answer, and give at least two examples to support your thinking.

Answer:
No, Jack is not correct.

Explanation:
As Jack said that if you take a number and multiply it by a fraction and the product will always be smaller than what you started with. He is not correct, as a fraction could increase a number if we multiply it. So if the numerator is higher than the denominator it will increase it, and if the numerator is smaller than the denominator it decreases it. For example (10 × 4) ÷ (1 × 3) which is \(\frac{40}{3}\) = 13.33 which is higher than 10. And the other example is (5 × 10) ÷ (1 × 3) which is \(\frac{50}{3}\) = 16.67 which is higher than 5.

Question 4.
There is an infinite number of ways to represent 1 on the number line. In the space below, write at least four expressions multiplying by 1. Represent one differently in each expression.

Question 5.
Maria multiplied by 1 to rename \(\frac{1}{4}\) as hundredths. She made factor pairs equal to 10. Use her method to change one-eighth to an equivalent decimal.

Answer:
\(\frac{125}{100}\) = 1.25.

Explanation:
Given that Maria multiplied by 1 to rename \(\frac{1}{4}\) as hundredths and she made factor pairs equal to 10. So by using her method to change one-eighth to an equivalent decimal is
\(\frac{1}{8}\) = \(\frac{1}{2×2×2}\) × \(\frac{5×5×5}{5×5×5}\)
= \(\frac{5×5×5}{(2×5)×(2×5)×(2×5)}\)
which will be \(\frac{125}{100}\) = 1.25.

Paulo renamed \(\frac{1}{8}\) as a decimal, too. He knows the decimal equal to \(\frac{1}{4}\), and he knows that \(\frac{1}{8}\) is half as much as \(\frac{1}{4}\) . Can you use his ideas to show another way to find the decimal equal to \(\frac{1}{8}\) ?

Eureka Math Grade 5 Module 4 Lesson 21 Exit Ticket Answer Key

Fill in the blanks to make the equation true.
\(\frac{9}{4}\) × 1 = \(\frac{9}{4}\) × – = \(\frac{45}{20}\)

Answer:
\(\frac{9}{4}\) × 1 = \(\frac{9}{4}\) × \(\frac{5}{5}\) = \(\frac{45}{20}\)

Explanation:
Given that \(\frac{9}{4}\) × 1, so to make the equation true we will place \(\frac{9}{4}\) × \(\frac{5}{5}\) which is \(\frac{45}{20}\).

Question 2.
Express the fractions as equivalent decimals.
a. \(\frac{1}{4}\) =

Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = 0.25.

Explanation:
Given \(\frac{1}{4}\) and we need to place \(\frac{25}{25}\) which is \(\frac{1}{4}\) × \(\frac{25}{25}\) = \(\frac{25}{100}\)  and the equivalent decimal of \(\frac{25}{100}\) is 0.25.

b. \(\frac{2}{5}\) =

Answer:
\(\frac{2}{5}\) × \(\frac{20}{20}\) = 0.40.

Explanation:
Given \(\frac{2}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{2}{5}\) × \(\frac{20}{20}\) = \(\frac{40}{100}\)  and the equivalent decimal of \(\frac{40}{100}\) is 0.40.

c. \(\frac{3}{25}\) =

Answer:
\(\frac{3}{25}\) × \(\frac{4}{4}\) = 0.12.

Explanation:
Given \(\frac{3}{25}\) and we need to place \(\frac{20}{20}\) which is \(\frac{3}{25}\) × \(\frac{4}{4}\) = \(\frac{12}{100}\)  and the equivalent decimal of \(\frac{12}{100}\) is 0.12.

d. \(\frac{5}{20}\) =

Answer:
\(\frac{5}{20}\) × \(\frac{5}{5}\) = 0.25.

Explanation:
Given \(\frac{5}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{5}{20}\) × \(\frac{5}{5}\) = \(\frac{25}{100}\)  and the equivalent decimal of \(\frac{25}{100}\) is 0.25.

Eureka Math Grade 5 Module 4 Lesson 21 Homework Answer Key

Fill in the blanks.
a. \(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) =/9

Answer:
\(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) = \(\frac{3}{9}\).

Explanation:
Given that \(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) which is \(\frac{3}{9}\)

b. \(\frac{2}{3}\) × 1 = \(\frac{2}{3}\) × – = \(\frac{14}{21}\)

Answer:
\(\frac{2}{3}\) × \(\frac{7}{7}\) = \(\frac{14}{21}\).

Explanation:
Given that \(\frac{2}{3}\) × 1, now we will place \(\frac{7}{7}\) to get the equation true. So \(\frac{2}{3}\) × \(\frac{7}{7}\) which is \(\frac{14}{21}\).

c. \(\frac{5}{2}\) × 1 = \(\frac{5}{2}\) × – = \(\frac{25}{}\)

Answer:
\(\frac{5}{2}\) × 1 = \(\frac{5}{2}\) × \(\frac{5}{5}\) = \(\frac{25}{10}\).

Explanation:
Given that \(\frac{5}{2}\) × 1, now we will place \(\frac{5}{5}\) to get the equation. So \(\frac{5}{2}\) × \(\frac{5}{10}\) which is \(\frac{25}{10}\).

d. Compare the first factor to the value of the product.

