## Everyday Mathematics 1st Grade Answer Key Unit 7 Subtraction Fact Strategies and Attributes of Shapes

Fact Families

Family Note
To day your child generated addition and subtraction facts from dominoes to create fact families. Fact families show related facts and help children relate addition to subtraction. Although most dominoes have two addition facts and two subtraction facts, children discussed fact families for doubles (for example, 4 + 4 = 8), which have only one addition fact and one subtraction fact.

Write the 3 numbers for each domino. Use the numbers to write a fact family.
Question 1.
Numbers: _______, _______, _______

Fact Family:
_______ – _______ = _______
_______ – _______ = _______
_______ + _______ = _______
_______ + _______ = _______

Numbers: 7, 5, 12

Fact Family:
12 – 7 = 5

12 – 5 =7

7 + 5 =12

5 + 7 = 12

Question 2.
Numbers: _______, _______, _______

Fact Family:
_______ – _______ = _______
_______ – _______ = _______
_______ + _______ = _______
_______ + _______ = _______

Numbers: 6, 9, 15

Fact Family:

15 – 6 = 9

15 – 9 = 6

6 + 9 = 15

9 + 6 = 15

Practice
Question 3.
Use a paper clip. Measure the lengths of two shoes.
My shoe: _______ paper clips
Someone else’s shoe: _______ paper clips
Whose shoe is longer? How much longer? _______ shoe is _______ paper clips longer.

My shoe: 3 paper clips
Someone else’s shoes: 2.5 paper clips

My shoe is longer. About 1/2 paper clip. My shoe is 1/2 paper clip longer.

Relating Special Addition and Subtraction Facts

Family Note
In recent lessons, children learned about fact families and how addition facts have related subtraction facts. In today’s lesson, your child solved subtraction problems by thinking about related addition facts, particularly with doubles and combinations of 10. For example, children might solve 18 – 9 = ☐ by thinking addition: 9 + ☐ = 18.

Write an addition fact, you can use to find the answer. Then write the answer in the blank.
Example: 16 – 8 = 8
8 + ________ = 16

Question 1.
6 – 3 = ________

3+3 = 6

Question 2.
10 – 7 = ________

3 + 7 = 10

Question 3.
12 – 6 = ________

6+6 = 12

Question 4.
10 – 1 = ________

1+9 = 10

Practice
Question 5.
Record the time you do each activity.

More Subtraction Fact Strategies

Family Note
This Home Link reviews some of the work your child has been doing in recent lessons that relates subtraction facts to addition facts. Encourage your child to include some subtraction names in the name-collection box in Problem 2. For example, a subtraction name for 14 is 16 – 2.
Also included in this Home Link are more Fact Triangles for further fact practice.

Question 1.
Write the 3 numbers for the domino. Use the numbers to write the fact family.

Numbers: ________, ________, ________
Fact Family:
________ + ________ = ________
________ + ________ = ________
________ – ________ = ________
________ – ________ = ________

Numbers:

5, 8, 13

Fact Family:

5 + 8 =13

8 + 5 = 13

13 – 8 = 5

13 – 5 = 8

Question 2.
Write as many names as you can for 1 4.

10 + 4 =14

7 + 7 = 14

15 – 1 = 14

9 + 5 =14

20 – 6 = 14

Question 3.
Cross out the names that do not belong.

Practice
Question 4.
Circle the tens digit.
4 0
9 2
3 9

Attributes of Shapes

Family Note
Today your child explored attributes of shapes. Some attributes of shapes are color, size, or number of sides or corners. Encourage your child to look carefully at objects all around—not just geometric objects—and identify their attributes.

List three attributes of each shape.
Question 1.

Color: White

Number of Angles: 6

Number of sides: 6

Question 2.

Color: Gray

Number of Angles: 4

Number of sides: 4

Practice
Question 3.
Record the time.

The time is 12:00

The time is 9:00

Exploring Attributes, Fractions, and Salute!

Family Note
Today your child explored the connection between addition and subtraction in the game Salute!, divided shapes in half, and further explored attributes of shapes. Children will continue working with shapes in future lessons. To prepare for this, help your child find objects with the shapes listed below.
Also included in this Home Link are more Fact Triangles for further fact practice.

Question 1.
Find something in your house that has a triangle on it. Write its name, or draw its picture.

A Slice of pizza has Triangle on it.

Question 2.
Find something in your house that has a circle on it. Write its name, or draw its picture.

The clock in my house has Circle on it.

Question 3.
Find something in your house that has a square on it. Write its name, or draw its picture.

Rubix cube in my house has square on it.

Practice
Question 4.
What number do the base-10 blocks show?
__________

53

Defining and Nondefining Attributes

Family Note
Today your child learned about the attributes that define triangles and rectangles, such as the numbers of sides and corners (also called vertices). Without these defining attributes, a shape cannot be a triangle or a rectangle. Children also learned about nondefining attributes of shapes, such as color and size.

Question 1.
Draw 2 different triangles. The triangles must have at least two attributes that are different.

The two attributes that are different are Color and size.

Question 2.
Name the attributes that are different.

Color, Size and the ways in which they point are the attributes that are different.

Question 3.
Name the attributes that are the same.

Three sides, Three Vertices, Three angles, all sides are straight are the attributes that are same.

Practice
Question 4.
Solve.
2 + 5 = ________
________ = 5 + 2
3 + 7 + 8 = __________

7

7

18

“What’s My Rule?”

Family Note
Ask your child to explain what the function machine is doing to the “in” numbers before he or she fills in the missing “out” numbers. For example, in the first problem, the function machine is adding 1 to each of the “in” numbers.

Also included in this Home Link are more Fact Triangles. This set of Fact Triangles includes three blanks. Fill them with whatever facts your child would like to practice more.

Fill in the missing rule and numbers.
Question 1.

Rule is +1

Question 2.

Rule is -2

Question 3.

Rule is -7

Practice
Solve.
Question 4.
4 + _______ = 8

4

Question 5.
10 = 6 + _______

4

Question 6.
________ = 8 – 1

7

“What’s My Rule?”

Family Note
Today your child talked about how mathematical rules can be used to help us solve other problems. After your child finds a rule for each problem below, name a few more in numbers and ask your child to use the rule to tell you what the out numbers would be.

Find the rules.
Question 1.

The Rule is +1

Question 2.

The Rule is -4

Question 3.

The Rule is +6

Question 4.

The Rule is -5

Practice
Question 5.
Cyrus started at 19 on his number line. He hopped backward and landed on 10.
How many hops did Cyrus make? ____________
Number model: ____________

Cyrus makes 9 hops

Number Model : 19-9 = 10

Family Note
In previous lessons, children solved “What’s My Rule?” problems in which they were asked to find outputs and rules. Today they solved problems in which they had to find inputs. Have your child share strategies for finding the input numbers in Problem 1 below.

Also included in this Home Link are more Fact Triangles. This last set of Fact Triangles are all blanks. Fill them with whatever facts your child would like to practice more.

Solve the “What’s My Rule?” problems. Complete the number sentences to check your answers.
Question 1.

7 + 7 = ________
________ + 7 = 13
0 + 7 = ________
________ + 7 = 1 7

7 + 7 = 14
6 + 7 = 13
0 + 7 = 7
10 + 7 = 1 7

Question 2.

________ – 6 = 7
________ – 6 = 0
________ – 6 = 9
________ – 6 = 4

13 – 6 = 7
6 – 6 = 0
15 – 6 = 9
10 – 6 = 4

Practice
Question 3.
__________

50

Time on a Digital Clock

Family Note
In Unit 6, your child learned about the hour hand of a clock and how it moves as hours pass. Children told time on clocks that had only hour hands. In today’s lesson, your child learned about the minute hand. Children told time to the hour on analog clocks with hour hands and minute hands. They also learned to read the time on digital clocks.

Record the time.
Question 1.

3:00

Question 2.

11:00

Draw hands to show the time.
Question 3.

Question 4.

Practice
Question 5.
Write <, >, or =.
13 42
106 105
16 + 23 39

13 < 42

106 > 105

16+23 = 39

Reviewing Measurement

Family Note
Today your child reviewed measurement ideas learned in first grade. Children measured length in paper clips, then made rulers with paper clips as the units. Work with your child to select and measure items around the home using the paper-clip ruler. Please make sure your child brings his or her ruler back to class, as it will be used again.

Find 5 paths or objects in your home to measure with your paper-clip ruler.
Question 1.
I measured ___________.
It is about ______ paper-clip units long.
I measured a pencil
It is about 8 paper-clip units long.

Exaplanation:
I took a pencil at my home and measured it with the paper clip ruler by placing the ruler beside the pencil and it is about 8 paper clips long.

Question 2.
I measured ___________.
It is about ______ paper-clip units long.
I measured a spoon.
It is about 5 paper-clip units long.

Explanation:
I took a spoon from kitchen, i measured it with the paper clip ruler by placing the ruler beside the spoon and i found that the spoon is 5 paper clip units long.

Question 3.
I measured ___________.
It is about ______ paper-clip units long.
I measured a telivision remote.
It is about 9 paper-clip units long.

Explanation:
I took a telivision remote, i measured it with the paper clip ruler by placing the ruler beside the remote and i found that the remote is 9 paper clip units long.

Question 4.
I measured ___________.
It is about ______ paper-clip units long.
I measured a pen.
It is about 8 paper-clip units long.

Explanation:
I took a pen, i measured it with the paper clip ruler by placing the ruler beside the pen and i found that the pen is 8 paper clip units long.

Question 5.
I measured ___________.
It is about ______ paper-clip units long.
I measured a cup.
It is about 3 paper-clip units long.

Explanation:
I took a cup, i measured it with the paper clip ruler by placing the ruler beside the cup and i found that the cup is 3 paper clip units long.

Practice
Question 6.
Write <, >, or =.
15 ______ 51
80 ______ 80
49 ______ 44
16 ______ 106
15 < 51
80 = 80
49 > 44
16 < 106

Explanation:
The number 15 is less than 51,
The number 80 is equal to 80,
The number 49 is greater than 44,
The number 16 is less than 106.

2-Digit Number Stories

Family Note
Today your child practiced adding and subtracting 2-digit numbers by pretending to shop at a school store.
Sample Story

I bought a ball and an eraser. I paid 52 ¢. Number model: 35¢ + 17¢ = 52¢

Question 1.
Think of two things to buy. Draw a picture and write a number story about buying them. Use the back of the page if needed. Then write a number model.
Number model: ___________

Pencil 28¢                Sharpener 18¢

Explanation:
I bought a pencil and a sharpener,
I paid 46¢.
Number model: 28¢ + 18¢ = 46¢.

Practice
Question 2.
Record the time.

______ : _______

Explanation:
In the first clock I recorded the time 3:30 in the given clock by pointing the hours hand towards 3 amd the minutes hand towards 6 which means 30 minutes.
The second clock shows the time 9:00.I wrote the time in the box below the clock as the hours hand is pointing towards 9 and the minutes hand towards 12 which tells that the time is 9:00.

Shopping for School Supplies

Family Note
Today your child practiced explaining solution strategies clearly. Clear explanations make sense to the listener and include all of the steps used to solve the problem. For example, “I started at 21 and counted up,” would not be a clear explanation for how a child added 21 and 7. An example of a clear explanation would be, “I started at 21. Then I counted up 7. I ended at 28. So, 21 + 7 = 28.”

After your child solves the problem below, ask him or her to explain the strategy used. Ask questions to encourage your child to explain the strategy clearly.

Question 1.
You bought these items at the school store. How much did you pay in all?

I paid _________ cents.
Explain to someone at home how you solved the problem.
I paid 61 cents.

Explanation:
I bought a pack of stickers, a crayon and a scissors.
The stickers costs 25cents, crayon 6cents and sicssors 30cents.
To find the total amount i paid,
First I started counting at 25. Then I counted up 6. I ended at 31. So, 25 + 6 = 31.
Later I started at 31. Then I counted up 30. I ended at 61. So, 31 + 30 = 61.
Therefore i paid 61 cents in all.

Practice
Question 2.
Solve.
20 = 8 + _______ + 5
17 = 6 + _______ + 7
20 = 8 + 7 + 5

Explanation:
I started counting at 8. Then I counted up 5. I ended at 13. So, 8 + 5 = 13.
I started counting at 20. Then i counted down 13. I ended at 7. So, 20-13=7.

17 = 6 + 4 + 7

Explanation:
I started counting at 6. Then I counted up 7. I ended at 13. So, 6 + 7 = 13.
I started counting at 17. Then i counted down 13. I ended at 4. So, 17-13=4.

Broken-Calculator Puzzles

Family Note
In one of today’s Exploration activities, your child solved broken-calculator puzzles. In these puzzles children came up with ways to make their calculators display a number, even though an important key was broken. They also divided a rectangle into equal shares, and they conducted a final Facts Inventory about which addition and subtraction facts they know.

Use + and – to solve the broken-calculator puzzles. Use a calculator to check your answers.
Question 1.
Imagine your 3-key is broken. Write at least three ways to show 30.
10 + 10 + 10 = 30
20 + 10 = 30
29 + 1 = 30

Explanation:
If my 3-key of calculator is broken the i can show the sum 30 in 3 ways by using the other keys like 0, 1,  2, 9 .I checked my answers in the calculator and i found that the answers are correct.

Question 2.
Imagine your 5-key is broken. Write at least three ways to show 15. Use subtraction in one of the ways.
8 + 7 = 15
14 + 1 = 15
16 – 1 = 15

Explanation:
If my 5-key of calculator is broken the i can show the sum 15 in 3 ways by using the other keys like 1, 4, 6, 7, 8 .I checked my answers in the calculator and i found that the answers are correct.

Question 3.
Imagine your 1-key is broken. Write at least three ways to show 18.
9 + 9 = 18
20 – 2 = 18
8 + 8 + 2 = 18

Explanation:
If my 1-key of calculator is broken the i can show the sum 18 in 3 ways by using the other keys like 2, 8, 9.I checked my answers in the calculator and i found that the answers are correct.

Practice
Question 4.
Jake has and . Show one exchange he could make.

Explanation:
In the above question it is given that jake has 9 tens and 2 ones,
One exchange he could make is dividing 1 tens into 10 ones.
Now jake has 8 tens and 12 ones.

Family Note

Solve.
Question 1.
How much does it cost to buy a pencil and a toy car ?
It costs 95¢ to buy a pencil and a toy car.

Explanation:
A pencil costs 30¢  and the toy car costs 65¢ .So, to find the cost of both a pencil and a car,
I started counting at 30. Then I counted up 65. I ended at 95. So, 30 + 65 = 95.

Question 2.
How much does it cost to buy a fruit bar and a ring?
It costs 95¢ to buy a fruit bar and a ring.

Explanation:
A fruit bar costs 45¢  and the ring costs 50¢ .So, to find the cost of both fruit bar and a ring,
I started counting at 45. Then I counted up 50. I ended at 95. So, 45 + 50 = 95.

Practice
Question 3.
Put together shapes to make 2 new shapes on the back of this paper. Use a triangle, square, and a half circle.

Explanation:
Using the shapes triangle, square and half circle i made the above two shapes.

More 2-Digit Number Stories

Family Note
Today your child solved more vending machine number stories and practiced adding and subtracting 2-digit numbers using a variety of strategies. Your child also wrote number stories and represented them with number models. Provide pennies and dimes for solving the problems below.

Solve the problems and write the number models. Ramona has 44¢. Scott has 26¢. A stamp costs 46¢.
Question 1.
Can Ramona or Scott buy a stamp?
No

Explanation:
The stamp costs 46¢ and Ramona has 44¢ and Scott has 26¢.They both have less money than the cost of the stamp.
Ramona and Scott cannot buy the stamp as they dont have enough money to buy.

Question 2.
How much more money does Ramona need? ________ ¢
Number model: ______________
Ramona need 2¢ more to buy the stamp
Number model: 44 + 2 = 46¢, 46 – 44 = 2¢.

Explanation:
Ramona has 44¢ as the stamp costs 46¢ i started counting at 46, then counted down 44.I ended at 2. So, 46-44=2¢.

Question 3.
How much more money does Scott need? _________ ¢
Number model: ______________
Scott need 20¢ more to buy the stamp
Number model: 26 + 20 = 46¢, 46 – 26 = 20¢.

Explanation:
Scott has 26¢ as the stamp costs 46¢ i started counting at 46, then counted down 26.I ended at 20. So, 46-26=20¢.

Question 4.
How much money do Ramona and Scott have all together? _________ ¢
Number model: ______________
Ramona and Scott have all together 70¢
Number model: 44 + 26 = 70¢

Explanation:
Ramona has 44¢ and Scott has 26¢
To find the money both Ramona and Scott have we have to add 44 and 26 So, I started counting at 44, then counted up 26.I ended at 70.So, 44 + 26 = 70¢

Question 5.
If they buy a stamp together, how much money will they have left? _______ ¢
Number model: ______________
If they buy a stamp together, the money they will have left is 24¢
Number model: 70 – 46 = 24, 46 + 24 = 70.

Explanation:
Ramona and Scott have all together 70¢ , the stamp costs 46¢ .
To find the money left, i started counting at 70, then counted down 46.I ended at 24. So, 70 – 46 = 24¢.

Practice
Question 6.
Solve.
30 + _______ = 100
67 = _________ + 45
12 + 21 = ________
30 + 70 = 100
67 = 22 + 45
12 + 21 = 33

Explanation:
I started counting at 100, then i counted down 30.I ended at 70.So, 30 + 70 = 100
I started counting at 67, then i counted down 45.I ended at 22.So, 67 = 22 + 45
I started counting at 12, then i counted up 21.I ended at 33.So, 12 + 21 = 33.