Question 2.
Express each fraction as an equivalent decimal. The first one is partially done for you.
a. \(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{3 × 25}{4 × 25}\) = \(\frac{}{100}\)=

Answer:
\(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{75}{100}\)= 0.75

Explanation:
Given that \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) and the equivalent decimal of \(\frac{75}{100}\) is 0.75.

b. \(\frac{1}{4}\) × \(\frac{25}{25}\) =

Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = \(\frac{25}{100}\)= 0.25

Explanation:
Given that \(\frac{1}{4}\) × \(\frac{25}{25}\) which is \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.

c. \(\frac{2}{5}\) × – =

Answer:
\(\frac{2}{5}\) × \(\frac{20}{20}\) = \(\frac{40}{100}\)= 0.40.

Explanation:
Given that \(\frac{2}{5}\) × \(\frac{20}{20}\) which is \(\frac{40}{100}\) and the equivalent decimal of \(\frac{40}{100}\) is 0.40.

d. \(\frac{3}{5}\) × – =

Answer:
\(\frac{3}{5}\) × \(\frac{20}{20}\) = \(\frac{60}{100}\)= 0.60

Explanation:
Given that \(\frac{3}{5}\) and we will place \(\frac{20}{20}\) which is \(\frac{3}{5}\) × \(\frac{20}{20}\) and the equivalent decimal of \(\frac{60}{100}\) is 0.60.

e. \(\frac{3}{20}\)

Answer:
\(\frac{3}{20}\) × \(\frac{5}{5}\) = \(\frac{15}{100}\)= 0.15.

Explanation:
Given that \(\frac{3}{20}\) and we will place \(\frac{5}{5}\) which is \(\frac{3}{20}\) × \(\frac{5}{5}\) = \(\frac{15}{100}\) and the equivalent decimal of \(\frac{15}{100}\) is 0.15.

f. \(\frac{25}{20}\)

Answer:
\(\frac{25}{20}\) × \(\frac{5}{5}\) = \(\frac{125}{100}\)= 1.25.

Explanation:
Given that \(\frac{25}{20}\) and we will place \(\frac{5}{5}\) which is \(\frac{25}{20}\) × \(\frac{5}{5}\) = \(\frac{125}{100}\) and the equivalent decimal of \(\frac{125}{100}\) is 1.25.

g. \(\frac{23}{25}\)

Answer:
\(\frac{23}{25}\) × \(\frac{4}{4}\) = \(\frac{92}{100}\)= 0.92.

Explanation:
Given that \(\frac{23}{25}\) and we will place \(\frac{4}{4}\) which is \(\frac{23}{25}\) × \(\frac{4}{4}\) = \(\frac{92}{100}\) and the equivalent decimal of \(\frac{92}{100}\) is 0.92..

h. \(\frac{89}{50}\)

Answer:
\(\frac{89}{50}\) × \(\frac{2}{2}\) = \(\frac{178}{100}\)= 1.78.

Explanation:
Given that \(\frac{89}{50}\) and we will place \(\frac{2}{2}\) which is \(\frac{89}{50}\) × \(\frac{2}{2}\) = \(\frac{178}{100}\) and the equivalent decimal of \(\frac{178}{100}\) is 1.78..

i. 3 \(\frac{11}{25}\)

Answer:
3\(\frac{11}{25}\) × \(\frac{4}{4}\) = \(\frac{344}{100}\)= 3.44.

Explanation:
Given that 3\(\frac{11}{25}\) and we will place \(\frac{4}{4}\) which is \(\frac{86}{25}\) × \(\frac{4}{4}\) = \(\frac{344}{100}\) and the equivalent decimal of \(\frac{344}{100}\) is 3.44.

j. 5 \(\frac{41}{50}\)

Answer:
5\(\frac{41}{50}\) × \(\frac{2}{2}\) = \(\frac{582}{100}\)= 5.82.

Explanation:
Given that 5\(\frac{41}{50}\) and we will place \(\frac{2}{2}\) which is \(\frac{291}{50}\) × \(\frac{2}{2}\) = \(\frac{582}{100}\) and the equivalent decimal of \(\frac{582}{100}\) is 5.82.

Question 3.
\(\frac{6}{8}\) is equivalent to \(\frac{3}{4}\) . How can you use this to help you write \(\frac{6}{8}\) as a decimal? Show your thinking to solve.

Answer:
\(\frac{75}{100}\) as decimal is 0.75.

Explanation:
Given that \(\frac{6}{8}\) is equivalent to \(\frac{3}{4}\), we can use this as \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) as decimal is 0.75.

Question 4.
A number multiplied by a fraction is not always smaller than the original number. Explain this and give at least two examples to support your thinking.

Answer:
In a fraction, the above number is the numerator and the below number is the denominator. There are many kinds of fractions, some of are proper fraction and improper fraction. In a proper fraction, the numerator is smaller than the denominator. For example \(\frac{3}{4}\), \(\frac{5}{6}\) and in a improper fraction the numerator is bigger than the denominator. For example \(\frac{4}{3}\), \(\frac{6}{5}\)

Question 5.
Elise has \(\frac{3}{4}\) of a dollar. She buys a stamp that costs 44 cents. Change both numbers into decimals, and tell how much money Elise has after paying for the stamp.

Answer:
The remaining money Elise has after paying for her stamps is $0.31.

Explanation:
Given that Elise has \(\frac{3}{4}\) of a dollar and she buys a stamp that costs 44 cents, so to change both numbers into decimals we will pace \(\frac{25}{25}\) which will be \(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{75}{100}\) and n decimals it will be 0.75 and Elise has 0.75 × $1 = $0.75. Now we will convert 44 cents to dollars which will be 44 × \(\frac{1}{100}\) = \(\frac{44}{100}\) and in decimals it will be $0.44. So the remaining money Elise has after paying for her stamps is $0.75 – $0.44 which is $0.31.

Engage NY Eureka Math 5th Grade Module 4 Lesson 19 Answer Key

Eureka Math Grade 5 Module 4 Lesson 19 Problem Set Answer Key

Question 1.
Convert. Express your answer as a mixed number, if possible. The first one is done for you.
a. 2 ft = \(\frac{2}{3}\) yd
2 ft = 2 × 1 ft
= 2 × \(\frac{1}{3}\) yd
= \(\frac{2}{3}\) yd

b. 4 ft = \(\frac{4}{3}\) yd
4 ft = 4 × 1 ft
= 4 × \(\frac{1}{3}\) yd
= \(\frac{4}{3}\) yd.

c. 7 in = \(\frac{7}{12}\) ft
7 in = 7 × 1 in
= 7 × \(\frac{1}{12}\) ft
= \(\frac{7}{12}\) ft.

d. 13 in = \(\frac{13}{12}\) ft
13 in = 13 × 1 in
= 13 × \(\frac{1}{12}\) ft
= \(\frac{13}{12}\) ft.

e. 5 oz = \(\frac{5}{16}\) lb.
5 oz = 5 × 1 oz
= 5 × \(\frac{1}{16}\) lb
= \(\frac{5}{16}\) lb.

f. 18 oz = 1 \(\frac{1}{8}\) lb. lb
18 oz = 18 × 1 oz
= 18 × \(\frac{1}{16}\) lb
= \(\frac{18}{16}\) lb
= \(\frac{9}{8}\) lb
= 1 \(\frac{1}{8}\) lb.

Question 2.
Regina buys 24 inches of trim for a craft project.
a. What fraction of a yard does Regina buy?

Answer:
The fraction of a yard does Regina buy is \(\frac{2}{3}\) yd.

Explanation:
Given that Regina buys 24 inches of trim for a craft project, so the fraction of a yard does Regina buy is
24 in = 24 × 1 in
= 24 × \(\frac{1}{36}\) yd
= \(\frac{2}{3}\) yd.

b. If a whole yard of trim costs $6, how much did Regina pay?

Answer:
Regina paid $4.

Explanation:
The Regina pays \(\frac{2}{3}\) of 6 which is $4.

Question 3.
At Yo-Yo Yogurt, the scale says that Sara has 8 ounces of vanilla yogurt in her cup. Her father’s yogurt weighs 11 ounces. How many pounds of frozen yogurt did they buy altogether? Express your answer as a mixed number.

Answer:
They bought 1 \(\frac{3}{16}\) lb pounds frozen yogurt altogether.

Explanation:
Given that Sara has 8 ounces of vanilla yogurt in her cup and her father’s yogurt weighs 11 ounces, so altogether it will be 8 + 11 which is 19 ounces which in pounds it will be
19 oz = \(\frac{19}{16}\) lb.
19 oz = 19 × 1 oz
= 19 × \(\frac{1}{16}\) lb
= 1 \(\frac{3}{16}\) lb.

Question 4.
Pheng-Xu drinks 1 cup of milk every day for lunch. How many gallons of milk does he drink in 2 weeks?

Answer:
Pheng drank \(\frac{7}{8}\) gallon of milk in two weeks.

Explanation:
Given that Pheng-Xu drinks 1 cup of milk every day for lunch, so the number of gallons of milk does he drink in 2 weeks is,
as 1 week is 7 days and for 2 weeks it will be 2 × 7 which is 14 days. And for 1 day it will be 1 cup and for 14 days it will be 14 cups. So 14 cups = 14 × 1 cup
= 14 × \(\frac{1}{16}\)
= \(\frac{14}{16}\)
= \(\frac{7}{8}\) gallon.
So Pheng drank \(\frac{7}{8}\) gallon of milk in two weeks.

Eureka Math Grade 5 Module 4 Lesson 19 Exit Ticket Answer Key

Convert. Express your answer as a mixed number, if possible.

a. 5 in = \(\frac{5}{12}\) ft ft
5 in = 5 × 1 in
= 5 × \(\frac{1}{12}\) ft
= \(\frac{5}{12}\) ft.

b. 13 in = ___________ ft
13 in = 13 × 1 in
= 13 × \(\frac{1}{12}\) ft
= \(\frac{13}{12}\) ft.

c. 9 oz = \(\frac{9}{16}\) lb lb
9 oz = 9 × 1 oz
= 9 × \(\frac{1}{16}\) lb
= \(\frac{9}{16}\) lb.

d. 18 oz = ___________ lb
18 oz = 18 × 1 oz
= 18 × \(\frac{1}{16}\) lb
= \(\frac{18}{16}\) lb
= 1\(\frac{1}{8}\) lb.