Family Note
Today your child continued using various strategies to solve number stories involving adding and subtracting larger numbers. Encourage your child to explain how more than one strategy can be used to solve each of the problems on this page.

Solve.
Write a number model for each story.
Question 1.
Daniel built a tower with blocks. It had 47 cubes and 20 cylinders. How many blocks are in Daniel’s tower? __________ blocks
Number model: _________________
Daniel’s tower has 67 blocks
Number model: 47 + 20 = 67

Explanation:
I started counting at 47, then i counted up 20.I ended at 67.So, 47 + 20 = 67.

Question 2.
Carmen used blocks to make a fort. She used 37 cubes and 37 cones. How many blocks are in her fort? __________ blocks
Number model: _________________
Carmen’s fort has 74 blocks
Number model: 37 + 37 = 74

Explanation:
I started counting at 37, then i counted up 37.I ended at 74.So, 37 + 37 = 74.

Question 3.
Janet built a tower out of blocks. She used 22 cubes, 26 cylinders, and 10 cones. How many blocks are in Janet’s tower? __________ blocks
Number model: __________ + __________ + __________ = __________
Janet’s tower has 58 blocks
Number model: 22 + 26 + 10 = 58

Explanation:
First I started counting at 22, then i counted up 26.I ended at 48.So, 22 + 26 = 48.
Later I started counting at 48, then i counted up 10.I ended at 58.So, 48 + 10 = 58.

Practice
Question 4.
Solve. Use dimes if you like.
90 – 40 = __________
80 – 20 = __________
60 – 30 = __________
70 – 30 = __________
90 – 40 = 50
80 – 20 = 60
60 – 30 = 30
70 – 30 =  40

Explanation:
I started counting at 90, then i counted down 40.I ended at 50.So, 90 – 40 = 50
I started counting at 80, then i counted down 20.I ended at 60.So, 80 – 20 = 60
I started counting at 60, then i counted down 30.I ended at 30.So, 60 – 30 = 30
I started counting at 70, then i counted down 30.I ended at 40.So, 90 – 40 = 40.

Review: Relations and Equivalence

Family Note
Today your child reviewed equivalence by determining whether number sentences were true or false. Children also added prices and wrote comparison number models.

Ryan and Janae are choosing things to buy. Circle the group that costs more money.
Write a number model with < or > to compare the prices.
Question 1.

Number model: _________________

Rubber bands and box of crayons
Number model: 56 < 88.

Explanation:
I circled the group rubberbands and box of crayons
The sum of stickers and pen is 25 + 31 = 56¢
The sum of rubber bands and box of crayons is 8 + 80 = 88¢
I sarted counting at 8, then i counted up 80.I ended at 88.So, 8 + 80 = 88¢
I started counting at 25, then i counted up 31.I ended at 56.So, 25 + 31 = 56¢
56 < 88
Therefore, the circled group has more money.

Question 2.

Number model: _________________

Eraser and ball
Number model: 62 < 67.

Explanation:
I circled the group eraser and ball
The sum of money of colored pencil, pen and paperclip is 29 + 31 + 2 = 62¢
The sum of eraser and ball is 17 + 50 = 67¢
First I sarted counting at 29, then i counted up 31.I ended at 60.So, 29 + 31 = 60¢, then I sarted counting at 60, then counted up 2.I ended at 62.So, 60 + 2 = 62¢
I started counting at 17, then i counted up 50.I ended at 67.So, 17 + 50 = 67¢
62 < 67
Therefore, the circled group has more money.

Practice
Question 3.
Jada and Martin cut a pizza in half to share. Then Min and Julius want to share the pizza, too. So they cut the pizza into fourths.
Are the shares now larger or smaller? ___________
The shares are now smaller.

Explanation:
If Jada and martin cut a pizza in half to share, their share will be half of pizza but when min and julius want to share pizza they cut the pizza into fourths, now their share will be quarter that is one fourth.

Review: Home Place Value

Family Note
Today your child reviewed place value. Children also completed number-grid puzzles for 2-digit numbers. Ask your child to explain how to solve each problem below.

Fill in the missing numbers.
Question 1.

Explanation:
I reviewed place value.The 2-digit numbers in 100chart.To complete the number-grid puzzles for 2-digit numbers, we have to count up by 1 to find the mising number to the right of the given number, count down by 1 to find the missing number to the left of the given number,count down by 10 to find the missing number at the top of the given number and count up by 10 to find the missing numbe rtat the bottom of the given number.

Question 2.

Question 3.

Question 4.

Practice
Question 5.
Subtract.
= 8 – 4
= 80 – 40
9 – 3 =
90 – 30 =
= 8 – 4
= 80 – 40
9 – 3 =
90 – 30 =

Explanation:
I started counting at 8, then i counted down 4.I ended at 4.So, 8 – 4 = 4
I started counting at 80, then i counted down 40.I ended at 40.So, 80 – 40 = 40
I started counting at 9, then i counted down 3.I ended at 6.So, 9 – 3 = 6
I started counting at 90, then i counted down 30.I ended at 60.So, 90 – 30 = 60

Review: 3-Dimensional Geometry

Family Note
Today your child reviewed attributes of 3-dimensional shapes. Ask your child to point out objects of various shapes around your home or outside and name their defining attributes.

Choose from the shapes above. Tell which shape is described.
Question 1.
Its faces are all squares. ___________
Cube

Explanation:
A cube has 6 faces and all faces of a cube are square faces.

Question 2.
It has exactly two flat faces. __________
Cylinder

Explanation:
A cylinder has 2 flat faces and 1 curved face.

Question 3.
It has 6 flat faces. ___________
Rectangular prism or Cube

Explanation:
A rectangular prism and a cube has 6 flat faces.

Question 4.
Some of its faces are triangles. ____________
Pyramid

Explanation:
A pryamid has 5 faces.One is a square and some are triangles.

Question 5.
One or more of its faces is a circle. ____________
Cone or Cylinder

Explanation:
A cone has 1 circle face and a cyliner has 2 circle faces.

Practice
Question 6.
Risa has 6 red ribbons, 4 blue ribbons, and 3 purple ribbons.
How many ribbons does she have? ____________
Number model: _______ + _______ + _______ = ________
Risa has 13 ribbons in all
Number model: 6 + 4 + 3 = 13

Explanation:
First I sarted counting at 6, then i counted up 4.I ended at 10.So, 6 + 4 = 10, then I sarted counting at 10, then counted up 3.I ended at 10.So, 10 + 3 = 13

Review: Equal Shares

Family Note
Today your child reviewed dividing rectangles and circles into 2 or 4 equal shares. Children were reminded about the different names for these shares and for the whole. Help your child divide the shapes below and compare the sizes of the shares.

Question 1.
Divide each shape in fourths. Shade 1 fourth.

Explanation:
I divided the given shapes into four equal parts by drawing 2 lines and i shaded 1 part of the four parts.

Question 2.
Divide each shape in half. Shade 1 half.

Explanation:
I divided the given shapes into two equal parts by drawing 1 line and i shaded 1 part of the two parts.

Question 3.
Put a check next to the circle with the largest shares. Put a check next to the rectangle with the largest shares.

Explanation:
I have marked right that circle and rectangle with the largest share.Th erecatngle in the first question and the circle in the second question has the largest share.

Practice
Question 4.
86 + 10 = _________
_______ = 45 – 10
70 – 50 = _________
86 + 10 = 96
35 = 45 – 10
70 – 50 = 20

Explanation:
I started counting at 86, then i counted up 10.I ended at 96.So, 86 + 10  = 96
I started counting at 45, then i counted down 10.I ended at 35.So, 45 – 10 = 35
I started counting at 70, then i counted down 50.I ended at 20.So, 70 – 50 = 20.

## Everyday Mathematics 6th Grade Answer Key Unit 4 Expressions and Equations

Using Order of Operations
Question 1.
Insert parentheses to make the expression equivalent to the target number.
Numerical Expression
8 – 2 + 5
15 – 3 ∗ 4 + 2
3 ∗ 5 + 4 ∗ 6

Target Number
1
50
162

Question 2.
Simplify each expression.
a. (3 + 9)2 ________
b. 24 ∗ 22 ________
c. 20 – (6 – 4) ________
d. ($$\frac{1}{2}$$ ÷ $$\frac{1}{4}$$) ∗ 6 ________

Question 3.
Complete the table

Question 4.
Use the given calculator keys to find an expression equivalent to the target number. You may use the keys more than once or not at all.

Practice
Write the opposite of each number.
Question 5.
12 ________

Question 6.
-2 ________

Question 7.
-3.5 ________

Question 8.
$$\frac{3}{5}$$ ________

Practicing Order of Operations
In Problems 1–3, tell whether the number sentence is true or false. If it is false, rewrite it with parentheses to make it true.

Question 4.
Evaluate.
a. 45 – (1 + 4)2 + 3

b. (2 + 4)2 ∗ (1 + 2)4

Question 5.
Write an expression for AT LEAST three of the following numbers using six 7s. All values can be found using only addition, subtraction, multiplication, and division.
1 = ____________
2 = ____________
3 = ____________
4 = ____________
5 = ____________
6 = ____________

Practice
Find the greatest common factor.
Question 6.
GCF (10, 50) = _______

Question 7.
GCF (80, 24) = _______

Question 8.
GCF (90, 54) = __________

Using Expressions
Question 1.
Write a numerical expression for calculating the number of shaded border tiles for the pictured 12-by-12 tiled floor.

b. Circle the expressions below that also represent the number of shaded tiles in the 12-by-12 tiled floor.
11 + 11 + 11 + 11
4 ∗ 12 + 4
(12 – 2) + (12 – 2) + 12 + 12
4 ∗ 12 – 2

c. Choose one of the expressions you circled in Part b and explain how it represents the number of shaded tiles

Question 2.
A rectangular tiled floor is shown at the right. Write an expression that models how you can find the number of shaded tiles in the 3-by-10 rectangular floor.

Question 3.
Write an expression that models how you can find the number of shaded tiles in the 3-by-13 rectangular floor shown at the right.

Try This
Question 4.
Write an algebraic expression for the number of shaded tiles in a 3-by-n rectangular floor. Use your expression to find the number of shaded tiles in a 3-by-125 tiled floor.

Practice
Find the least common multiple.
Question 5.
LCM (3, 5) = ________

Question 6.
LCM (10, 12) = ________

Question 7.
LCM (6, 12) = ________

Algebraic Expressions
Write an algebraic expression. Use your expression to solve the problem.
Question 1.
Kayla has x hats. Miriam has 6 fewer hats than Kayla. _______
If Kayla has 22 hats, how many hats does Miriam have? _______

Question 2.
The width of Rectangle A is half of its height. Write an algebraic expression for the width of Rectangle A.
a. Define your variable. Let ____ represent ________.
b. Algebraic expression: _______________
c. Using the variable you defined in Part a, write an algebraic expression for the perimeter of Rectangle A __________.

Question 3.
Larry ran 2.5 miles more than Jusef.
Write an algebraic expression for how far Larry ran.
a. Define your variable. Let _______ represent __________.
b. Algebraic expression: __________
c. If Jusef ran 5 miles, how many miles did Larry run? __________

Question 4.
For each situation, choose an expression from the box that matches the situation, and write it in the matching blank. You may use an expression more than once.

a. With 4 bags of n potatoes, the total number of potatoes is __________.
b. If you exchange n quarters for dollars, you get __________ dollars.
c. There are n pens in a box. Denise has 4 pens more than 2 boxes of pens. The total number of pens Denise has is __________.

Practice
Use <, >, or = to make the number sentence true.
Question 5.
$$\frac{3}{4}$$ ________ $$\frac{3}{7}$$

Question 6.
0.4 _______ 0.400

Question 7.
0.8 ________ 0.67

Question 1.
Look for a pattern in the set of numerical equations. Describe the pattern in words. Use a variable and write an equation that represents the pattern.
36 = 32 ∗ 34
586 = 582 ∗ 584
(0.25)6 = (0.25)2 ∗ (0.25)4
a. Description: ____________________
b. Equation that generalizes the pattern: ____________________
c. Write two more examples of the pattern: ____________________

Question 2.
For each equation, circle the number of solutions you could find.

Question 3.
Circle the answer that best describes each equation.

Question 4.

Try This
Question 5.
The numbers 4, 5, and 6 are called consecutive numbers because they follow each other in order. The sum of 4, 5, and 6 is 15—that is, 4 + 5 + 6 = 15. Circle all equations that generalize finding a sum of 170 for three consecutive numbers.
a. x + 2x + 3x = 170
b. 170 = x + (x + 1) + (x + 2)
c. 3x + 3 = 170

Practice
Estimate whether each sum is closest to 0, $$\frac{1}{2}$$, 1, or 1 $$\frac{1}{2}$$.
Question 6.
$$\frac{8}{9}$$ + $$\frac{5}{8}$$ _________

Question 7.
$$\frac{1}{10}$$ + $$\frac{1}{11}$$ __________

Question 8.
$$\frac{5}{6}$$ + $$\frac{2}{16}$$ _________

The Distributive Property
Question 1.
Each of the expressions describes the area of the shaded part of one of the rectangles. Write the letter of the correct rectangle next to each expression.

a. 4 ∗ (11 – 6) _________
b. 44 – 20 _________
c. 30 _________
d. (6 ∗ 9) – (6 ∗ 4) _________
e. (4 ∗ 11) – (4 ∗ 6) _________
f. (11 – 5) ∗ 4 _________
g. (11 ∗ 4) – (5 ∗ 4) _________
h. 6 ∗ (9 – 4) _________

Question 2.
Circle the equations that are examples of the Distributive Property.
a. (80 ∗ 5) + (120 ∗ 5) = (80 + 120) ∗ 5
b. 6 ∗ (3 – 0.5) = (6 ∗ 3) – 0.5
c. (9 ∗ $$\frac{3}{8}$$) – ($$\frac{2}{3}$$ ∗ $$\frac{3}{8}$$) = (9 – $$\frac{2}{3}$$) ∗ $$\frac{3}{8}$$
d. (16 ∗ 4) + 12 = (16 + 12) ∗ (4 + 12)

Write an equation to show how the Distributive Property can help you solve each problem.
Question 3.
Kelly signed copies of her new book at a local bookstore. In the morning she signed 36 books, and in the afternoon she signed 51 books. It took her 5 minutes to sign a book. How much time did she spend signing books?
Equation: __________________
Solution: __________________

Question 4.
Mr. Katz gave a party because all the students scored 100% on their math tests. He had budgeted $1.15 per student. It turned out that he spent$0.25 less per student. How much money did he spend for 30 students?
Equation: __________________
Solution: __________________

Practice
Write the reciprocal.
Question 5.
5 ________

Question 6.
$$\frac{2}{9}$$ ________

Question 7.
3 $$\frac{1}{3}$$ _______

Applying the Distributive Property

Question 1.
Match each property with a generalized form of the property

Question 2.
For each equation below, use general equations for properties to determine whether it is true or false. For each true number sentence, list the property or properties that apply. For false number sentences, write “None.”
a. (9 – 4) ∗ 3 = (9 – 3) ∗ (4 – 3) _______ Property: ____________
b. (8 + 5) ∗ 2 = (8 + 2) ∗ (5 + 2) _______ Property: ____________
c. (8 + 5) ∗ 2 = 2 ∗ (8 + 5) _______ Property: ____________

Use the Distributive Property to solve Problems 3–4.
Question 3.
Show how to solve the problems mentally.
a. 85 ∗ 101 = ____________
b. 156 ∗ 9 = ____________
c. 48 ∗ 24 = ____________

Question 4.
Rewrite each expression as a product by taking out a common factor
a. 48 + 24 = _______ ∗ (_______ + _______) = _______ ∗ _______
b. 72 – 56 = _______ ∗ (_______ – _______) = _______ ∗ _______
c. (2y) + (3 ∗ y) = (_______ + _______) ∗ _______ = _______ ∗ _______

Practice
Use <, >, or = to make the sentence true.
Question 5.
$$\frac{2}{3}$$ _________ $$\frac{2}{5}$$

Question 6.
0.7 _______ $$\frac{4}{5}$$

Question 7.
0.3 ______ 0.23

Question 8.
1 $$\frac{1}{4}$$ _______ 1.25

Building with Toothpicks
Yaneli is building a pattern with toothpicks. The pattern grows in the following way:

Question 1.
How many toothpicks are needed for Design 5? _________

Question 2.
How many toothpicks are needed for Design 10? __________

Question 3.
Describe in words how you see the toothpick design growing. What stays the same from one figure to the next? What changes?

Question 4.
Write an expression to represent how many toothpicks are needed for Design n?

Question 5.
What toothpick design number could you build with exactly 82 toothpicks? ________

Question 6.
Describe how you can figure out the number of toothpicks you need for any design number.

Practice
Evaluate each expression.
Question 7.
72 = ________

Question 8.
_________ = 24

Question 9.
15 = __________

Question 10.
43 = ____________

Inequalities
Question 1.
Amelia’s cell phone plan lets her send a maximum of 500 text messages per month.
Define a variable.
Write an inequality to represent Amelia’s situation.

Question 2.
The temperature in the freezer should be no higher than -18°C.
Define a variable.
Write an inequality to represent the situation.

Question 3.
Sam scored 68 in miniature golf. What score would beat Sam’s score?
Define a variable:
Write an inequality to represent the situation.

Question 4.
Choose the number sentence that represents each statement

A number is less than 42. __________
b. A number is greater than 42. __________
c. A number is at least 42. __________
d. A number is no greater than 42. __________

Practice
Question 5.
______ = 5.6 + 11.7

Question 6.
9.2 + _______ = 12.1

Question 7.
19.37 – 9.29 = _______

Question 8.
______ = 0.834 – 0.75

Solving and Graphing Inequalities
Describe the solution set for each inequality. Graph the solutions for each inequality.
Question 1.
a. 5 < n _____________

b. q < 5 ______________

c. w > -3 __________________

Question 2.
Write the inequality represented by each graph below.
a.

b.

c. List three numbersthat are part of the solution set for Part a.