Eureka Math Grade 5 Module 4 Lesson 19 Homework Answer Key

Question 1.
Convert. Express your answer as a mixed number, if possible.
a. 2 ft = \(\frac{2}{3}\) yd
2 ft = 2 × 1 ft
= 2 × \(\frac{1}{3}\) yd
= \(\frac{2}{3}\) yd

b. 6 ft = 2 yd
6 ft = 6 × 1 ft
= 6 × \(\frac{1}{3}\)yd
= 2 yd.

c. 5 in = ________ ft
5 in = 5 × 1 in
= 5 × \(\frac{1}{12}\) ft
= \(\frac{5}{12}\) ft.

d. 14 in = ________ ft
14 in = 14 × 1 in
= 14 × \(\frac{1}{12}\) ft
= \(\frac{14}{12}\) ft
= 1 \(\frac{1}{6}\)

e. 7 oz = \(\frac{7}{16}\) lb
7 oz = 7 × 1 oz
= 7 × \(\frac{1}{16}\) lb
= \(\frac{7}{16}\) lb.

f. 20 oz =1 \(\frac{1}{4}[/latex lb
20 oz = 20 × 1 oz
= 20 × [latex]\frac{1}{16}\) lb
= \(\frac{20}{16}\) lb
= \(\frac{5}{4}\) lb
= 1 \(\frac{1}{4}\) lb.

g. 1 pt = \(\frac{1}{2}\) qt
1 pt = 1 × 1 pt
= 1 × \(\frac{1}{2}\) pt
= \(\frac{1}{2}\) pt.

h. 4 pt = ________ qt
4 pt = 4 × 1 pt
= 4 × \(\frac{1}{2}\) pt
= 2 pt.

Question 2.
Marty buys 12 ounces of granola.

a. What fraction of a pound of granola did Marty buy?

Answer:
The fraction of a pound of granola did Marty bought is \(\frac{12}{16}\) lb.

Explanation:
Given that Marty buys 12 ounces of granola, so the fraction of a pound of granola did Marty bought is 12 over 16 which is \(\frac{12}{16}\) lb.

b. If a whole pound of granola costs $4, how much did Marty pay?

Answer:
Marty pays $3.

Explanation:
As a whole pound of granola costs $4, Marty pays \(\frac{12}{16}\) × 4 which is $3.

Question 3.
Sara and her dad visit Yo-Yo Yogurt again. This time, the scale says that Sara has 14 ounces of vanilla yogurt in her cup. Her father’s yogurt weighs half as much. How many pounds of frozen yogurt did they buy altogether on this visit? Express your answer as a mixed number.

Answer:
1\(\frac{5}{16}\) pounds.

Explanation:
Given that Sara has 14 ounces of vanilla yogurt in her cup and her father’s yogurt weighs half as much. So the frozen yogurt did they buy altogether is 14 + 7 which is 21 ounces. In pounds, it will be 21 × \(\frac{1}{16}\) which is 1\(\frac{5}{16}\) pounds.

Question 4.
An art teacher uses 1 quart of blue paint each month. In one year, how many gallons of paint will she use?

Answer:
The number of gallons of paint will she use is 3 gallons.

Explanation:
Given that the teacher uses 1 quart of blue paint each month, so in one year the number of gallons of paint will she use is \(\frac{112}{4}\) which is 3 gallons.

Engage NY Eureka Math 5th Grade Module 4 Lesson 14 Answer Key

Eureka Math Grade 5 Module 4 Lesson 14 Sprint Answer Key

A
Multiply a Fraction and a Whole Number

Question 1.
\(\frac{1}{5}\) × 2 =

Answer:
\(\frac{2}{5}\)

Explanation:
The multiplication of \(\frac{1}{5}\) × 2 is \(\frac{2}{5}\).

Question 2.
\(\frac{1}{5}\) × 3 =

Answer:
\(\frac{3}{5}\)

Explanation:
The multiplication of \(\frac{1}{5}\) × 3 is \(\frac{3}{5}\).

Question 3.
\(\frac{1}{5}\) × 4 =

Answer:
\(\frac{4}{5}\)

Explanation:
The multiplication of \(\frac{1}{5}\) × 4 is \(\frac{4}{5}\).

Question 4.
4 × \(\frac{1}{5}\) =

Answer:
\(\frac{4}{5}\)

Explanation:
The multiplication of \(\frac{1}{5}\) × 4 is \(\frac{4}{5}\).

Question 5.
\(\frac{1}{8}\) × 3 =

Answer:
\(\frac{3}{8}\)

Explanation:
The multiplication of \(\frac{1}{8}\) × 3 is \(\frac{3}{8}\).

Question 6.
\(\frac{1}{8}\) × 5 =

Answer:
\(\frac{5}{8}\)

Explanation:
The multiplication of \(\frac{1}{8}\) × 5 is \(\frac{5}{8}\).

Question 7.
\(\frac{1}{8}\) × 7 =

Answer:
\(\frac{7}{8}\)

Explanation:
The multiplication of \(\frac{1}{8}\) × 7 is \(\frac{7}{8}\).

Question 8.
7 × \(\frac{1}{8}\) =

Answer:
\(\frac{7}{8}\)

Explanation:
The multiplication of \(\frac{1}{8}\) × 7 is \(\frac{7}{8}\).

Question 9.
3 × \(\frac{1}{10}\) =

Answer:
\(\frac{3}{10}\)

Explanation:
The multiplication of \(\frac{1}{10}\) × 3 is \(\frac{3}{10}\).

Question 10.
7 × \(\frac{1}{10}\) =

Answer:
\(\frac{7}{10}\)

Explanation:
The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 11.
\(\frac{1}{10}\) × 7 =

Answer:
\(\frac{7}{10}\)

Explanation:
The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 12.
4 ÷ 2 =

Answer:
4 ÷ 2 = 2

Explanation:
The division of 4 ÷ 2 is 2.

Question 13.
4 × \(\frac{1}{2}\) =

Answer:
4 × \(\frac{1}{2}\) = 2

Explanation:
The multiplication of 4 × \(\frac{1}{2}\) is 2.

Question 14.
6 ÷ 3 =

Answer:
6 ÷ 3 = 2

Explanation:
The division of 6 ÷ 3 is 2.

Question 15.
\(\frac{1}{3}\) × 6 =

Answer:
\(\frac{1}{3}\) × 6 = 2.

Explanation:
The multiplication of \(\frac{1}{3}\) × 6 is 2.

Question 16.
10 ÷ 5 =

Answer:
10 ÷ 5 = 2.

Explanation:
The division of 10 ÷ 5 is 2.

Question 17.
10 × \(\frac{1}{5}\) =

Answer:
10 × \(\frac{1}{5}\) = 2.

Explanation:
The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 18.
\(\frac{1}{3}\) × 9 =

Answer:
\(\frac{1}{3}\) × 9 = 3.

Explanation:
The multiplication of \(\frac{1}{3}\) × 9 is 3.

Question 19.
\(\frac{2}{3}\) × 9 =

Answer:
\(\frac{2}{3}\) × 9 = 6.

Explanation:
The multiplication of \(\frac{2}{3}\) × 9 is 6.

Question 20.
\(\frac{1}{4}\) × 8 =

Answer:
\(\frac{1}{4}\) × 8 = 2.

Explanation:
The multiplication of \(\frac{1}{4}\) × 8 is 2.

Question 21.
\(\frac{3}{4}\) × 8 =

Answer:
\(\frac{3}{4}\) × 8 = 6.

Explanation:
The multiplication of \(\frac{3}{4}\) × 8 is 6.

Question 22.
\(\frac{1}{6}\) × 12 =

Answer:
\(\frac{1}{6}\) × 12 = 2.

Explanation:
The multiplication of \(\frac{1}{6}\) × 12 is 2.

Question 23.
\(\frac{5}{6}\) × 12 =

Answer:
\(\frac{5}{6}\) × 12 = 10.

Explanation:
The multiplication of \(\frac{5}{6}\) × 12 is 10.

Question 24.
\(\frac{1}{3}\) × 15 =

Answer:
\(\frac{1}{3}\) × 15 = 5.

Explanation:
The multiplication of \(\frac{1}{3}\) × 15 is 5.

Question 25.
\(\frac{2}{3}\) × 15 =

Answer:
\(\frac{2}{3}\) × 15 = 10.

Explanation:
The multiplication of \(\frac{2}{3}\) × 15 is 10.

Question 26.
15 × \(\frac{2}{3}\) =

Answer:
15 × \(\frac{2}{3}\) = 10.

Explanation:
The multiplication of 15 × \(\frac{2}{3}\) is 10.

Question 27.
\(\frac{1}{5}\) × 15 =

Answer:
\(\frac{1}{5}\) × 15 = 3.

Explanation:
The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 28.
\(\frac{2}{5}\) × 15 =

Answer:
\(\frac{2}{5}\) × 15 = 6.

Explanation:
The multiplication of \(\frac{2}{5}\) × 15 is 6.

Question 29.
\(\frac{4}{5}\) × 15 =

Answer:
\(\frac{1}{5}\) × 15 = 3.

Explanation:
The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 30.
\(\frac{3}{5}\) × 15 =

Answer:
\(\frac{3}{5}\) × 15 = 9.

Explanation:
The multiplication of \(\frac{3}{5}\) × 15 is 9.

Question 31.
15 × \(\frac{3}{5}\) =

Answer:
15 × \(\frac{3}{5}\) = 9.

Explanation:
The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 32.
18 × \(\frac{1}{6}\) =

Answer:
18 × \(\frac{1}{6}\) = 3.

Explanation:
The multiplication of 18 × \(\frac{1}{6}\) is 3.

Question 33.
18 × \(\frac{5}{6}\) =

Answer:
18 × \(\frac{5}{6}\) = 15.

Explanation:
The multiplication of 18 × \(\frac{5}{6}\) is 15.

Question 34.
\(\frac{5}{6}\) × 18 =

Answer:
\(\frac{5}{6}\) × 18 = 15.