Question 3.
a. Write an inequality with a solution set that is all numbers less than 0.
b. Find three numbers that are not in the solution set for Part a.
c. Write an inequality with a solution set that does not have any numbers in common with the solution set in Part a or the numbers you wrote in Part

Practice
Solve.
Question 4.
3.45 ∗ 2 = ________

Question 5.
3.2 ∗ 4.5 = _________

Question 6.
________ = 1.53 ∗ 3.3

Graphing Alligator Facts
Question 1.
If the temperature of an alligator nest is below 86°F, the female alligators hatch.
Define a variable: _______________
Represent the statement with inequalities: _______________
Graph the solution set that makes both inequalities true.

Describe how your graph represents the situation.

Question 2.
If the temperature of an alligator nest is above 93°F, the male alligators hatch. Use the same variable you used in Problem 1.
Represent the statement with inequalities: _______________
Graph the solution set that makes both inequalities true.

Question 3.
Adult alligators are at least 6 feet long. The longest one on record was 19 feet.
Define a variable: _______________
Represent the statement with inequalities: _______________
Graph the solution set that makes both inequalities true.

Question 4.
Alligators lay 20–50 eggs in a clutch. Variable: _______________
Represent the statement with inequalities: _______________
Graph the solution set that makes both inequalities true.

Describe how your graph represents the situation.

Practice
Evaluate.
Question 5.
15% of 60 ______

Question 6.
25% of 300 ______

Question 7.
250% of 18 ________

Absolute Value
Question 1.
a. On the number line, plot points at two numbers whose absolute values are 8.

b. Explain why you get a positive number when you take the absolute value of a negative number.

Question 2.
Complete.
a. |20| = ________
b. |8.25| = ________
c. |-79| = ________
d. |-0.004| = ________
e. |-10 $$\frac{1}{2}$$ | = ________
f. |0| = ________

Question 3.
Find at least three numbers that answer each riddle.
a. A number with an absolute value that is equal to itself ___________
b. A number with an absolute value that is its opposite ____________

Question 4.
Make up your own absolute value riddle

Try This
Question 5.
Find at least three numbers that make each statement true
a. |x| = – x ___________
b. |x| > – x ___________

Practice
Divide.
Express your remainder as a fraction.
Question 6.

Question 7.

Using Absolute Value
For Problems 1–2, do the following:

• Plot the numbers on the number line.

Question 1.
The freezing point of water is 0°C. In Chicago, it is -7°C. In Montreal, it is -9°C.

Which city’s temperature is farther from 0? ________
-7 > -9 or |-9| > |-7|

Question 2.
Rita has a debt of $14, and Jamal has a debt of$18.

Whose balance is farther from 0? ________
|-18| > |-14| or -18 < -14

Question 3.
Explain how you know whether you need to use absolute value to answer the question. What do you have to consider?

Question 4.
Find the distance between the ordered pairs.
a. (-2, -1) and (-2, 3) Distance: ________
b. (-2, 3) and (3, 3) Distance: ________
c. (3, -1) and (3, -4.5) Distance: ________
d. (-11, 9) and (-11, -32) Distance: ________

Practice
Solve
Question 5.
2 $$\frac{1}{2}$$ ÷ $$\frac{3}{4}$$ = __________

Question 6.
1 $$\frac{2}{3}$$ ÷ $$\frac{1}{3}$$ = ________

Question 7.
3 $$\frac{3}{4}$$ ÷ $$\frac{1}{3}$$ = _________

Temperatures in Seattle
The city of Seattle is located in the state of Washington. It is located 113 miles south of the U.S.–Canadian border at a latitude of 47°37′ N. The city is located at sea level on Puget Sound, near the Pacific Ocean.
Question 1.
Use the information above to predict whether Seattle’s monthly average temperature data will have a large or small mean absolute deviation. Explain your answer.

Question 2.
The average monthly temperatures for Seattle are given below. Find the listed data landmarks and measures of spread. Round your answers to the nearest tenth.

a. Minimum: _________
b. Maximum: _________
c. Median: _________
d. Mean: _________
e. Range: _________
f. Mean absolute deviation: _________

Question 3.
Use the data landmarks and measures of spread you found in Problem 2 to draw some conclusions about Seattle’s average monthly temperatures.

Bring in one 3-dimensional shape with faces made up of polygons. It will go in the class Shapes Museum. Find a shape that has at least one face that is not a rectangle. See pages 246–248 in your Student Reference Book for examples of the kinds of shapes to bring.
Practice
Solve.
Question 4.
_______ = 0.09 ÷ 0.03

Question 5.
0.75 ÷ 0.3 = _______

Question 6.
24 ÷ 0.48 = ______

Question 7.
________ = 5.2 ÷ 1.6

## Everyday Mathematics 6th Grade Answer Key Unit 5 Area and Volume Explorations

Polygon Side Lengths
Question 1.
Find any missing coordinates. Plot and label the points on the coordinate grid. Draw the polygon by connecting the points.

a. Rectangle ABCD
A: (1, 1) B: (-1, 1)
The length of $$\overline{B C}$$ is represented by
|1| + |-4| = _______.
C: (_______, _______)
D: (_______, _______)

b. Right triangle XYZ
X: (-5, 1) Z: (-3, 6)
The length of $$\overline{Z Y}$$ is represented by |6| – |1| = _______.
The length of $$\overline{X Y}$$ is represented by |-5| – |-3| = _______.
Y: (_______, _______)

Question 2.
Use rectangle ABCD and triangle XYZ to fill in the following tables. The first row has been done as an example.

Practice
Divide.
Write any remainders using R.
Question 3.

Question 4.

Question 5.

Question 6.

Finding the Areas of Parallelograms
Find the area of each parallelogram. Show your work.
Question 1.

Area: ___________

Question 2.

Area: ___________

Question 3.

Area: ___________

Question 4.

Area: ___________

Try This
The area of each parallelogram is given. Find the length of each base.
Question 5.

Area: 26 square inches
Base: ___________

Question 6.

Area: 5,015 square meters
Base: ___________

Practice
Evaluate.
Question 7.
20% of 45 ________

Question 8.
45% of 60 ________

Question 9.
83% of 110 ________

Triangle Area
Find the area of each triangle. Remember: A = $$\frac{1}{2}$$bh.
Question 1.

Number model: _________
Area = _________

Question 2.

Number model: _________
Area = _________

Question 3.

Number model: _________
Area = _________

Question 4.

Number model: _________
Area = _________

Question 5.
Find the length of the base.

Area = 18 in.2
Base = _________

Try This
Question 6.
Draw a height for the triangle. Find the length of the height.

Area = 48 m2
Height = _________

Practice
Compute.
Question 7.
|-7| = ____

Question 8.
|4| = ____

Question 9.
______ = |-3|

Areas of Complex Shapes
In Problems 1–4, decompose the shapes into polygons for which area formulas can be used. Label the areas. Find the total area for each shape. Use appropriate units.
Question 1.

Area: ________

Question 2.

Area: ________

Question 3.

Area: ________

Try This
Question 4.

Area: ________

Practice
Calculate.
Question 5.
12 – 8.25 = ________

Question 6.
_______ = 9.03 + 0.7 + 18

Question 7.
125.29 – 16.7 = ______

Question 8.
_______ = 0.01 + 0.99

Real- World Nets
Circle the solid that can be made from each net.
Question 1.

Question 2.

Question 3.
Use the net and its corresponding geometric solid in Problem 2.
a. Which polygons make up the faces of your solid? How many are there of each kind? __________
b. Which faces are parallel? __________
c. Which faces are congruent? __________
d. How many edges are there? How many vertices? __________

Practice
Multiply.
Question 4.
5.2 ∗ 3 = ______

Question 5.
1.04 ∗ 2 = ______

Question 6.
______ = 0.14 ∗ 3

Surface Area Using Nets
Silly Socks is trying to choose a type of plastic box for their socks. The nets for three different box designs are given below.

Question 1.
Without calculating, predict which design will require the least amount of plastic to produce.

Question 2.
Find the surface area for each plastic-box design. Write a number sentence to show how you found the surface area. Remember to use the correct order of operations.

Question 3.
Explain how to find the surface area for any rectangular or triangular prism.

Practice
Question 4.

Question 5.

Question 6.

Surface Area
Question 1.
Sam is painting the outside of a doghouse dark green (except for the bottom, which is on the ground).

The doghouse measures 3 feet wide by 4.5 feet long. It is 4 feet high.
The roof is flat, so the doghouse looks like a rectangular prism.
The entrance to the dog house is 1.5 feet wide by 2 feet high.
a. Label the doghouse diagram with the measurements.

b. On the grid below, draw a net for a prism that could represent Sam’s doghouse.
Scale: ☐ = 1 square foot

c. How many square feet is he painting?

d. One pint of paint covers about 44 ft2. How many pints does he need?

Practice
Evaluate.
Question 2.
43 ______

Question 3.
1.52 _______

Question 4.
150 ______

Question 5.
($$\frac{2}{3}$$)2 ______

Jayson was comparing the areas of the polygons at the right.

Here is Jayson’s reasoning: I think that Polygons K and L have the same area. I lined up the sides of each polygon and they were equal, so I labeled the sides with the same variables. So the area of Polygon K is equal to the area of Polygon L.
Question 1.
Explain the flaw in Jayson’s reasoning.

Trace Polygon K above, and cut out your tracing. Use it to help you solve Problems 2–3.
Question 2.
Draw two different polygons that have the same area as PolygonK.

Question 3.
Choose one of your polygons from Problem 2. Describe how you used Polygon K to draw a polygon that has the same area.

For Lesson 5-9, bring a rectangular prism, such as an empty tissue box, to class.
Practice
Find the whole.
Question 4.
10% is 7, so 100% is ______.

Question 5.
25% is 90, so 100% is _______.

Volume of Rectangular Prisms
Find the volume for each prism.
Question 1.

Volume ________

Question 2.

Volume _______

Question 3.
The Blueberry Blast cereal box is a rectangular prism that is 12 inches × 8 inches × 4 inches.

a. Label the diagram with the dimensions.
b. What is its volume?

Question 4.
Greta’s gift shop has three sizes of gift boxes. They are all shaped like rectangular prisms. The dimensions are shown below.
Small: 10 cm × 10 cm × 10 cm
Large: 40 cm × 30 cm × 15 cm
Medium: The area of the base is 1,000 cm2 and the height is 8 cm.
Find the volume of each gift box
Small: ________
Large: ________
Medium: ________

Practice
Evaluate
Question 5.
$$\frac{2}{3}$$ + $$\frac{5}{6}$$ = ________

Question 6.
4$$\frac{3}{4}$$ + $$\frac{7}{8}$$ = _________

Question 7.
$$\frac{4}{5}$$ – $$\frac{3}{4}$$ = _________

Question 8.
10 – $$\frac{5}{12}$$ = __________

Calculating Luggage Volume
You may want to consider how much volume your luggage holds when you travel. If you know how to calculate the area of a rectangular prism, you can also find the approximate volume of a suitcase. Below are the measurements of some common suitcase sizes.

Question 1.
a. Find the volume of each suitcase.

b. Find the approximate volume of the interiors. Round to the nearest 0.01 in.3.

Suitcase 1
Exterior: 17″ × 15″ × 8″
a. Volume: __________
Interior: 16″ × 13.75″ × 6.5″
b. Volume:__________

Suitcase 2
Exterior: 21″ × 14″ × 7″
a. Volume: __________
Interior: 19.5″ × 13″ × 5.75″
b. Volume: __________

Suitcase 3
Exterior: 24″ × 16″ × 9.75″
a. Volume: __________
Interior: 22.5″ × 14.75″ × 8.25″
b. Volume: __________

Suitcase 4
Exterior: 28″ × 19″ × 9″
a. Volume: __________
Interior: 26″ × 17.5″ × 7.5″
b. Volume: __________

Question 2.
Describe how you can estimate the interior volume of a suitcase if you know the exterior measurements.

Practice
Evaluate.
Question 3.
$$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$ = ________

Question 4.
$$\frac{5}{12}$$ ÷ $$\frac{7}{12}$$ = _________

Question 5.
_________ = 2$$\frac{2}{3}$$ ÷ $$\frac{1}{2}$$

Question 6.
8 ÷ 2$$\frac{2}{3}$$ = ____________

Volume of Letters
The Santiago Balloon Emporium sells custom balloons shaped like letters of the alphabet. Clarissa orders balloons that spell DOLLIE for her friend’s birthday. She wants the balloons to float, so she plans to fill them with helium. To estimate how much it will cost, Clarissa needs to calculate the approximate volume of helium she will need to fill the balloons.
The volume of each balloon can be estimated based on rectangular prisms.

Measure the dimensions in millimeters for each rectangular part of the letters.
Question 1.
The scale is 1 mm = 1 inch. Each letter has a depth of 5 inches. Estimate the volume of each letter.
D: _________ O: _________ L:_________
I: _________ E: _________

Question 2.
What is the approximate total volume of helium (in cubic inches) needed to fill the letters?

Question 3.
a. Helium comes in tanks that hold either 8.9 ft3, which cost $19.99 each, or 14.9 ft3, which cost$28.99 each. What is the least amount Clarissa can spend to fill her letters with helium? Hint: There are 1,728 in.3 in 1 ft3.

Practice
Divide.
Question 4.

Question 5.

Question 6.

Question 7.

Could a Giant Breathe?
Think about how area and volume change in relation to changes in linear measurements.
Question 1.
How many centimeters are in 1 meter? ____________

Question 2.
How many square centimeters are in 1 square meter? ____________

Question 3.
How many cubic centimeters are in 1 cubic meter? ____________
One cubic centimeter of water has a mass of about 1 gram.

Question 4.
One cubic meter of water has a mass of:
____________ grams ____________ kilograms

Question 5.
One kilogram has a weight equivalent to about 2.2 pounds.
One cubic meter of water weighs about how many pounds? ____________

Question 6.
A giant who is 10 times as tall as you would have lungs that provide ____________ as much oxygen as your lungs.

Question 7.
If the surface area of the giant’s lungs were 100 times greater than yours, and if the giant required oxygen in the same proportions as a human, how do you know the giant would not have enough oxygen? Explain.

Try This
Question 8.
Your lungs fit in a relatively small space inside your rib cage. Research how your lungs increase surface area to be able to supply all the oxygen you need.

Practice
For Problems 9–10 , record the opposite of the number.
Question 9.
-7 _______

Question 10.
0 ______

Question 11.
The opposite of the opposite of -3 ________

## Everyday Mathematics 6th Grade Answer Key Unit 8 Applications: Ratios, Expressions, and Equations

Increasing Yield per Square Foot
The diagram below shows the layout of a garden that has both rows and squares.

Use the yields on the diagram and the table information to determine which plant is in each row or square foot.
Question 1.
Label each garden bed to show what kind of plant and how many of the plants fill the row or square foot.

Question 2.
a. What is the total expected yield for the garden in Problem 1? ____________
b. What is ? ____________

a.  The total expected yield for the garden in problem 1 is 68.5 pounds

b.  The overall rate of plants per square foot is about 2/3 plant to 1 ft 2

Question 3.
a. About how much more should the garden yield if beds I and II are changed from row garden beds to square-foot garden beds? (Assume the same plant would still be planted in each.) ____________
b. What would the overall rate of plants per square foot be? ____________

a. About  2 more pounds should the garden yield if beds I and II are changed from row garden beds to square-foot garden beds.

b. The overall rate of plants per square foot is is 1 plant to 1  ft 2

Practice
Solve the equations.
Question 4.
$$\frac{1}{2}$$p = 87; p = ________

174

Explanation :

1/2 x p = 87

p = 87 x 2 = 174

Therefore, the value of p is 174

Question 5.
$$\frac{2}{3}$$d = 56; d = __________

84

Explanation :

2/3 x d = 56

d = 56 x 3 / 2

d = 28 x 3 = 84

Therefore, the value of d is 84

Question 6.
$$\frac{7}{8}$$k = 84; k = __________

96

Explanation :

7/8 x k = 84

k = 84 x 8 /7

K = 12 x 8 = 96

Therefore, the value of k is 96

Question 1.
Using Scale Drawings Julian made a scale drawing of his bedroom wall. He has artwork that he and his brother made hanging on the wall. His wall is 7 feet high and 12 feet long.

a. What scale did he use? ________
b. Use his scale drawing to complete the table.

a.  The scale he used is 1/2 inch equals to 1 foot ( 1/2 inch = 1 foot )

b.

Question 2.
Explain how you found the actual dimensions for Artwork B.
_______________________
______________________

2 Squares = 1 foot

4 Squares = 2 feet

So, 5 squares = 25 Feet

Question 3.
Why might someone make a scale drawing of a planned artwork arrangement?
_______________________
________________________

To make sure that result is so perfect and so accurate.

Practice Solve.
Question 4.
15% of x is 6. 100% of x is ________

40

Explanation :

15 % = 15/100

Given,

15% of x is 6

= 15/100 X x -= 6

x = 100 X 6 /15

x = 40

And 100% = 100/100 = 1

Therefore, 100% of 40 is 1 x 40 = 40.

Question 5.
90% of y is 18. 100% of y is ________.

20

Explanation:

90% = 90/100

Given,

90% of y is 18

= 90/100 X y = 18

y = 18 X 100 /90

y = 20

And  100% = 100/100 = 1

Therefore, 100% of 20 is 1 X 20  =20

Stretching Triangles
Question 1.
Plot the original ordered pairs from the table in Problem 2, and connect points to make triangle ABC and triangle ADE.