Explanation:
The multiplication of \(\frac{5}{6}\) × 18 is 15.

Question 35.
24 × \(\frac{1}{4}\) =

Answer:
24 × \(\frac{1}{4}\) = 6.

Explanation:
The multiplication of 24 × \(\frac{1}{4}\) is 6.

Question 36.
\(\frac{3}{4}\) × 24 =

Answer:
\(\frac{3}{4}\) × 24 = 18.

Explanation:
The multiplication of \(\frac{3}{4}\) × 24 is 18.

Question 37.
32 × \(\frac{1}{8}\) =

Answer:
32 × \(\frac{1}{8}\) = 4.

Explanation:
The multiplication of 32 × \(\frac{1}{8}\) is 4.

Question 38.
32 × \(\frac{3}{8}\) =

Answer:
32 × \(\frac{3}{8}\) = 12.

Explanation:
The multiplication of 32 × \(\frac{3}{8}\) is 12.

Question 39.
\(\frac{5}{8}\) × 32 =

Answer:
\(\frac{5}{8}\) × 32= 20.

Explanation:
The multiplication of \(\frac{5}{8}\) × 32 is 20.

Question 40.
32 × \(\frac{7}{8}\) =

Answer:
32 × \(\frac{7}{8}\)= 28.

Explanation:
The multiplication of 32 × \(\frac{7}{8}\) is 28.

Question 41.
\(\frac{5}{9}\) × 54 =

Answer:
\(\frac{5}{9}\) × 54= 30.

Explanation:
The multiplication of \(\frac{5}{9}\) × 54 is 30.

Question 42.
63 × \(\frac{7}{9}\) =

Answer:
63 × \(\frac{7}{9}\) = 49.

Explanation:
The multiplication of 63 × \(\frac{7}{9}\) is 49.

Question 43.
56 × \(\frac{3}{7}\) =

Answer:
56 × \(\frac{3}{7}\) = 24.

Explanation:
The multiplication of 56 × \(\frac{3}{7}\) is 24.

Question 44.
\(\frac{6}{7}\) × 49 =

Answer:
\(\frac{6}{7}\) × 49 = 42.

Explanation:
The multiplication of \(\frac{6}{7}\) × 49 is 42.

B
Multiply a Fraction and a Whole Number

Question 1.
\(\frac{1}{7}\) × 2 =

Answer:
\(\frac{1}{7}\) × 2 = \(\frac{2}{7}\).

Explanation:
The multiplication of \(\frac{1}{7}\) × 2 is \(\frac{2}{7}\).

Question 2.
\(\frac{1}{7}\) × 3 =

Answer:
\(\frac{1}{7}\) × 3 = \(\frac{3}{7}\).

Explanation:
The multiplication of \(\frac{1}{7}\) × 3 is \(\frac{3}{7}\).

Question 3.
\(\frac{1}{7}\) × 4 =

Answer:
\(\frac{1}{7}\) × 4 = \(\frac{4}{7}\).

Explanation:
The multiplication of \(\frac{1}{7}\) × 4 is \(\frac{4}{7}\).

Question 4.
4 × \(\frac{1}{7}\) =

Answer:
4 × \(\frac{1}{7}\) = \(\frac{4}{7}\).

Explanation:
The multiplication of 4 × \(\frac{1}{7}\) is \(\frac{4}{7}\).

Question 5.
\(\frac{1}{10}\) × 3 =

Answer:
\(\frac{1}{10}\) × 3 = \(\frac{3}{10}\).

Explanation:
The multiplication of \(\frac{1}{10}\) × 3 is \(\frac{3}{10}\).

Question 6.
\(\frac{1}{10}\) × 7 =

Answer:
\(\frac{1}{10}\) × 7 = \(\frac{7}{10}\).

Explanation:
The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 7.
\(\frac{1}{10}\) × 9 =

Answer:
\(\frac{1}{10}\) × 9 = \(\frac{9}{10}\).

Explanation:
The multiplication of \(\frac{1}{10}\) × 9 is \(\frac{9}{10}\).

Question 8.
9 × \(\frac{1}{10}\) =

Answer:
9 × \(\frac{1}{10}\) = \(\frac{9}{10}\).

Explanation:
The multiplication of 9 × \(\frac{1}{10}\) is \(\frac{9}{10}\).

Question 9.
3 × \(\frac{1}{8}\) =

Answer:
3 × \(\frac{1}{8}\) = \(\frac{3}{8}\).

Explanation:
The multiplication of 3 × \(\frac{1}{8}\) is \(\frac{3}{8}\).

Question 10.
5 × \(\frac{1}{8}\) =

Answer:
5 × \(\frac{1}{8}\) = \(\frac{5}{8}\).

Explanation:
The multiplication of 5 × \(\frac{1}{8}\) is \(\frac{5}{8}\).

Question 11.
\(\frac{1}{8}\) × 5 =

Answer:
\(\frac{1}{8}\) × 5 = \(\frac{5}{8}\).

Explanation:
The multiplication of \(\frac{1}{8}\) × 5 is \(\frac{5}{8}\).

Question 12.
10 ÷ 5 =

Answer:
10 ÷ 5 = 2

Explanation:
The division of 10 ÷ 5 is 2.

Question 13.
10 × \(\frac{1}{5}\) =

Answer:
10 × \(\frac{1}{5}\) = 2.

Explanation:
The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 14.
9 ÷ 3 =

Answer:
9 ÷ 3 = 3.

Explanation:
The division of 9 ÷ 3 is 3.

Question 15.
\(\frac{1}{3}\) × 9 =

Answer:
10 × \(\frac{1}{5}\) = 2.

Explanation:
The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 16.
10 ÷ 2 =

Answer:
10 ÷ 2 = 5.

Explanation:
The division of 10 ÷ 2 is 5.

Question 17.
10 × \(\frac{1}{2}\) =

Answer:
10 × \(\frac{1}{2}\) = 5.

Explanation:
The multiplication of 10 × \(\frac{1}{2}\) is 5.

Question 18.
\(\frac{1}{3}\) × 6 =

Answer:
\(\frac{1}{3}\) × 6 = 2.

Explanation:
The multiplication of \(\frac{1}{3}\) × 6 is 2.

Question 19.
\(\frac{2}{3}\) × 6 =

Answer:
\(\frac{2}{3}\) × 6 = 4.

Explanation:
The multiplication of \(\frac{2}{3}\) × 6 is 4.

Question 20.
\(\frac{1}{6}\) × 12 =

Answer:
\(\frac{1}{6}\) × 12 = 2.

Explanation:
The multiplication of \(\frac{1}{6}\) × 12 is 2.

Question 21.
\(\frac{5}{6}\) × 12 =

Answer:
\(\frac{5}{6}\) × 12 = 10.

Explanation:
The multiplication of \(\frac{5}{6}\) × 12 is 10.

Question 22.
\(\frac{1}{4}\) × 8 =

Answer:
\(\frac{1}{4}\) × 8 = 2.

Explanation:
The multiplication of \(\frac{1}{4}\) × 8 is 2.

Question 23.
\(\frac{3}{4}\) × 8 =

Answer:
\(\frac{3}{4}\) × 8 = 6.

Explanation:
The multiplication of \(\frac{3}{4}\) × 8 is 6.

Question 24.
\(\frac{1}{5}\) × 15 =

Answer:
\(\frac{1}{5}\) × 15 = 3.

Explanation:
The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 25.
\(\frac{2}{5}\) × 15 =

Answer:
\(\frac{2}{5}\) × 15 = 6.

Explanation:
The multiplication of \(\frac{2}{5}\) × 15 is 6.

Question 26.
\(\frac{4}{5}\) × 15 =

Answer:
\(\frac{4}{5}\) × 15 = 12.

Explanation:
The multiplication of \(\frac{4}{5}\) × 15 is 12.

Question 27.
\(\frac{3}{5}\) × 15 =

Answer:
\(\frac{3}{5}\) × 15 = 9.

Explanation:
The multiplication of \(\frac{3}{5}\) × 15 is 9.

Question 28.
15 × \(\frac{3}{5}\) =

Answer:
15 × \(\frac{3}{5}\) = 9.

Explanation:
The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 29.
\(\frac{1}{3}\) × 15 =

Answer:
15 × \(\frac{3}{5}\) = 9.

Explanation:
The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 30.
\(\frac{2}{3}\) × 15 =

Answer:
\(\frac{2}{3}\) × 15 = 10.

Explanation:
The multiplication of \(\frac{3}{5}\) × 15 is 10.

Question 31.
15 × \(\frac{2}{3}\) =

Answer:
15 × \(\frac{2}{3}\) = 10.

Explanation:
The multiplication of 15 × \(\frac{2}{3}\) is 10.

Question 32.
24 × \(\frac{1}{6}\) =

Answer:
24 × \(\frac{1}{6}\) = 4.

Explanation:
The multiplication of 24 × \(\frac{1}{6}\) is 4.

Question 33.
24 × \(\frac{5}{6}\) =

Answer:
24 × \(\frac{5}{6}\) = 20.

Explanation:
The multiplication of 24 × \(\frac{5}{6}\) is 20.

Question 34.
\(\frac{5}{6}\) × 24 =

Answer:
\(\frac{5}{6}\) × 24 = 20.

Explanation:
The multiplication of \(\frac{5}{6}\) × 24 is 20.

Question 35.
20 × \(\frac{1}{4}\) =

Answer:
20 × \(\frac{1}{4}\) = 5.

Explanation:
The multiplication of 20 × \(\frac{1}{4}\) is 5.

Question 36.
\(\frac{3}{4}\) × 20 =

Answer:
\(\frac{3}{4}\) × 20 = 15.

Explanation:
The multiplication of \(\frac{3}{4}\) × 20 is 15.

Question 37.
24 × \(\frac{1}{8}\) =

Answer:
24 × \(\frac{1}{8}\) = 3.

Explanation:
The multiplication of 24 × \(\frac{1}{8}\) is 3.

Question 38.
24 × \(\frac{3}{8}\) =

Answer:
24 × \(\frac{3}{8}\) = 9.

Explanation:
The multiplication of 24 × \(\frac{3}{8}\) is 9.

Question 39.
\(\frac{5}{8}\) × 24 =

Answer:
\(\frac{5}{8}\) × 24 = 15.