Question 2.
If you want to make triangle ABC and triangle ADE twice as tall and twice as wide, what would the new coordinates be? Write them in the table below.

Question 3.
What is the distance from D to E in the enlarged figure? ________

The distance from D to E in the enlarged figure is 4 units

Question 4.
What is the distance from D to E in the original figure? __________

The distance from D to E in the original figure is 2 Units

Question 5.
Use ratio notation to represent the ratio of side length $$\ over line{D E}$$ in the enlarged figure to side length $$\over line{D E}$$ in the original figure. _______

2 :1

Practice Solve.
Question 6.
$$\frac{3}{4}$$ (4 – $$\frac{2}{3}$$) = _______

3/4 X [4-2/3]

3/4 X[ 10/3]

= 5/2

Question 7.

3 + $$\frac{1}{2}$$ ÷ 3 = ________

3 + [ 1/2 / 3]

3 + [1/6]

= 19/6

Question 8.
______ = 2$$\frac{1}{2}$$ ÷ ($$\frac{4}{3}$$ – $$\frac{1}{2}$$)

[5/2] / (4/3-1/2)

[5/2] / ( 5/6)

= 3

Modeling Distances in the Solar System
Today the class made scale models of celestial bodies.
Imagine you are modeling the distance of each planet from the Sun.
Question 1.
Calculate the distance from the Sun in your model using the scale given in the table. Complete the table.

Question 2.
Would this scale work for building the model in your classroom? Why or why not?
_____________________________
______________________________

No, this scale not work for building the model in our classroom. Because, this scale is too large  for the distances.

Question 3.
What scale for distance might work for a model in your classroom?
___________________________________

The scale for distance might work for a model in our classroom is

1 cm = 10 million kilometres

Practice
Solve.
Question 4.
$$\frac{t}{12}$$ = 8 ______

t/12 =8

t = 8 X 12

Therefore, t = 96

Question 5.
p ÷ 9 = 11 _______

p/9 =11

p= 99

Question 6.
n + 0.35 = 5 ________

n+0.35 = 5

n = 4.65

Comparing Player Density
The dimensions of the playing surfaces for four sports are listed below.
Football: 360 ft by 160 ft
Hockey: 200 ft by 85 ft (Ignore round corners)
Basketball: 50 ft by 94 ft
Baseball: 108,500 ft2 (Average for major league parks)
During a game, there are 22 players on a football field, 10 on a basketball court, 10 on a baseball diamond (not counting base runners), and 12 on an ice hockey rink. Calculate the square feet of playing area per player for each sport.
Question 1.
Football playing area: ___________
Area per player: ____________

Football playing area is 57,600 Square feet

Area per player is 2618 Square feet

Question 2.
Area per player: ____________

Basketball playing area is 4700 Square feet

Area per player is 470 Square feet

Question 3.
Hockey playing area: ____________
Area per player: ____________

Hockey playing area is 17,000 Square feet

Area per player is 1417 Square feet

Question 4.
Baseball playing area: ____________
Area per player: ____________

Baseball playing area is 108,500 Square feet

Area per player is 10,850 Square feet

Question 5.
a. Which sport is the most “crowded”? ____________

a. Basket ball is the sport is most crowded

b. Number of players are same as other sports even though  Basketball has the smallest area. Hence, Basketball is most crowded.

Question 6.
Describe the relationship between square feet per player and player density.
__________________________

The relationship between square feet per player and player density is “the  number of square feet per player is directly proportional to spread of the player ” means the larger the number of square feet per player, the more spread of the players.

Question 7.
If the player density is lower, how might that affect their role in the game?
___________________________

The team in which the player density is low , then it’ll be in a chance of losing side. Hence, it is the responsibility of each player to cover more of the playing the field.

Practice Simplify the expressions.
Question 8.
7t – 4t ________

7t-4t = 3t

Question 9.
5 + 7r – 1.5 – 2r _______

5 + 7r – 1.5 – 2r

(5-1.5) +(7r-2r)

3.5+5r

Question 10.
9(3c) ______

27c

Question 11.
$$\frac{1}{2}$$ (4b + 12) _______

1/2 (4b/12)

(4b/2)/(12/2)

2b/6.

Mobiles
The mobiles shown in Problems 1 and 2 are in balance.
All measures are in feet for distances or pounds for weight.
Question 1.
What is the weight of the object on the left of the fulcrum?

W = __________
D = _________
w = _________
d = _________
Equation: _________
Solution: _________
Weight: _________

W = 3x
D = 8
w = 15
d = 8
Equation : (3x)8 =(15)8
Solution: x = 15 ,5
Weight:

Question 2.
What is the distance of each object from the fulcrum?

W = _________
D = _________
w = _________
d = _________
Equation: _________
Solution: _________
Distance on the left of the fulcrum: _________
Distance on the right of the fulcrum: _________

W = 8
D = x+4
w = 16
d = x-4
Equation: 8(x+4) = 16(x-4)
Solution:  x=12
Distance on the left of the fulcrum:  16 lb
Distance on the right of the fulcrum:  8 lb

Question 3.
a. Sketch a mobile that will balance.
Label all lengths and weights.

b. Use the mobile formula to explain why your mobile balances.

Practice
Divide.
Question 4.
34.5 ÷ 0.5 = ______

69

Question 5.
8.46 ÷ 4.7 = _______

1.8

Question 6.
______ = 1.22 ÷ 4

0.305

Question 7.
______ = 26.88 ÷ 0.48

56

Generalizing Patterns
Question 1.
Use the pattern pictured below. Shade a constant part of the pattern.
a. In the table, record numeric expressions for the total number of squares that represent what is shaded and how the pattern is growing.

Plan your numeric expressions to show one part of the expression as constant and the other part as varying.
b. Write an algebraic expression for the number of squares in Step n.

a.

b.

an algebraic expression for the number of squares in Step ‘n’  is 5+2(n-1)

Question 2.
Circle an expression for finding the number of squares needed to build Step n that best represents how the pattern is shaded.

3 + 2n + n + 1
4 + 3n
6 + n + 2(n – 1)
7 + 3(n – 1)

3+2n+n+1

Question 3.
Explain why the expression you chose in Problem 2 is the best match.

The expression  3+2n+n+1 is best match because it is showing the third (3rd) row is shaded  and also showing that multiple of 2 is added on top and also the number added at the bottom also the same number shaded at bottom.

Practice Simplify.
Question 4.
5(x + 10) = ______

5x+50

Question 5.
2(x + 8) = _______

2x+16

Question 6.
6x + 2x = _____

8x

Using Anthropometry
The following passage is from Gulliver’s Travels by Jonathan Swift. The setting is Lilliput, a country where the people are only 6 inches tall. “Two hundred seamstresses were employed to make me shirts . . . . The seamstresses took my measure as I lay on the ground, one standing at my neck, and another at my mid leg, with a strong cord extended, that each held by the end, while the third measured the length of the cord with a rule of an inch long. Then they measured my right thumb and desired no more; for by a mathematical computation, that twice round the thumb is once round the wrist, and so on to the neck and the waist, and by the help of my old shirt, which I displayed on the ground before them for a pattern, they fitted me exactly.”

Question 1.
Four body parts are referenced in the text. What are they?
Choose a variable to represent each one.

Four body parts are Neck (N) , Leg (L) , Thumb(T) , Waist(W)

Question 2.
Take these four measures on yourself, measuring to the nearest $$\frac{1}{4}$$ inch.

The four measurements are 1/4, 2/4, 3/4, 4/4.

Question 3.
Use the variables you recorded in Problem 1 to write three rules described in the text.

The three rules are W=2T ; N=2W ; L=2N

Question 4.
Based on your data, how well do you think Gulliver’s new clothes fit? Explain.

Being the measurements are by a mathematical computation, the measurements are accurately and fit exactly for Gulliver.

Practice
Evaluate.
Question 5.
5 $$\frac{1}{2}$$ ÷ $$\frac{1}{4}$$ = ________

22

Question 6.
______ = 2 $$\frac{2}{3}$$ ÷ $$\frac{3}{4}$$

32/9

Which Would You Rather Have ?
Don’s boss is offering him two choices to get paid for June.

• Choice #1 is to receive $10 on June 1st,$20 on June 2nd, $30 on June 3rd, and so on through June 30th. • Choice #2 is to receive 1 penny the first day, 2¢ the second day, 4¢ the third day, and so on, doubling the amount each day for the rest of the month. Question 1. a. Predict which is the better plan. _________ b. Explain how you made your choice. ___________ Answer: a. Choice 1 b. Because, at the end of the month, total will be higher in first case when compared to second case Question 2. Enter formulas to complete the table for the first five days of each plan. Answer: for choice 1 : 10x for second case : (0.01)(2^(x-1)) Question 3. Use a spreadsheet program or a calculator to determine how much Don would receive for the day on June 30th for each choice. Choice 1: _________ Choice 2: _________ Answer: Choice 1:$300
Choice 2: 5,368,709.12

Question 4.
If you have a spreadsheet program, find the total amount Don receives for both choices. If you do not, explain how to find the totals on the back of this page
Choice 1: _________
Choice 2: ________

Choice 1: $4,650 Choice 2:$10,737,418.23

Practice
Write three equivalent ratios for each ratio.
Question 5.
2.5 to 2 ______

1.25:1 , 5:4 , 10:8

Question 6.
1 : 1.4 ________

2:2.8 , 20:28 , 40:56

Question 7.
$$\frac{1}{2}$$ to 3 _______

1:6 , 2:12 , 5:30

Question 8.
$$\frac{1}{2}$$ : $$\frac{3}{4}$$ _______

1:1.5 , 2:3 , 4:6

## Everyday Mathematics 6th Grade Answer Key Unit 3 Decimal Computation and Percents

Reviewing Place Value with Decimals

Question 1.
Record two decimals that are equivalent to each decimal below.
a. 0.2 ____

The two decimals that are equivalent to 0.2 = 0.20 and 0.200.

Explanation:
In the above-given question,
given that,
The decimal is 0.2.
0.2 = 0.20.
0.2 = 0.200.
so the the two decimals that are equivalent to 0.2 = 0.20 and 0.200.

b. 0.13

The two decimals that are equivalent to 0.13 = 0.1 and 0.11.

Explanation:
In the above-given question,
given that,
The decimal is 0.13.
0.13 = 0.1.
0.13 = 0.11.
so the the two decimals that are equivalent to 0.13 = 0.1 and 0.11.

c. 2.145

The two decimals are equivalent to 2.145 = 2.143 and 2.144.

Explanation:
In the above-given question,
given that,
The decimal is 2.145.
2.145 = 2.143.
2.145 = 2.144.
so the the two decimals that are equivalent to 2.145 = 2.143 and 2.144.

d. 7.06

The two decimals are equivalent to 7.06 = 7.006 and 7.0006.

Explanation:
In the above-given question,
given that,
The decimal is 7.06.
7.06 = 7.006.
7.06 = 7.0006.
so the the two decimals that are equivalent to 7.06 = 7.006 and 7.0006.

Question 2.
Compare using <, >, or =.
a. 0.05 ___ 0.050

0.05 = 0.050.

Explanation:
In the above-given question,
given that,
compare the decimals.
0.05 = 0.050.
0.05 is equals to 0.050.

b. 0.05 __ 0.5

0.05 < 0.5.

Explanation:
In the above-given question,
given that,
compare the decimals.
0.05 < 0.5.
0.05 is less than 0.5.

c. 0.503 ___ 0.53

0.503 < 0.53.

Explanation:
In the above-given question,
given that,
compare the decimals.
0.503 < 0.53.
0.503 is less than 0.53.

Question 3.
Explain why the zeros are necessary in 10.03 but not in 0.350.

Question 4.
Circle the numbers that are equivalent.

The numbers that are equivalent is 0.21 and 0.210.

Explanation:
In the above-given question,
given that,
circle the numbers that are equivalent.
0.21 = 0.210.
so the numbers that are equivalent is 0.21 and 0.210.

Question 5.
Cross out the names that do not belong. Add two names to each box.

a. 0.23 = 23/100.
b. 10.045/1000.

Explanation:
In the above-given question,
given that,
0.23 and 10.045.
0.23 = 23/100.
10.045 = 10.045/1000.

Practice

Question 6.
6 ÷ $$\frac{1}{2}$$ = 7

6 ÷ 1/2 = 12.

Explanation:
In the above-given question,
given that,
6 ÷ 1/2.
1/2 = 0.5.
6 ÷ 0.5 = 12.

Question 7.
2 ÷ $$\frac{1}{4}$$ = ___

2 ÷ 1/4 = 8.

Explanation:
In the above-given question,
given that,
2 ÷1/4.
1/4 = 0.25.
2 ÷ 0.25 = 8.

Question 8.
5 ÷ $$\frac{1}{3}$$ = ___

5 ÷ 1/3 = 15.1.

Explanation:
In the above-given question,
given that,
5 ÷ 1/3.
5 ÷ 0.33.
5 ÷ 0.33 = 15.1.

Decimals on the Number Line

Fido the flea is at it again. He starts at 0 and wants to go to the Flea Fair at 0.28 on the number line. Hop Set 1 takes a total of 10 hops to reach 0.28. Hop Set 2 takes a total of 28 hops to reach 0.28. Remember that the size of Fido’s hops are
always 1 tenth, 1 hundredth, or 1 thousandth.

Question 1.
Show the two different hop sets on the number lines below.

The two different hop sets are : a. 0.18 b. 0.08.

Explanation:
In the above-given question,
given that,
Hop Set 1 takes a total of 10 hops to reach 0.28. Hop Set 2 takes a total of 28 hops to reach 0.28.
10 + 0.18 = 0.28.
20 + 0.08 = 0.28.
so the two different hop sets are 0.18 and 0.08.

Question 2.
Write a number sentence to represent each hop set to 0.28.
Hop Set 1: _______________
Hop Set 2: _____________

10 + 0.18 = 0.28.
20 + 0.08 = 0.28.

Explanation:
In the above-given question,
given that,
the number sentence to represent each hop set to 0.28.
10 + 0.18 = 0.28.
20 + 0.08 = 0.28.

Question 3.
a. Write 3.48 in expanded form as the sum of multiplication with decimals.
______________

3 + 0.4 + 0.08.

Explanation:
In the above-given question,
given that,
3.48.
(3 x 1) + (4 x 1/10) + (8 x 1/100).
3 + 0.4 + 0.08.

b. Write a number between 3.48 and 3.49.

3.489.

Explanation:
In the above-given question,
given that,
the number between 3.48 and 3.49.
3.48 = 3.489.
so the number between 3.48 and 3.49 is 3.489.

c. Explain how the expanded form of the number you wrote for Part b would be similar to the expanded form of 3.48 you recorded for Part a.

3 + 0.4 + 0.08 + 0.009.

Explanation:
In the above-given question,
given that,
3.489.
(3 x 1) + (4 x 1/10) + (8 x 1/100) + ( 9 x 1/1000).
3 + 0.4 + 0.08 + 0.009.

Question 4.
Circle the numbers below that are between 8.032 and 8.033.

The numbers are between 8.032 and 8.033 =

Explanation:
In the above-given question,
given that,
the numbers are 8.032 and 8.033.
8.0329, 8.03222, 8.023.
so the numbers are between 8.032 and 8.033 = 8.0329, 8.0322, and 8.023.

Practice

Insert <, >, or = to make each number sentence true.

Question 5.
3.4 ___ 3.40

3.4 = 3.40.

Explanation:
In the above-given question,
given that,
compare the numbers.
3.4 = 3.40.
3.4 is equal to 3.40.

Question 6.
17.062 ___ 17.006

17.062 = 17.006.

Explanation:
In the above-given question,
given that,
compare the decimals.
17.602 = 17.006.
17.602 is equal to 17.006.

Question 7.
12.405 ___ 12.41

12.405 < 12.41.

Explanation:
In the above-given question,
given that,
compare the decimals.
12.405 < 12.41.
12.41 is greater than 12.405.

Great Accomplishments in Sports

Question 1.
Geoffrey Mutai (Kenya) set the record for the New York City Marathon in 2011. His time was 2 hours, 5.10 minutes.
In 2013, he won the marathon again with a time of 2 hours, 8.40 minutes.
How much faster was Mutai’s time in 2011 than in 2013? _____________

The faster was Mutai’s time in 2011 than in 2013 = 3.30 minutes.

Explanation:
In the above-given question,
given that,
In 2011, his time was 2 hours, 5.10 minutes.
In 2013 his time was 2 hours, 8.40 minutes.
40 – 10 = 30.
8 – 5 = 3.
3.30 minutes.
so the faster was Mutai’s time in 2011 than in 2013 = 3.30 minutes.

Question 2.
At the 1908 Olympics, Erik Lemming (Sweden) won the javelin throw. He threw the javelin 54.82 meters. He won again in 1912 with a throw of 60.64 meters.
How much longer was his 1912 throw than his 1908 throw? ____

so the length was his 1912 throw than his 1908 throw = 5.82 meters.

Explanation:
In the above-given question,
given that,
At the 1908 Olympics, Erik lemming(Sweden) won the javelin throw.
He threw the javelin 54.82 meters.
He won again in 1912 with a throw of 60.64 meters.
60.64 – 54.82.
5.82.
so the length was his 1912 throw than his 1908 throw = 5.82 meters.

Question 3.
At the 1984 Olympics, Gregory Louganis (United States) won a gold medal in men’s springboard diving.
To calculate a diver’s final score, the average scores from 11 dives are added.

What was Louganis’s winning final score? ________

The Louganis’s winning final score = 754.41.

Explanation:
In the above-given question,
given that,
the average scores from 11 dives are added.
47.52 + 53.01 + 44.16 + 40.32 + 68.88 + 81.00 + 85.56 + 77.40 + 71.1 + 93.06 + 92.40.
754.41.
so the Louganis’s winning final score = 754.41.

Question 4.
Driver Buddy Baker (Oldsmobile, 1980) holds the record for the fastest winning speed in the Daytona 500. His speed was 177.602 miles per hour. Bill Elliott (Ford, 1987) has the second-fastest winning speed. Elliott’s speed was 1.339 miles per hour slower than Baker’s speed.
What was Elliott’s speed? _______

The speed of Elliott’s = 176.263 miles per hour.

Explanation:
In the above-given question,
given that,
Daytona speed was 177.602 miles per hour.
Elliott’s speed was 1.339 miles per hour slower than Baker’s speed.
177.602 – 1.339 = 176.263 miles.
so the speed of the Elliott’s = 176.263 miles per hour.

Practice

Question 5.
$$\frac{4}{5}$$ ÷ $$\frac{1}{2}$$ = ____

4/5 ÷ 1/2 = 1.6.

Explanation:
In the above-given question,
given that,
4/5 ÷ 1/2.
4/5 = 0.8.
1/2 = 0.5.
0.8 ÷ 0.5 = 1.6.

Question 6.
$$\frac{3}{4}$$ ÷ $$\frac{2}{3}$$ = ______

3/4 ÷ 2/3 = 1.13.

Explanation:
In the above-given question,
given that,
3/4 ÷ 2/3.
3/4 = 0.75.
2/3 = 0.66.
0.75 ÷ 0.66 = 1.13.

Question 7.
$$\frac{5}{6}$$ ÷ $$\frac{1}{4}$$ = ________

5/6 ÷ 1/4 = 4.

Explanation:
In the above-given question,
given that,
5/6 ÷ 1/4.
5/6 = 0.8.
1/4 = 0.2.
0.8 ÷ 0.2 = 4.

Question 8.
$$\frac{2}{3}$$ ÷ $$\frac{3}{4}$$ = ______

2/3 ÷ 3/4 = 1.6.

Explanation:
In the above-given question,
given that,
2/3 ÷ 3/4.
2/3 = 0.6.
3/4 = 0.75.
0.6 ÷ 0.75 = 1.6.

Decimal-Multiplication Review

Use estimation to solve Problems 1–2.

Question 1.
Carlos is building a flower bed that is 13.2 m by 6.75 m. When he multiplied, Carlos got 89100.
Show where he should place the decimal point _______

13.2 x 6.75 = 89.1

Explanation:
In the above-given question,
given that,
Carlos is building a flower bed that is 13.2 m by 6.75 m.
13.2 x 6.75.
89.1.
so he should place the decimal point before 1.

Question 2.
Stephanie says 1.95 ∗ 6.6 = 12.87.
Dante says the answer is 128.7. Who is right? Explain how an estimate might help you decide.

Stephanie was correct.

Explanation:
In the above-given question,
given that,
Stephanie says 1.95 x 6.6 = 12.87.
Dante says the answer is 128.7.
1.95 x 6.6 = 12.87.
so Stephanie was correct.

For Problems 3–5, record a number sentence to show how you estimated. Then use the U.S. traditional multiplication algorithm to solve. Use your estimate to check your work.

Question 3.
3.4 ∗ 3.29
Estimate: ___

3.4 x 3.29 = 11.186.

Explanation:
In the above-given question,
given that,
3.4 x 3.29.
3.4 x 3.29 = 11.186.

Question 4.
70.1 ∗ 4.8
Estimate: _____

70.1 x 4.8 = 336.48.

Explanation:
In the above-given question,
given that,
70.1 x 4.8.
70.1 x 4.8 = 336.48.

Question 5.
Mr. Murphy is building a fence. He bought 7 packages of wooden fencing. One package costs $56.45. How much do they cost all together? Estimate: ___ Number model: ___ Solution: ___ Answer: The cost all together =$395.15.

Explanation:
In the above-given question,
given that,
Mr. Murphy is building a fence.
He bought 7 packages of wooden fencing.
One package costs $56.45.$56.45 x 7 = 395.15.
so the cost of all together = $395.15. Try This Question 6. Dr. Goode prescribes 0.2 gram of cold medicine for Donald. This medicine comes in tablets that are 0.05 gram or 0.5 gram. Should Donald take 4 of the 0.5 gram tablets or 4 of the 0.05 gram tablets? ____ How do you know? ___ Practice Compare with >, <, or = Question 7. -7 ___ -3 Answer: -7 > -3. Explanation: In the above-given question, given that, compare the numbers. -7 and -3. -7 > -3. Question 8. 4 ___ -4 Answer: 4 > -4. Explanation: In the above-given question, given that, compare the numbers. 4 and -4. 4 > -4. Question 9. 0 __ -3 Answer: 0 > -3. Explanation: In the above-given question, given that, compare the numbers. 0 and -3. 0 > -3. Question 10. -2 __ -5 Answer: -2 < -5. Explanation: In the above-given question, given that, compare the numbers. -2 and -5. -2 < -5. ### Everyday Math Grade 6 Home Link 3.5 Answer Key Long Division Solve each problem. Write a number sentence to show how you checked your answer. Question 1. Check: ______ Answer: 38 / 966 = 16. Explanation: In the above-given question, given that, 38/966. Question 2. Check: ______ Answer: 43/5938 = Explanation: In the above-given question, given that, 43/5938. Fill in the missing numbers. Question 3. Answer: 41 / 3.408 = 5. Explanation: In the above-given question, given that, fill in the missing numbers. 41/3.408. Question 4. Answer: 34/2.349 = 3. Explanation: In the above-given question, given that, fill in the missing boxes. 34/2.349. Question 5. There are about 1,575 beads in a large economy-size tub at the craft store. There are 49 different colors. If the colors are distributed equally, about how many beadsof each color are there? ____ Answer: The number of beads are shared equally = 33. Explanation: In the above-given question, given that, There are about 1,575 beads in a large economy-size tub at the craft store. there are 49 different colors. 49 x 33 = 1575. so the number of beads are shared equally = 33 beads. Question 6. The book The Phantom Tollbooth by Norton Juster (Random House, 1961) has 42,156 words. It is 256 pages long. On average, how many words are on each page? _____ Answer: so the average number of words on each page = 166. Explanation: In the above-given question, given that, The book has 42,156 words. it is 256 pages long. 256 x 166 = 42,496. so the average number of words on each page = 166. Practice Question 7. ___ = $$\frac{3}{4}$$ ∗ $$\frac{2}{3}$$ Answer: 3/4 x 2/3 = 0.45. Explanation: In the above-given question, given that, 3/4 x 2/3. 3/4 = 0.75. 2/3 = 0.6. 0.75 x 0.6 = 0.45. 3/4 x 2/3 = 0.45. Question 8. $$\frac{4}{5}$$ ∗ $$\frac{1}{8}$$ = ____ Answer: 4/5 x 1/8 = 0.1. Explanation: In the above-given question, given that, 4/5 x 1/8. 4/5 = 0.8. 1/8 = 0.125. 0.8 x 0.125 = 0.1. 4/5 x 1/8 = 0.1. Question 9. 9$$\frac{2}{7}$$ ∗ $$\frac{3}{5}$$ = ____ Answer: 9(2/7) x 3/5 = 5.5. Explanation: In the above-given question, given that, 9(2/7) x 3/5. 7 x 9 = 63. 63 + 2 = 65. 65/7 x 3/5. 65/7 = 9.2. 3/5 = 0.6. 9.2 x 0.6 = 5.5. Question 10. ___ =$$\frac{1}{3}$$ ∗ $$\frac{2}{9}$$ Answer: 1/3 x 2/9 = 0.6. Explanation: In the above-given question, given that, 1/3 x 2/9. 1/3 = 0.3. 2/9 = 0.2. 0.3 x 0.2 = 0.6. ### Everyday Math Grade 6 Home Link 3.6 Answer Key Question 1. Put the decimal point in the correct position in each quotient. Use multiplication to check your answer. Answer: 564 x 3.9 = 219.96. Explanation: In the above-given question, given that, 564 x 3.9 = 219.96. 687 x 0.52 = 357.24. 345 x 6.8 = 2346. 87 x 1.95 = 169.65. Divide and check. Question 2. Check: _______ Answer: 0.72/5.976 = 0. Explanation: In the above-given question, given that, divide. 0.72/5.976. Question 3. Check: _______ Answer: 1.6 / 7.712 = Explanation: In the above-given question, given that, divide. 1.6 / 7.712. Question 4. Jaime has 3 cups of berries. Each fruit-and-yogurt parfait he makes contains 0.4 cup of berries. How many parfaits can he make? Number sentence: ____ Solution: ____ Check: ________ Answer: The number of parfaits he can make = 7.5. Explanation: In the above-given question, given that, Jaime has 3 cups of berries. Each fruit-and-yogurt parfait he makes contains 0.4 cups of berries. 3/0.4 = 7.5. so the number of parfaits he can make = 7.5. Practice Question 5. GCF (10, 3) = _____ Answer: GCF of 10 and 3 = 1. Explanation: In the above-given question, given that, GCF of 10 and 3. factors of 10 = 1, 2, 5, 10. factors of 3 = 1, 3. among those factors 1 is the common factor. Question 6. GCF (12, 24) = ____ Answer: GCF of 12 and 24 = 12. Explanation: In the above-given question, given that, GCF of 12 and 24. factors of 12 = 1, 2, 3, 4, 6, 12. factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. among those factors 12 is the greatest common factor. Question 7. GCF (100, 80) = ____ Answer: GCF of 100 and 80 = 20. Explanation: In the above-given question, given that, GCF of 100 and 80. factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100. factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20. among those factors 20 is the greatest common factor. Question 8. GCF (18, 42) = ____ Answer: GCF of 18 and 42 = 6. Explanation: In the above-given question, given that, GCF of 18 and 42. factors of 18 = 1, 2, 3, 6, 9, 18. factors of 42 = 1, 2 3, 6, 7, 14, 21, 42. among those factors 6 is the greatest common factor. ### Everyday Math Grade 6 Home Link 3.7 Answer Key Decimal Operations Margaret is making a pair of purple pajama pants for her daughter Marie. To figure out how much purple fabric she needs, Margaret must do the following: • Measure the length from Marie’s waist to her ankle. • Double this measurement. • Add 12 inches. Question 1. From waist to ankle, Marie measures 33 inches. How many inches of the purple fabric does Margaret need? ____ Answer: The purple fabric does Margaret needs = 78 inches. Explanation: In the above-given question, given that, from waist to ankle, Marie measures 33 inches. 33 + 33 = 66. 66 + 12 = 78 inches. so the purple fabric does Margaret needs = 78 inches. Question 2. Cloth is sold in yards. How many yards of purple fabric will Margaret buy? Explain why your answer makes sense. Answer: so the number of yards of purple fabric will Margaret buy = 1.56 yds. Explanation: In the above-given question, given that, 1 inch = 0.02 yds. 78 x 0.02 = 1.56. so the number of yards of purple fabric will Margaret buy = 1.56 yds. Question 3. The purple fabric costs$5.50 per yard. The tax added to Margaret’s bill is $1.23. How much does Margaret spend on the fabric? ____ Show your work. Answer: The Margaret spend on the fabric =$6.73.

Explanation:
In the above-given question,
given that,
The purple fabric costs $5.50 per yard. The tax added to Margaret’s bill is$1.23.
$5.50 +$ 1.23 = $6.73. so the Margaret spend on the fabric =$6.73.

Question 4.
Margaret pays with a $20 bill. How much change does she receive? ___ Answer: The change does she receive =$13.27.