Explanation:
The multiplication of \(\frac{5}{8}\) is 24.

Question 40.
24 × \(\frac{7}{8}\) =

Answer:
24 × \(\frac{7}{8}\) = 21.

Explanation:
The multiplication of 24 × \(\frac{7}{8}\) is 21.

Question 41.
\(\frac{5}{9}\) × 63 =

Answer:
\(\frac{5}{9}\) × 63 = 35.

Explanation:
The multiplication of \(\frac{5}{9}\) × 63 is 35.

Question 42.
54 × \(\frac{7}{9}\) =

Answer:
54 × \(\frac{7}{9}\) = 42.

Explanation:
The multiplication of 54 × \(\frac{7}{9}\) is 42.

Question 43.
49 × \(\frac{3}{7}\) =

Answer:
49 × \(\frac{3}{7}\) = 21.

Explanation:
The multiplication of 49 × \(\frac{3}{7}\) is 21.

Question 44.
\(\frac{6}{7}\) × 56 =

Answer:
\(\frac{6}{7}\) × 56 = 48.

Explanation:
The multiplication of \(\frac{6}{7}\) × 56 is 48.

Eureka Math Grade 5 Module 4 Lesson 14 Problem Set Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking. Then, write a number sentence. An example has been done for you.
Example:

a. \(\frac{1}{3}\) of \(\frac{3}{4}\) = \(\frac{1}{3}\) of ____ fourth(s) = ____ fourth(s)

Answer:
3, 1.

Explanation:
Given that \(\frac{1}{3}\) of \(\frac{3}{4}\) = \(\frac{1}{4}\), so \(\frac{1}{3}\) of 3 fourth(s) = 1 fourth(s)

b. \(\frac{1}{2}\) of \(\frac{4}{5}\) = \(\frac{1}{2}\) of ____ fifth(s) = ____ fifth(s)

c. \(\frac{1}{2}\) of \(\frac{2}{2}\) =

d. \(\frac{2}{3}\) of \(\frac{1}{2}\) =

e. \(\frac{1}{2}\) × \(\frac{3}{5}\) =

f. \(\frac{2}{3}\) × \(\frac{1}{4}\) =

Question 2.
\(\frac{5}{8}\) of the songs on Harrison’s music player are hip-hop. \(\frac{1}{3}\) of the remaining songs are rhythm and blues. What fraction of all the songs are rhythm and blues? Use a tape diagram to solve.

Question 3.
Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.
a. What fraction of all the students are girls with blond hair?

b. What fraction of all the students are boys without brown hair?

Question 4.
Cody and Sam mowed the yard on Saturday. Dad told Cody to mow \(\frac{1}{4}\) of the yard. He told Sam to mow \(\frac{1}{3}\) of the remainder of the yard. Dad paid each of the boys an equal amount. Sam said, “Dad, that’s not fair! I had to mow one-third, and Cody only mowed one-fourth!” Explain to Sam the error in his thinking. Draw a picture to support your reasoning.

Eureka Math Grade 5 Module 4 Lesson 14 Exit Ticket Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking. Then, write a number sentence.
\(\frac{1}{3}\) of \(\frac{3}{7}\) =

Question 2.
In a cookie jar, \(\frac{1}{4}\) of the cookies are chocolate chip, and \(\frac{1}{2}\) of the rest are peanut butter. What fraction of all the cookies is peanut butter?

Eureka Math Grade 5 Module 4 Lesson 14 Homework Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking.
a. \(\frac{1}{2}\) of \(\frac{2}{3}\) = \(\frac{1}{2}\) of ____ third(s) = ____ third(s)

b. \(\frac{1}{2}\) of \(\frac{4}{3}\) = \(\frac{1}{2}\) of ____ third(s) = ____ third(s)

c. \(\frac{1}{3}\) of \(\frac{3}{5}\) =

d. \(\frac{1}{2}\) of \(\frac{6}{8}\) =

e. \(\frac{1}{3}\) × \(\frac{4}{5}\) =

f. \(\frac{4}{5}\) × \(\frac{1}{3}\) =

Question 2.
Sarah has a photography blog. \(\frac{3}{7}\) of her photos are of nature. \(\frac{1}{4}\) of the rest are of her friends. What fraction of all of Sarah’s photos is of her friends? Support your answer with a model.

Question 3.
At Laurita’s Bakery, \(\frac{3}{5}\) of the baked goods are pies, and the rest are cakes. \(\frac{1}{3}\) of the pies are coconut. 1/6 of the cakes are angel food.
a. What fraction of all of the baked goods at Laurita’s Bakery are coconut pies?

b. What fraction of all of the baked goods at Laurita’s Bakery are angel food cakes?

Question 4.
Grandpa Mick opened a pint of ice cream. He gave his youngest grandchild \(\frac{1}{5}\) of the ice cream and his middle grandchild \(\frac{1}{4}\) of the remaining ice cream. Then, he gave his oldest grandchild \(\frac{1}{3}\) of the ice cream that was left after serving the others.
a. Who got the most ice cream? How do you know? Draw a picture to support your reasoning.

b. What fraction of the pint of ice cream will be left if Grandpa Mick serves himself the same amount as the second grandchild?