Explanation:
In the above-given question,
given that,
Margaret pays with a $20 bill. 20 – 6.73 =$13.27.
so the change does she receive = $13.27. Bring in examples of how percents are used in the world around us. You can write down, cut out, or print examples from newspapers, television, the Internet, and so on. We will collect these in a Percent Museum. Practice Find the LCM. Question 5. LCM (8, 12) = ____ Answer: LCM of 8 and 12 = 24. Explanation: In the above-given question, given that, LCM of 8 and 12. multiples of 8 = 8, 16, 24, 32, 40. multiples of 12 = 12, 24, 36, 48. among those 24 is the least common factor. Question 6. LCM (4, 14) = _____ Answer: LCM of 4 and 14 = 28. Explanation: In the above-given question, given that, LCM of 4 and 14. multiples of 4 = 4, 8, 12, 16, 20, 24, 28. multiples of 14 = 14, 28, 42, 56. among those 28 is the least common factor. Question 7. LCM (10, 15) = ____ Answer: LCM of 10 and 15 = 30. Explanation: In the above-given question, given that, LCM of 10 and 15. multiples of 10 = 10, 20, 30, 40, 50. multiples of 15 = 15, 30, 45, 60. among those 30 is the least common factor. Question 8. LCM (9, 12) = ____ Answer: LCM of 9 and 12 = 36. Explanation: In the above-given question, given that, LCM of 9 and 12. multiples of 9 = 9, 18, 27, 36. multiples of 12 = 12, 24, 36, 48. among those 36 is the least common factor. ### Everyday Math Grade 6 Home Link 3.8 Answer Key Question 1. A recent survey investigated whether Summit Middle School students prefer to wear school uniforms. Here are the results: • 63 percent prefer school uniforms. • 32 percent do not prefer school uniforms. • 5 percent do not have a preference. Shade each percent on the grids below. Record the decimal and fraction equivalents. Answer: Decimal = 0.63, 0.32, 0.5. Fraction = 63/100, 32/100, 5/100. Explanation: In the above-given question, given that, 63% prefer school uniforms. 32% do not prefer school uniforms. 5% no preference. decimal = 0.63, 0.32, 0.5. fraction = 63/100, 32/100, 5/100. Question 2. Teresa was designing a game to play at lunchtime with her friends. She wanted to know which number on a die is the luckiest. She rolled a die 50 times. The die landed showing the number five 20 times. She claimed she rolled a five 20% of the time. a. Explain her mistake. Answer: b. For what percent of her 50 rolls did she roll a five? Answer: c. How did you get your answer for Part b? Answer: Practice Question 3. 14.7 – 13.2 = ____ Answer: 14.7 – 13.2 = 1.5. Explanation: In the above-given question, given that, subtract. 14.7 – 13.2. Question 4. 4.52 – 3.5 = ____ Answer: 4.52 – 3.5 = 1.02. Explanation: In the above-given question, given that, subtract. 4.52 – 3.5. Question 5. 1.2 – 0.006 = ____ Answer: 1.2 – 0.006 = 1.194. Explanation: In the above-given question, given that, subtract. 1.2 – 0.006. Question 6. 3.424 – 3.006 = ___ Answer: 3.424 – 3.006 = 0.418. Explanation: In the above-given question, given that, subtract. 3.424 – 3.006. Everyday Math Grade 6 Home Link 3.9 Answer Key Solving Percent Problems Question 1. a. Shade in the grid to represent that 2 out of every 10 moviegoers buy their tickets ahead of time. Answer 20/100. Explanation: In the above-given question, given that, 2 out of every 10 moviegoers buy their tickets ahead of time. 2 – 10. 4 – 20. 6 – 40. 20 -100. b. What fraction of moviegoers buy their tickets ahead of time? Answer: 20/100. Explanation: In the above-given question, given that, 2 out of every 10 moviegoers buy their tickets ahead of time. 2 – 10. 4 – 20. 6 – 40. 20 -100. c. What percent of moviegoers buy their tickets ahead of time? Answer: 0.2. Explanation: In the above-given question, given that, 2 out of every 10 moviegoers buy their tickets ahead of time. 2 – 10. 4 – 20. 6 – 40. 20 -100. d. If 200 people go to the movies, how many would buy their tickets ahead of time? Answer: Question 2. a. Shade in the grid to represent that 11 out of every 20 people prefer watching movies at home instead of watching them at the theater. b. What fraction of people preferto watch movies at home? c. What percent of people prefer to watch movies at home? d. If 60 people are asked, how many prefer to watch movies at home? Answer: 11/20. 55%. 33. Explanation: In the above-given question, given that, 11 people out of 20 watch movies at home. 11/20. 55 percent of people prefer to watch movies at home. 11 + 11 + 11 = 33. Question 3. a. 10% of 60:___ Answer: 10% of 60 = 0.16. Explanation: In the above-given question, given that, 10% of 60. 10/60 = 0.16. b. 25% of 80: Answer: 25% of 80 = 0.31. Explanation: In the above-given question, given that, 25% of 80. 25/80 = 0.31. c. Explain how you found the answer to Part b. Answer: Question 4. a. Write $$\frac{9}{10}$$ as a percent. ____ Answer: 9/10 = 0.9. Explanation: In the above-given question, given that, 9/10. 9/10 = 0.9. b. Write $$\frac{2}{5}$$ as a percent. _____ Answer: 0.04. Explanation: In the above-given question, given that, 2/5. 2/5 x 100 = 0.04. Practice Find the median. Question 5. 109, 121, 134, 115, 146 _____ Answer: Median = 134. Explanation: In the above-given question, given that, Median of 109, 121, 134, 115, 146. median = 134. Question 6. 11, 17, 22, 13, 35, 27 _____ Answer: Median = 17.5. Explanation: In the above-given question, given that, Median of 11, 17, 22, 13, 35, 27. 35/2 = 17.5. ### Everyday Math Grade 6 Home Link 3.10 Answer Key Percents as Ratios Question 1. Fill in the missing numbers and shade the grid. Use ratio/rate tables to solve each problem. Answer: Fraction = 35/100, 52/100, 40/100. Explanation: In the above-given question, given that, fraction = 35/100, 52/100, 40/100. decimal = 0.35, 0.52, 0.40. percent = 35%, 52%, 40%. Question 2. Kiese has read 80% of his library book. The book has 200 pages. How many pages has he read? Answer: The number of pages he has read = 0.4. Explanation: In the above-given question, given that, Kiese has read 80% of his library book. The book has 200 pages. 80/200 = 0.4. Question 3. A bakery donated 30 loaves of bread to a homeless shelter. That was 25% of the loaves they made that morning. How many loaves did they make that morning? Answer: The number of loaves they make that morning = 1.2. Explanation: In the above-given question, given that, A bakery donated 30 loaves of bread to a homeless shelter. That was 25 % of the loaves they made that morning. 30/25 = 1.2. Practice Write an equivalent ratio. Question 4. 2 : 3 ___ Answer: Equivalent ratio of 2:3 = 40:55. Explanation: In the above-given question, given that, 2/3 = 40:55. Question 5. 5 : 6 ____ Answer: Equivalent ratio of 5:6 = 10:12. Explanation: In the above-given question, given that, 5 x 2 = 10. 6 x 2 = 12. 5 : 6 = 10:12. Question 6. 3 : 9 ____ Answer: Equivalent ratio of 3:9 = 6:18. Explanation: In the above-given question, given that, 3 x 2 = 6. 9 x 2 = 18. 3 : 9 = 6 : 18. Question 7. 14 : 20 ____ Answer: Equivalent ratio of 14:20 = 28:40. Explanation: In the above-given question, given that, 14 = 7 x 2. 20 = 10 x 2. 14 : 20 = 28: 40. ### Everyday Math Grade 6 Home Link 3.11 Answer Key Tiger Facts Solve. Question 1. Tigers have a hunting success rate of about 10%. A tiger successfully hunts 4 times in one week. How many attempts did the tiger make? Answer: The number of attempts did the tiger make = 4%. Explanation: In the above-given question, given that, Tigers have a hunting success rate of about 10%. A tiger successfully hunts 4 times in one week. 4%. so the number of attempts did the tiger make = 4%. Question 2. A Bengal tiger’s tail is around 30% of its total length. The total length of one Bengal tiger’s tail is 96 cm. Around how long is the tiger? Answer: The length of the tiger = 3.2 cm. Explanation: In the above-given question, given that, A Bengal tiger’s tail is around 30% of its total length. The total length of one Bengal tiger’s tail is 96 cm. 96/30 = 3.2 Question 3. At the start of the 20th century, there were about 100,000 tigers in the wild. In 2014, there were about 3,200. By about what percent did the tiger population decrease? Answer: The population of the tiger = 96,800. Explanation: In the above-given question, given that, At the start of the 20th century, there were about 100,000 tigers in the wild. In 2014, there were about 3,200. 100,000 – 3200. 96,800. so the population decrease = 96,800. Question 4. Tiger cubs are around 2 years old when they leave their mothers. In the wild, tigers live about 11 years. About what percent of their lives do tigers spend with their mothers? Answer: The percent of their lives do tigers spend with their mothers = 5.5%. Explanation: In the above-given question, given that, Tiger cubs are around 2 years old when they leave their mothers. In the wild, tigers live about 11 years. 2/11 = 5.5. so the percent of their lives do tigers spend with their mothers = 5.5%. Try This Question 5. About 5,000 tigers live in captivity in the United States. About 10% of these tigers live in reputable zoos. Around how many of these tigers DO NOT live in reputable zoos? Answer: The tigers do not live in reputable Zoos = 500. Explanation: In the above-given question, given that, About 5000 tigers live in capacity in the United States. About 10 % of these live in reputable zoos. 1000 – 10% = 100. 5000 – 10% = 500. so the tigers do not live in reputable zoos = 500. Practice Compare using >, <, or =. Question 6. 2.58 ___ 2.576 Answer: 2.58 > 2.576. Explanation: In the above-given question, given that, compare the decimals. 2.58 > 2.576. 2.58 is greater than 2.576. Question 7. $$\frac{5}{6}$$ ___ $$\frac{8}{9}$$ Answer: 5/6 < 8/9. Explanation: In the above-given question, given that, compare the decimals. 5/6 = 0.83. 8/9 = 0.88. 0.83 < 0.88. Question 8. $$\frac{7}{8}$$ ___ 0.875 Answer: 7/8 = 0.875. Explanation: In the above-given question, given that, compare the decimals. 7/8 = 0.875. 0.875 = 0.875. Question 9. $$\frac{4}{7}$$ __ 0.59 Answer: 4/7 < 0.59. Explanation: In the above-given question, given that, compare the decimals. 4/7 = 0.57. 0.57 < 0.59. ### Everyday Math Grade 6 Home Link 3.12 Answer Key Box Plots Fill in the blanks about a five-number summary you could use to make a box plot. Question 1. These five numbers divide the data into four ______. Answer: Question 2. What can you NOT tell from a box plot? _____ Answer: Use the box plot to answer the questions in Problems 3–5. Question 3. Half of the juniper leaves are longer than what measurement? ___ Answer: The juniper leaves are longer than rose. Explanation: In the above-given question, given that, Hawthorn leaves = 5 cm. Rose = 3 cm. Juniper = 4.5 cm. Question 4. Which plant has the shortest leaves? How do you know? Answer: Rose has the shortest leaves. Explanation: In the above-given question, given that, Hawthorn leaves = 5 cm. Rose = 3 cm. Juniper = 4.5 cm. Question 5. Which type of leaf varies the most in length? ____ Use the box plot to answer the questions in Problems 6–7. Answer: Question 6. The middle 50% of attendance at MLB stadiums is between ___ and ___ million people. Answer: Question 7. Which quarter of the data has the greatest range? ____ Practice Question 8. If 50% of a number is 14, then 100% of the number is ____. Answer: The number is 28. Explanation: In the above-given question, given that, If 50% of a number is 14. then 100% of the number = 28. Question 9. If 10% of a number is 6, then 100% of the number is ___. Answer: The number is 60. Explanation: In the above-given question, given that, if 10% of a number is 6. then 100% = ? 100% is 60. ### Everyday Math Grade 6 Home Link 3.13 Answer Key Box Plots for Olympic Medals Countries often win more than one medal at the Olympic games. Nineteen countries won more than 12 medals each at the London Olympic games in 2012. Listed below are the numbers of medals won by each of those countries. • Gold: 1, 3, 3, 5, 6, 6, 6, 7, 7, 7, 8, 8, 11, 11, 13, 24, 29, 38, 46 • Silver: 1, 2, 3, 4, 5, 5, 5, 6, 8, 9, 10, 11, 14, 16, 17, 19, 26, 27, 29 • Bronze: 4, 5, 5, 5, 6, 7, 8, 9, 9, 11, 12, 12, 12, 14, 17, 19, 23, 29, 32 Question 1. List the five-number summary for each type of medal. Gold: ___ Silver: ___ Bronze: ___ Answer: Gold = 1, 3, 3, 5, 6. Silver = 1, 2, 3, 4, 5. Bronze = 4, 5, 5, 5, 6. Explanation: In the above-given question, given that, Gold = 1, 3, 3, 5, 6. Silver = 1, 2, 3, 4, 5. Bronze = 4, 5, 5, 5, 6. Question 2. Make a box plot for each type of medal: gold, silver, and bronze. Make all three box plots, one above the other, on the number line at right. Answer: Question 3. List the IQR for each type of medal. Gold: ___ Silver: ___ Bronze: ____ Answer: Question 4. What does the IQR tell you about the number of gold medals that were won? Answer: Practice Find the equivalent unit ratio. Question 5. 4 : 8 Answer: Question 6. 5 : 15 Answer: Question 7. 66 : 33 Answer: Question 8. 56 : 14 Answer: ### Everyday Math Grade 6 Home Link 3.14 Answer Key Matching Histograms and Box Plots Below are two histograms and two box plots. Question 1. Box Plot __ matches Histogram A. Answer: Question 2. Box Plot __ matches Histogram B. Answer: Question 3. Sketch each box plot above its corresponding histogram. Answer: Question 4. Explain how you know which box plot matches the data shown in Histogram A. Answer: Question 5. Explain how you know which box plot matches the data shown in Histogram B. Answer: Try This Question 6. The title Median Family Income by State (in thousands) matches Histogram ___. Answer: Question 7. The title Percent of Adults with College Degrees by State matches Histogram ___. Answer: Practice Divide. Question 8. 4.2 ÷ 2.1 = ___ Answer: 4.2 /2.1 = 2. Explanation: In the above-given question, given that, divide. 4.2/2.1. 2. Question 9. 36 ÷ 0.6 = ___ Answer: 36/0.6 = 60. Explanation: In the above-given question, given that, divide. 36/0.6 = 60. Question 10. 0.15 ÷ 0.05 = ___ Answer: 0.15 /0.05 = 3. Explanation: In the above-given question, given that, divide. 0.15/0.05 = 3. ## Everyday Math Grade 6 Answers Unit 2 Fraction Operations and Ratios ## Everyday Mathematics 6th Grade Answer Key Unit 2 Fraction Operations and Ratios ### Everyday Math Grade 6 Home Link 2.1 Answer Key Finding the Greatest Common Factor Question 1. Use any method to find the greatest common factor for the number pairs. a. GCF (42, 56) = ___ b. GCF (32, 80) = ___ c. GCF (72, 16) = ___ d. GCF (10, 40, 25) = ____ Answer: a. GCF of 42 and 56 = 14. b. GCF of 32 and 80 = 16. c. GCF of 72 and 16 = 8. d. GCF of 10, 40, and 25 = 5. Explanation: In the above-given question, given that, Use any method to find the greatest common factor for the number pairs. GCF = Greatest Common Factor. a. GCF of 42 and 56 = 14. factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42. factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56. so among those the greatest common factor is 14. b. GCF of 32 and 80 = 16. factors of 32 = 1, 2, 4, 8, 16, and 32. factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. so among those the greatest common factor is 16. c. GCF of 72 and 16 = 8. factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. factors of 16 = 1, 2, 4, 8, and 16. so among those the greatest common factor is 8. d. GCF of 10, 40, and 25 = 5. factors of 10 = 1, 2, 5, and 10. factors of 40 = 1, 2, 4, 5, 8, 10, 20, and 40. factors of 25 = 1, 5, and 25. so among those the greatest common factor is 5. Question 2. Explain how you found GCF (42, 56) in Problem 1a. Answer: GCF of 42 and 56 = 14. Explanation: In the above-given question, given that, GCF = Greatest Common Factor. GCF of 42 and 56 = 14. factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42. factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56. so among those, the greatest common factor is 14. Question 3. Use the GCF to find an equivalent fraction for $$\frac{48}{64}$$. Show your work. Answer: 48/64 = 3/4. Explanation: In the above-given question, given that, use the GCF to find an equivalent fraction for 48/64. 48 = 6 x 8. 64 = 8 x 8. 6/8 = 3/4. 6 = 2 x 3. 8 = 2 x 4. so 48/64 = 6/8. Question 4. Jenny will use 28 blue beads and 21 red beads to make identical bracelets. a. What is the greatest number of bracelets she can make? Answer: The greatest number of bracelets she can make = 7. Explanation: In the above-given question, given that, Jenny will use 28 blue beads and 21 red beads to make identical bracelets. factors of 28 = 1, 2, 4, 7, 14, and 28. factors of 21 = 1, 3, 7, and 21. so among those, the greatest common factor = 7. b. How many blue beads and how many red beads will be on each bracelet? Answer: The number of blue beads and red beads will be on each bracelet = 7. Explanation: In the above-given question, given that, the number of blue beads = 4. the number of red beads = 3. 4 + 3 = 7. so the number of blue beads and red beads will be on each bracelet = 7. Question 5. Explain how a set of numbers can have a GCF greater than 1. Answer: Try This Question 6. GCF (12, 24, 30, 42) = Answer: GCF of 12, 24, 30, and 42= 6. Explanation: In the above-given question, given that, GCF of 12, 24, 30, and 42. factors of 12 = 1, 2, 3, 4, 6, and 12. factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24. factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30. factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42. so among those, the greatest common factor = 6. Practice Insert the missing digits to make each number sentence true. Question 7. ___, ____ 63 – 3,9 ___ 9 = 2,83 ___ Answer: Question 8. 71, __ 4 ___ – 4,8 6 = 6 ___ ,270 Answer: ### Everyday Mathematics Grade 6 Home Link 2.2 Answers Least Common Multiple Question 1. Find the least common multiple for each pair of numbers. a. LCM (10, 15) = ___ b. LCM (12, 15) = ___ c. LCM (6, 10) = ___ d. LCM (7, 5) = _____ Answer: a. LCM of 10 and 15 = 30. b. LCM of 12 and 15 = 60. c. LCM of 6 and 10 = 30. d. LCM of 7 and 5 = 35. Explanation: In the above-given question, given that, LCM of 10 and 15. 2 x 5 = 10. 3 x 5 = 15. 5 x 1 = 5. 2 x 3 x 5 = 30. so LCM of 10 and 15 = 30. LCM of 12 and 15. 12 = 3 x 4. 15 = 3 x 5. 3 x 4 x 5 = 60. LCM of 6 and 10. 6 = 2 x 3. 10 = 2 x 5. 3 x 1 = 3. 5 = 5 x 1. 2 x 3 x 5 = 30. LCM of 5 and 7. 5 x 7 = 35. Question 2. Find the greatest common factor and least common multiple for each pair of numbers. a. GCF (75, 100) = ___ LCM (75, 100) = Answer: a. GCF of 75 and 100 = 25. b. LCM of 75 and 100 = 300. Explanation: In the above-given question, given that, LCM of 75 and 100. 75 = 5 x 15. 100 = 5 x 20. 15 = 5 x 3. 20 = 5 x 4. 5 x 5 x 3 x 4 = 300. GCF of 75 and 100. 75 = 3 x 5 x 5. 100 = 2 x 2 x 5 x 5. 5 x 5 = 25. b. GCF (36, 48) = ___ LCM (36, 48) = Answer: a. GCF of 36 and 48 = 12. b. LCM of 36 and 48 = 144. Explanation: In the above-given question, given that, LCM of 36 and 48. 36 = 2 x 2 x 3 x 3. 48 = 2 x 2 x 2 x 2 x 3. 2 x 3 x 2 x 2 x 2 = 144. GCF of 36 and 48. 36 = 2 x 2 x 3 x 3. 48 = 2 x 2 x 2 x 2 x 3. 2 x 2 x 3 = 12. Use the LCM to find equivalent fractions with the least common denominator. Question 3. $$\frac{3}{4}$$ and $$\frac{5}{6}$$ LCM (4, 6) = ____ Fractions: ____ Answer: LCM of 4 and 6 = 12. Explanation: In the above-given question, given that, LCM of 4 and 6. 4 = 2 x 2. 6 = 2 x 3. 2 x 2 x 3 = 12. Question 4. $$\frac{1}{6}$$ and $$\frac{3}{8}$$ LCM (6, 8) = ___ Fractions: ____ Answer: LCM of 6 and 8 = 24. Explanation: In the above-given question, given that, LCM of 6 and 8. 8 = 2 x 4. 6 = 2 x 3. 2 x 4 x 3 = 24. Question 5. $$\frac{4}{25}$$ and $$\frac{4}{15}$$ LCM (25, 15) = ___ Fractions: ____ Answer: LCM of 25 and 15 = 75. Explanation: In the above-given question, given that, LCM of 25 and 15. 25 = 5 x 5. 15 = 3 x 5. 5 x 5 x 3 = 75. Question 6. a. On a website, there is an ad for jeans every 5 minutes, an ad for sneakers every 10 minutes, and an ad for scarves every 45 minutes. If they all appeared together at 9:00 P.M., when is the next time they will all appear together? _____ Answer: The next time they will all appear together = 10:00 P.M. Explanation: In the above-given question, given that, On a website, there is an ad for jeans every 5 minutes, an ad for sneakers every 10 minutes, and an ad for scarves every 45 minutes. 5 + 10 = 15. 45 + 15 = 60 minutes. 60 minutes = 1 hour. 9:00 + 1 hour = 10: 00. the next time they will all appear together = 10:00 p.m. b. Explain how you used GCF or LCM to solve the problem. Answer: LCM of 5, 10, and 45 = 450. GCF of 5, 10, and 45 = 5. Explanation: In the above-given question, given that, LCM of 5, 10, and 45. 5 = 5 x 1. 10 = 2 x 5. 45 = 3 x 15. 15 = 3 x 5. 2 x 3 x 3 x 5 x 5 = 450. GCF of 5, 10, and 45. 5 = 1, 5. 10 = 5, 1, 10, and 2. 45 = 1, 45, 15, 3, 5, 9. among all those, the greatest common factor is 5. Question 7. Explain why the LCM is at least as large as the GCF. Answer: LCM = Least common multiple. GCF = greatest common factor. Explanation: In the above-given question, given that,Aa In LCM we will write the answer as the least common multiple. In GCF we will write the answer as the greatest common factor. Practice Estimate. Question 8. 5,692 ∗ 3 = ____ Answer: 5692 x 3 = 17076. Explanation: In the above-given question, given that, 5692 x 3. Question 9. 69 ∗ 54 = ___ Answer: 69 x 54 = 3726. Explanation: In the above-given question, given that, 69 x 54. Question 10. 78 ∗ 123 = ___ Answer: 78 x 123 = 9594. Explanation: In the above-given question, given that, 78 x 123. ### Everyday Math Grade 6 Home Link 2.3 Answer Key Fraction-Multiplication Review Represent the problem on a number line, and then solve the problem. Question 1. $$\frac{2}{3}$$*$$\frac{9}{12}$$ = ___ Answer: 2/3 x 9/12 = 0.42. Explanation: In the above-given question, given that, 2/3 x 9/12. 2/3 = 0.6. 9/12 = 0.7. 0.6 x 0.7 = 0.42. 5/12 = 0.42. 2/3 x 9/12 = 5/12. Question 2. Maliah has $$\frac{2}{3}$$ cup of raisins. She used $$\frac{1}{2}$$ of her raisins to make muffins. What fraction of a cup of raisins did she use? Number sentence: ____ Answer: 2/3 – 1/2 = 0.6. Explanation: In the above-given question, given that, Maliah has 2/3 cups of raisins. she used 1/2 of her raisins to make muffins. 2/3 = 0.6. 0.3 + 0.3 = 0.6. so Maliah use 0.6 cups of her raisins. Question 3. On the back of this page, write and solve a number story for $$\frac{1}{4}$$ * $$\frac{1}{2}$$. Answer: 1/4 x 1/2 = 1/10. Explanation: In the above-given question, given that, 1/4 x 1/2. 1/4 = 0.25. 1/2 = 0.5. 0.2 x 0.5 = 0.1. Try This Question 4. Ryse sprinted $$\frac{3}{4}$$ of a lap around the running track at school. A whole lap is $$\frac{1}{4}$$ mile. How far did he sprint? Number sentence: _______ Answer: 3/4 x 1/4 = 1/2. Explanation: In the above-given question, given that, Ryse sprinted 3/4 of a lap around the running track at school. A whole lap is 1/4 mile. 3/4 x 1/4. 3/4 = 0.75. 1/4 = 0.25.. 0.75 – 0.25 = 0.50. 1/2 = 0.5. Practice Estimate. Question 5. 845 ÷ 24 = ___ Answer: 845 ÷ 24 = 35. Explanation: In the above-given question, given that, 845 ÷ 24 = 35. Question 6. 6,450 ÷ 639 = ___ Answer: 6450 ÷ 639 = 10. Explanation: In the above-given question, given that, 6450 ÷ 639 = 10. Question 7. 129 ÷ 19 = ___ Answer: 129 ÷ 19 = 10. Explanation: In the above-given question, given that, 129 ÷ 19 = 10. Everyday Mathematics Grade 6 Home Link 2.4 Answers Companion Gardening Draw and label area models and write number sentences to represent and solve Problems 1–2. Question 1. In companion planting, marigold flowers are used to repel insects that harm melon plants. Community gardeners plant $$\frac{2}{3}$$ of a rectangular garden bed with melon plants. They plant $$\frac{3}{4}$$ of the melon area with marigolds. What fraction of the garden bed will have both plants growing together? _____ Number sentence: _______ Answer: Question 2. Two plants that grow well together are tomatoes and basil. This year, $$\frac{1}{5}$$ of a garden bed was planted with tomatoes and basil. Next year, the area will be 3 times as large. What will the area be next year? ____ Number sentence: ____ Answer: First estimate, then use a partial-products diagram to solve Problem 3. Question 3. Last year a community garden produced 5$$\frac{1}{3}$$ pounds of carrots. This year, better weather resulted in a harvest 2$$\frac{2}{3}$$ times as large. How many pounds of carrots were harvested this year? Estimate: ____ Number sentence: ___ Practice Find equivalent fractions. Question 4. $$\frac{3}{4}$$ = Answer: 3/4 = 9/12. Explanation: In the above-given question, given that, equivalent fractions of 3/4. 3/4 = 3 x 3/4 x 3. 3 x 3 = 9. 4 x 3 = 12. 3/4 = 9/12. Question 5. $$\frac{18}{20}$$ = Answer: 18/20 = 9/10. Explanation: In the above-given question, given that, equivalent fraction of 18/20. 18/20 = 9 x 2/10 x 2. 9 x 2 = 18. 10 x 2 = 20. 18/20 = 9/10. Question 6. $$\frac{6}{7}$$ = Answer: 6/7 = 24/28. Explanation: In the above-given question, given that, equivalent fraction of 6/7. 6/7 = 6 x 4/7 x 4. 6 x 4 = 24. 7 x 4 = 28. 6/7 = 24/28. Question 7. $$\frac{24}{36}$$ Answer: 24/36 = 2/3. Explanation: In the above-given question, given that, equivalent fraction of 24/36. 24/36 = 60/90. 6/9 = 4/6. 4/6 = 2/3. 24/26 = 2/3. ### Everyday Math Grade 6 Home Link 2.5 Answer Key Fraction Multiplication Mara’s strategy: $$\frac{6}{8}$$ ∗ $$\frac{2}{3}$$ = (6 ∗ $$\frac{1}{8}$$) ∗ (2 ∗ $$\frac{1}{3}$$) = (6 ∗ 2) ∗ ($$\frac{1}{8}$$ ∗ $$\frac{1}{3}$$) = 12 ∗ $$\frac{1}{24}$$ = $$\frac{12}{24}$$ Question 1. Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. Then group your factors to make the problem easier. Show the steps you use. a. $$\frac{5}{2}$$ ∗ $$\frac{2}{4}$$= w Answer: $$\frac{10}{8}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (5 ∗ $$\frac{1}{2}$$) ∗ (2 ∗ $$\frac{1}{4}$$) (5 ∗ 2) ∗ ($$\frac{1}{2}$$ ∗ $$\frac{1}{4}$$) = 10 ∗ $$\frac{1}{8}$$ = $$\frac{10}{8}$$ b. $$\frac{10}{8}$$ ∗ $$\frac{8}{10}$$ = Answer: $$\frac{80}{80}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (10 ∗ $$\frac{1}{8}$$) ∗ (8 ∗ $$\frac{1}{10}$$) (10 ∗ 8) ∗ ($$\frac{1}{8}$$ ∗ $$\frac{1}{10}$$) = 80 ∗ $$\frac{1}{80}$$ = $$\frac{80}{80}$$ c. __ = 12 ∗ $$\frac{5}{6}$$ Answer: $$\frac{60}{6}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (12 ∗ $$\frac{5}{6}$$). (12 ∗ 5) ∗ ($$\frac{1}{6}$$. = 60 ∗ $$\frac{1}{6}$$ = $$\frac{60}{6}$$ d. ___ = $$\frac{5}{2}$$ ∗ 4 Answer: $$\frac{20}{2}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (4 ∗ $$\frac{5}{2}$$). (4 ∗ 5) ∗ ($$\frac{1}{2}$$. = 20 ∗ $$\frac{1}{2}$$ = $$\frac{20}{2}$$ e. $$\frac{21}{3}$$ ∗ $$\frac{6}{7}$$ = ___ Answer: $$\frac{126}{21}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (21 ∗ $$\frac{1}{3}$$) ∗ (6 ∗ $$\frac{1}{7}$$) (21 ∗ 6) ∗ ($$\frac{1}{3}$$ ∗ $$\frac{1}{7}$$) = 126 ∗ $$\frac{1}{21}$$ = $$\frac{126}{21}$$ f. 9 ∗ $$\frac{2}{9}$$ = ___ Answer: $$\frac{18}{9}$$. Explanation: In the above-given question, given that, Use Mara’s strategy to rename the fractions as whole numbers and unit fractions. (9 ∗ $$\frac{2}{9}$$). (9 ∗ 2) ∗ ($$\frac{1}{9}$$. = 18 ∗ $$\frac{1}{9}$$ = $$\frac{18}{9}$$ Question 2. Choose two problems from above that are alike in some way. Describe how they are alike. Answer: Use any model or strategy to solve Problems 3–4. Write a number sentence. Question 3. Samantha had 6 pages of homework. She finished $$\frac{2}{3}$$ of her assignment. How many pages did she finish? Number sentence: _____________ Answer: The number of pages did she finish = 5 pages. Explanation: In the above-given question, given that, Samantha had 6 pages of homework. She finished 2/3 of her assignment. 2/3 = 0.6. 6 – 0.6 = 5.4. so the number of pages did she finish = 5 pages. Question 4. A room measures 8$$\frac{1}{2}$$ feet by 10$$\frac{2}{3}$$feet. What is the area of the room? Number sentence: ________________ Answer: $$\frac{160}{6}$$. Explanation: In the above-given question, given that, (8 ∗ $$\frac{1}{2}$$) ∗ (10 ∗ $$\frac{2}{3}$$) (8 ∗ 10) ∗ ($$\frac{1}{2}$$ ∗ $$\frac{2}{3}$$) = 80 ∗ $$\frac{2}{6}$$ = $$\frac{160}{6}$$ Practice Question 5. 389 ∗ 17 = _________ Answer: 389 x 17 = 6613. Explanation: In the above-given question, given that, 389 x 17. Question 6. ____ = 176 ∗ 48 Answer: 176 x 48 = 8448. Explanation: In the above-given question, given that, 176 x 48. Question 7. 453 ∗ 24 = ____ Answer: 453 x 24 = 10872. Explanation: In the above-given question, given that, 453 x 24. ### Everyday Mathematics Grade 6 Home Link 2.6 Answers Division Using Home Link 2-6 Common Denominators Question 1. Draw a picture or diagram and solve the problem. Rudi has 4 cups of almonds. His trail mix recipe calls for $$\frac{2}{3}$$ cup of almonds. How many batches of trail mix can he make? Answer: Question 2. Use common denominators to solve the problems. Write a number sentence to show how you rewrote the problem with common denominators. Check your answers. a. $$\frac{3}{4}$$ ÷ $$\frac{3}{8}$$ = _______ Number sentence: _________ Answer: 3/4 ÷ 3/8 = 2. Explanation: In the above-given question, given that, Use common denominators to solve the problems. 3/4 = 0.75. 3/8 = 0.3. 0.75/0.375 = 2. b. 3$$\frac{1}{3}$$ ÷ $$\frac{5}{6}$$ = ___ Number sentence: ____ Answer: 3(1/3) ÷ 5/6 = 4. Explanation: In the above-given question, given that, Use common denominators to solve the problems. 3 x 3 = 9. 9 + 1 = 10. 10/3 = 3.3. 5/6 = 0.8. 3.3/0.8 = 4.1. c. $$\frac{36}{8}$$ ÷ $$\frac{1}{2}$$ = ___ Number sentence: _______ Answer: 36/8 ÷ 1/2 = 9. Explanation: In the above-given question, given that, Use common denominators to solve the problems. 36/8 = 4.5. 1/2 = 0.5. 4.5/0.5 = 9. Question 3. Michelle is cutting string to make necklaces. She has 15 feet of string. She needs 1$$\frac{1}{2}$$ feet of string for each necklace. How many necklaces can she make? Number model: ______ Solution: _________ Answer: The number of necklaces she can make = 10. Explanation: In the above-given question, given that, Michelle is cutting string to make necklaces. She has 15 feet of string. she needs 3/2 feet of string for each necklace. 3/2 = 1.5. 1.5 x 10 = 15. so she can make 10 necklaces. Question 4. A rectangular window has an area of 4$$\frac{1}{2}$$ square meters. Its width is $$\frac{3}{4}$$ meter. What is its length? Number model: ____ Solution: ___ Answer: The length of the rectangular window = 6 m. Explanation: In the above-given question, given that, A rectangular window has an area of 4 x 1/2 sq m. 4 x 2 = 8. 8 + 1 = 9. 9/2 = 4.5. width = 3/4. 3/4 = 0.75. area = l x w. 4.5 = l x 0.75. l = 4.5/0.75. length = 6. so the length of the rectangular window = 6 meters. Practice Solve. Question 5. GCF (20, 30) = ___ Answer: GCF of 20 and 30 = 10. Explanation: In the above-given question, given that, GCF of 2 and 30. GCF = greatest common factor. factors of 20 = 1, 2, 4, 5, 10, and 20. factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30. among all those 10 is the common factor. Question 6. GCF (6, 16) = ___ Answer: GCF of 6 and 16 = 2. Explanation: In the above-given question, given that, GCF of 6 and 16. GCF = greatest common factor. factors of 6 = 1, 2, and 3. factors of 16 = 1, 2, 4, and 8. among all those 2 is the common factor. Question 7. GCF (36, 54) = __ Answer: GCF of 36 and 54 = 2. Explanation: In the above-given question, given that, GCF of 36 and 54. GCF = greatest common factor. factors of 36 = 1, 2, and 3. factors of 54 = 1, 2, 4, and 8. among all those 2 is the common factor. ### Everyday Math Grade 6 Home Link 2.7 Answer Key More Exploring Fraction Division For problems 1–3, circle the best estimate and the correct number model. Then solve the problem. Question 1. Stan is in wood working class with 6 friends. They have to split a board that is 4$$\frac{2}{3}$$ feet long equally among the seven of them. How long will each person’s piece be? Answer: ____ The long will each person’s piece be = 4.6 feet. Explanation: In the above-given question, given that, Stan is in woodworking class with 6 friends. They have to split a board that is 4$$\frac{2}{3}$$ feet long equally among the seven of them. 4(2/3) = 3 x 4 = 12. 12 + 2 = 14. 14/3 = 4.6. Question 2. The area of a rectangle is 10$$\frac{1}{2}$$ square feet. The length is 5$$\frac{1}{4}$$ feet. How wide is the rectangle? Answer: ____ The width of the rectangle = 2 ft. Explanation: In the above-given question, given that, the area of a rectangle is 10(1/2) sq ft. length = 5 (1/4) ft. 10 x 2 = 20. 20 + 1 = 21. 21/2 = 10.5. 5 x 4 = 20. 20 + 1 = 21. 21/4 = 5.25. area = l x w. 10.5 = 5.25 x w. w = 10.5/5.25. w = 2 ft. so the width of the rectangle = 2 ft. Question 3. Sounya walks dogs on Saturdays. It takes $$\frac{3}{4}$$ of an hour to walk each dog. She has 5$$\frac{1}{4}$$ hours. How many dogs can she walk? Answer: ___ The number of dogs she can walk = more than 5 dogs. Explanation: In the above-given question, given that, Sounya walks dogs on Saturdays. It takes 3/4 of an hour to walk each dog. she has 5(1/4) hours. 3/4 = 0.75. 5(1/4) = 5 x 4 = 20. 20 + 1 = 21. 21/4 = 5.25. Practice Find the LCM. Question 4. LCM (3, 7) = ___ Answer: LCM of 3 and 7 = 21. Explanation: In the above-given question, given that, LCM of 3 and 7. LCM = least common multiple. 3 = 3 x 1. 7 = 7 x 1. 3 x 7 = 21. Question 5. LCM (8, 4) = __ Answer: LCM of 8 and 4 = 8. Explanation: In the above-given question, given that, LCM of 8 and 4. LCM = least common multiple. 4 = 2 x 2. 2 = 2 x 1. 8 = 2 x 4. 4 = 2 x 2. 2 = 2 x 1. 2 x 2 x 2 = 8. Question 6. LCM (10, 4) = ___ Answer: LCM of 10 and 4 = 20. Explanation: In the above-given question, given that, LCM of 10 and 4. LCM = least common multiple. 10 = 2 x 5. 4 = 2 x 2 5 = 5 x 1. 2 x 2 x 5 = 20. ### Everyday Mathematics Grade 6 Home Link 2.8 Answers Fraction Division Rewrite and solve the division problems using the Division of Fractions Property. Example: $$\frac{3}{8}$$ ÷ $$\frac{2}{5}$$ = $$\frac{3}{8}$$ ∗ $$\frac{5}{2}$$ = $$\frac{15}{16}$$ Question 1. 3 ÷ $$\frac{2}{3}$$ = ___ Answer: 3 ÷ 2/3 = 9/2. Explanation: In the above-given question, given that, 3 ÷ 2/3. 3 ÷ 3/2. 9/2. Question 2. $$\frac{1}{5}$$ ÷ $$\frac{8}{9}$$ = ___ Answer: $$\frac{9}{40}$$. Explanation: In the above-given question, given that, $$\frac{1}{5}$$ ÷ $$\frac{8}{9}$$ $$\frac{1}{5}$$ ∗ $$\frac{8}{9}$$. $$\frac{1}{5}$$ ∗ $$\frac{9}{8}$$. $$\frac{9}{40}$$ Question 3. 4 ÷ $$\frac{5}{7}$$ = ___ Answer: $$\frac{28}{5}$$ Explanation: In the above-given question, given that, 4 ÷ $$\frac{5}{7}$$ 4 ∗ $$\frac{5}{7}$$. 4 ∗ $$\frac{7}{5}$$. $$\frac{28}{5}$$ Question 4. 1$$\frac{2}{3}$$ ÷ $$\frac{3}{5}$$ = ______ Answer: $$\frac{25}{9}$$ Explanation: In the above-given question, given that, 1$$\frac{2}{3}$$ ÷ $$\frac{3}{5}$$ $$\frac{5}{3}$$ ∗ $$\frac{3}{5}$$. $$\frac{5}{3}$$ ∗ $$\frac{5}{3}$$. $$\frac{25}{9}$$ Question 5. $$\frac{2}{5}$$ ÷ $$\frac{3}{4}$$ = ____ Answer: $$\frac{8}{15}$$. Explanation: In the above-given question, given that, $$\frac{2}{5}$$ ÷ $$\frac{3}{4}$$ $$\frac{2}{5}$$ ∗ $$\frac{3}{4}$$. $$\frac{2}{5}$$ ∗ $$\frac{4}{3}$$. $$\frac{8}{15}$$ Question 6. $$\frac{3}{5}$$ ÷ 4 = ____ Answer: $$\frac{20}{3}$$ Explanation: In the above-given question, given that, 4 ÷ $$\frac{3}{5}$$ 4 ∗ $$\frac{3}{5}$$. 4 ∗ $$\frac{5}{3}$$. $$\frac{20}{3}$$ Question 7. How many $$\frac{1}{4}$$-cup servings of cottage cheese are in a 3-cup container? Division number model: ______ Multiplication number model: _______ Solution: _________ Answer: $$\frac{12}{1}$$ Explanation: In the above-given question, given that, 3 ÷ $$\frac{1}{4}$$ 3 ∗ $$\frac{1}{4}$$. 3 ∗ $$\frac{4}{1}$$. $$\frac{12}{1}$$ Question 8. Philip went on a 3$$\frac{1}{2}$$-mile hike. He hiked for 2 hours. About how far did he go in 1 hour? Division number model: ____ Multiplication number model: ______ Solution: _________ Answer: Question 9. Adam is using ribbon to decorate name tags for the class picnic. He has 8$$\frac{2}{3}$$ feet of blue ribbon. He needs $$\frac{1}{3}$$ foot of ribbon for each name tag. How many name tags can he decorate? Division number model: ______ Multiplication number model: ________ Solution: _______ Answer: The number of name tags he can decorate = 28. Explanation: In the above-given question, given that, Adam is using ribbon to decorate name tags for the class picnic. he as 8(2/3) feet of blue ribbon. 8 x 3 = 24. 24 + 2 = 26. 26/3 = 8.6. 1/3 = 0.3. 0.3 x 28 = 8.6. so the number of name tags he can decorate = 28. Practice Add or subtract. Question 10.$4.50 + $3 = ___ Answer:$4.50 + $3 =$7.5.

Explanation:
In the above-given question,
given that,
$4.50 +$3.
$7.5. Question 11.$5.00 – $3.20 = ___ Answer:$5 – $3.2 =$1.8.

Explanation:
In the above-given question,
given that,
$5 –$3.2.
$1.8. Question 12. ___ =$6.30 + $0.45 +$1.35

$6.30 +$0.45 + $1.35 =$8.1

Explanation:
In the above-given question,
given that,
$6.30 +$0.45 + $1.35.$6.30 + $0.45 =$6.75.
$6.75 +$1.35 = $8.1. ## Everyday Math Grade 6 Home Link 2.9 Answer Key Using Ratios to Represent Situations Question 1. Lenore’s dog gave birth to a litter of 9 puppies. Two of the puppies are male. Write ratios for the following: Number of female puppies to the total number of puppies ___________ Number of male puppies to female puppies ________ Answer: The number of female puppies to the total number of puppies = 7: 9. The number of male puppies to the total number of puppies = 2: 9. Explanation: In the above-given question, given that, Lenore’s dog gave birth to a litter of 9 puppies. Two of the puppies are male. The number of female puppies to the total number of puppies = 7: 9. The number of male puppies to the total number of puppies = 2: 9. For Problems 2–4, draw a picture to help you solve the problem. Record a ratio. Question 2. There are 15 tiles. 2 out of 5 tiles are white. How many tiles are white? ____ Write the ratio of white tiles to total tiles. Answer: The ratio of white tiles to total tiles = 5:15. Explanation: In the above-given question, given that, There are 15 tiles. 2 out of 5 tiles are white. 5:15. so the ratio of white tiles to the total tiles = 5;15. Question 3. There are 24 tiles. 3 out of 4 tiles are white. How many tiles are white? ___ Write the ratio of white tiles to shaded tiles. Answer: The ratio of white tile to shaded tiles = 3:20. Explanation: In the above-given question, given that, There are 24 tiles. 3 out of 4 tiles are white. 3: 20. so the ratio of white tiles to shaded tiles = 3:20. Question 4. There are 3 times as many white tiles as there are shaded tiles. Write this ratio. How many tiles are white if there are 12 tiles in total? Answer: The number of tiles are white = 9. Explanation: In the above-given question, given that, There are 3 times as many white tiles as there are shaded tiles. 3 x 3 = 9. so the number of tiles are white = 9. Question 5. The Mighty Marble Company fills bags of marbles with a ratio of 3 Special Swirls out of every 9 marbles. How many Special Swirls are in a bag that has 21 marbles? ____ Answer: The number of Special Swirls are in a bag that has 21 marbles = 7. Explanation: In the above-given question, given that, The Mighty marble Company fills bags of marbles with a ratio of 3 special swirls out of every 9 marbles. 3 x 3 = 9. 6 x 3 = 18. 7 x 3 = 21. so the number of special swirls are in a bag that has 21 marbles = 7. Try This Question 6. One class of 28 students has a ratio of 3 girls to 4 boys. What is the ratio for the number of boys to total number of students in the class? ______________ There are 60 girls in the whole sixth grade and the ratio is the same. How many students are there in sixth grade? Answer: The total number of boys to the total number of students = 7:28. Explanation: In the above-given question, given that, One class of 28 students has a ratio of 3 girls to 4 boys. 7 x 4 = 28. 7: 28. so the total number of boys to the total number of students = 7:28. Practice Solve. Question 7. $$\frac{5}{6}$$ ∗ $$\frac{3}{4}$$ = ___ Answer: 5/6 x 3/4 = 0.6225. Explanation: In the above-given question, given that, 5/6 x 3/4. 5/6 = 0.8. 3/4 = 0.75. 0.83 x 0.75 = 0.6225. Question 8. $$\frac{2}{3}$$ ∗ 1$$\frac{1}{2}$$ = ___ Answer: 2/3 x 3/2 = 0.9. Explanation: In the above-given question, given that, 2/3 x 1(1/2). 2 x 1 = 2. 2 + 1 = 3. 3/2 = 1.5. 2/3 = 0.6. 2/3 x 3/2 = 0.9. Question 9. $$\frac{8}{9}$$ ∗ $$\frac{2}{7}$$ = Answer: 8/9 x 2/7 = 0.16. Explanation: In the above-given question, given that, 8/9 x 2/7. 8/9 = 0.8. 2/7 = 0.2. 8/9 x 2/7 = 0.16. ### Everyday Mathematics Grade 6 Home Link 2.10 Answers More with Tape Diagrams Draw tape diagrams to solve the problems. Label your diagrams and your answers. Frances is helping her father tile their bathroom floor. They have tiles in two colors: green and white. They want a ratio of 2 green tiles to 5 white tiles. a. They use 30 white tiles. How many green tiles do they use? ______________ Answer: b. How many white tiles would they need if they use 16 green tiles? Answer: c. They use 35 tiles in all. How many are green? Answer: d. They use 49 tiles. How many of each color did they use? Answer: e. Explain how you used the tape diagram to solve Part d. Answer: Try This Question 2. Frances and her father decide to also tile their kitchen floor. For every 3 white tiles they plan to use 7 green tiles. The kitchen floor has room for 63 tiles total. Explain why they cannot cover the kitchen floor using the ratio 3 : 7. Answer: Yes, they cannot cover the kitchen floor using 3:7. Explanation: In the above-given question, given that, Frances and her father decide to also tile their kitchen floor. For every 3 white tiles, they plan to use 7 green tiles. but they used to keep for every 9 white tiles they plan to use 7 green tiles. 7 x 9 = 63. Practice Divide. Question 3. $$\frac{4}{5}$$ ÷ $$\frac{1}{5}$$ = ____ Answer: 4/5 ÷ 1/5 = 4. Explanation: In the above-given question, given that, 4/5 = 0.8. 1/5 = 0.2. 0.8/0.2 = 4. 4/5 ÷ 1/5 = 4. Question 4. $$\frac{1}{5}$$ ÷ $$\frac{4}{5}$$ = ____ Answer: 1/5 ÷ 4/5 = 1/4. Explanation: In the above-given question, given that, 4/5 = 0.8. 1/5 = 0.2. 0.2/0.8 = 0.25. 1/5 ÷ 4/5 = 1/4. Question 5. 7 ÷ $$\frac{1}{2}$$ = _____ Answer: 7 ÷ 1/2 = 14. Explanation: In the above-given question, given that, 1/2 = 0.5. 7 ÷ 0.5 = 14. Everyday Mathematics Grade 6 Home Link 2.11 Answers Finding Equivalent Ratios Use the pictures to help you figure out the equivalent ratios Question 1. Answer: 1 foot = 12 inches. 3 feet = 36 inches. 7 feet = 84 inches. 144 inches = 12 feet. Explanation: In the above-given question, given that, the ratio of the foot to inches. 1 foot = 12 inches. 3 feet = 36 inches. 3 x 12 = 36. 7 feet = 84 inches. 7 x 12 = 84. 12 feet = 144 inches. 12 x 12 = 144. Question 2. Answer: 10 mm = 1 cm. 50 mm = 5 cm. 3000 mm = 300 cm. 250 mm = 25 cm. Explanation: In the above-given question, given that, the ratio of the mm to cm. 10 mm = 1 cm. 50 mm = 5 cm. 5 x 10 = 50 mm. 3000 mm = 300 cm. 300 x 10 = 3000. 250 mm = 25 cm. 25 x 10 = 250. Question 3. Answer: 8 legs = 1 spider. Explanation: In the above-given question, given that, the ratio of the legs to the spider. 8 legs are there in the figure. 8 legs = 1 spider. Question 4. a. Circle the similar rectangles. Answer: The rectangles are not similar. Explanation: In the above-given question, given that, circle the similar rectangles. the area of the rectangle = l x b. where l = length and b = breadth. the area of A = 4 x 2. 4 x 2 = 8. rectangle B = 3 x 2 3 x 2 = 6. rectangle C = 6 x 4. 6 x 4 = 24. rectangle D = 5 x 1. 5 x 1 = 5. b. Explain why the rectangles you circled are similar. Answer: The rectangles are not similar. Explanation: In the above-given question, given that, rectangle A = 4 x 2. 4 x 2 = 8. rectangle B = 3 x 2 3 x 2 = 6. rectangle C = 6 x 4. 6 x 4 = 24. rectangle D = 5 x 1. 5 x 1 = 5. so the rectangles are not similar. c. Under each rectangle, use fraction notation to write the width-to-height ratio. Answer: Rectangle A = 4 : 2. Rectangle B = 3 : 2. Rectangle C = 6 : 4. Rectangle D = 5 : 1. Explanation: In the above-given question, given that, rectangle A = 4 x 2. 4 x 2 = 8. rectangle B = 3 x 2 3 x 2 = 6. rectangle C = 6 x 4. 6 x 4 = 24. rectangle D = 5 x 1. 5 x 1 = 5. Practice Multiply mentally to find the cost. Question 5. 4 pens at$2.98 each ___

4 x $2.98 = 11.92. Explanation: In the above-given question, given that, 4 pens at$2.98 each.
4 x $2.98. 11.92. Question 6. 3 books at$24.95 each ____

3 x $24.95 =$74.85.

Explanation:
In the above-given question,
given that,
3 books at $24.95 each. 3 x$24.95.
$74.85. ### Everyday Math Grade 6 Home Link 2.12 Answer Key Using Ratios to Make Fruit Cups Oliver has two fruit-cup recipes that have different ratios of raspberries and watermelon. Question 1. a. Which fruit-cup recipe would have a stronger raspberry taste? ______ Answer: Recipe A has a stronger raspberry taste. Explanation: In the above-given question, given that, Oliver has two fruit-cup recipes that have different ratios of raspberries and watermelon. Recipe A has 2 cups raspberries and 3 cups watermelon. Recipe B has 5 cups raspberries 11 cups total. so Recipe A has a stronger raspberry taste. b. Draw a picture or diagram to support your answer. Answer: c. Explain how your picture or diagram supports your answer. Answer: Question 2. Create a fruit-cup recipe that would taste the same as Recipe B, but uses more than 11 cups of fruit. List your ingredients: ______ Answer: The ingredients are bananas and grapes. Explanation: In the above-given question, given that, create a fruit-cup recipe that would taste the same as Recipe B, but uses more than 11 cups of fruit. the 8 cups of bananas and 4 cups of grapes. Question 3. Create a fruit-cup recipe that would make a fruit cup with a weaker raspberry taste than Recipes A and B. List your ingredients: _______ Answer: The ingredients are bananas and grapes. Explanation: In the above-given question, given that, create a fruit-cup recipe that would make a fruit cup with a weaker raspberry taste than recipes A and B. the 8 cups of bananas and 3 cups of grapes. Try This Question 4. If you only want 1 cup of fruit salad made from Recipe A, what measurements of watermelon and raspberries do you need? Answer: Practice Divide. Question 5. 560 ÷ 7 = ____ Answer: 560 ÷ 7 = 80. Explanation: In the above-given question, given that, 560 / 8. Question 6. 842 ÷ 2 = ____ Answer: 842 ÷ 2 = 421. Explanation: In the above-given question, given that, 842 / 2. Question 7. 930 ÷ 3 = ____ Answer: 930 ÷ 3 = 310. Explanation: In the above-given question, given that, 930 / 3. Everyday Math Grade 6 Home Link 2.13 Answer Key Ratio/Rate Tables and Unit Rates Question 1. List three examples of a rate: ____________ Draw a ratio/rate table to solve each problem. The first table has been drawn for you, but it is not complete. Answer: Question 2. One 12-ounce can of frozen juice is mixed with three 12-ounce cans of water. How many cans of water do you need for 4 cans of juice? _____________ Answer: The number of cans of water need for 4 cans of juice = 12 cans. Explanation: In the above-given question, given that, One 12-ounce can of frozen juice is mixed with three 12-ounce cans of water. 1 x 3 = 3. 4 x 3 = 12. so the 4 cans of juice are mixed with 12 cans of water. Question 3. A hiker’s map has a scale of 3 inches to 10 miles. The trail is 4 inches long on the map. How long is the actual hike? ______ Answer: Question 4. Amy types 125 words in 2 minutes. About how long will it take her to type a 1,500-word report? ____ Answer: Amy types a 1,500-word report in 24 minutes. Explanation: In the above-given question, given that, Amy types 125 words in 2 minutes. 125 + 125 = 250. 250 x 6 = 1500. Amy types a 1,500-word report in 24 minutes. Try This Question 5. A recipe for lime salad dressing calls for $$\frac{1}{4}$$ cup lime juice and $$\frac{3}{4}$$ cup olive oil. How much lime juice would you use with 1 cup olive oil? _______ Answer: Practice Record >, <, or =. Question 6. -3 ___ -5 Answer: -3 > -5. Explanation: In the above-given question, given that, -3 and -5. -3 is greater than -5. -3 > -5. Question 7. 6 ____ -7 Answer: 6 > -7. Explanation: In the above-given question, given that, 6 and -7. 6 is greater than -7. 6 > -7. Question 8. -8 ____ -9 Answer: -8 > -9. Explanation: In the above-given question, given that, -8 and -9. -8 is greater than -9. -8 > -9. Everyday Math Grade 6 Home Link 2.14 Answer Key Graphing Rates Snails move slowly. Jada, Reality, and Barb had a snail race. Then they compared the rates at which the snails crawled. Question 1. Fill in the ratio/rate table with equivalent rates. Answer: Question 2. Treat each rate as an ordered pair. Graph each snail’s rate using a different color. Answer: Question 3. Which snail is the fastest? Use the graph to explain how you know Answer: Practice Insert >, <, or = to make each sentence true. Question 4. 7 ___ 4.65 Answer: 7 > 4.65. Explanation: In the above-given question, given that, 7 and 4.65. 7 is greater than 4.65. 4.65 = 5. 7 > 4.65. Question 5. 0.1 __ 0.01 Answer: 0.1 > 0.01. Explanation: In the above-given question, given that, 0.1 and 0.01. 0.1 is greater than 0.01. 0.1 > 0.01. Question 6. 0.205 ___ 0.22 Answer: 0.205 < 0.22. Explanation: In the above-given question, given that, 0.205 and 0.22. 0.205 is less than 0.22. 0.205 < 0.22. ## Everyday Math Grade 6 Answers Unit 1 Data Displays and Number Systems ## Everyday Mathematics 6th Grade Answer Key Unit 1 Data Displays and Number Systems ### Everyday Math Grade 6 Home Link 1.2 Answer Key Exploring Dot Plots and Landmarks Question 1. Draw a dot plot for the following spelling test scores: 100, 100, 95, 90, 92, 93, 96, 90, 94, 90, 97 Answer: Question 2. The mode of the data in Problem 1 is ___. Answer: Mode = Most repeated observation Given sequence = 100, 100, 95, 90, 92, 93, 96, 90, 94, 90, 97 So, Mode = 90 {Repeated 3 times} Therefore, Mode of the data = 90 Question 3. Draw a dot plot that represents data with the landmarks shown below. Use at least 10 numbers. Answer: Question 4. Explain how you decided where to place your data on the dot plot in Problem 3. Answer: The difference between numbers 1. From 0, to right side, add 1 number From 0, to left side, subtract 1 number Question 5. Describe a situation the data in the dot plot in Problem 3 might represent. Answer: Integers i.e., positive numbers, negative numbers including zero. Question 6. Give the dot plot a title. Be sure to label the unit (for example, dollars or miles) for the number line. Answer : Integers i.e., positive numbers, negative numbers including zero. Find an interesting graph on the Internet or in a newspaper or magazine. Bring it to class tomorrow. Answer: ### Everyday Mathematics Grade 6 Home Link 1.3 Answers Using the Mean to Solve Problems Question 1. Ms. Li brought pumpkin seed packs for her class. Each student received a pack. Her class predicted that there were 30 seeds in each pack. Here are the total number of seeds per pack the students in one group found when they counted: 20, 21, 23, 20, 22, 20. Find the group mean for the pumpkin seed packs. ____ pumpkin seeds Answer: 21 Explanation : Given, Number of seeds student counted : 20,20,20,21,22,23 Total no. of observations =6 Mean = sum of observations / total number of observations Group mean = 20+20+20+21+22+23 /6 = 126/6 = 21 Therefore, group mean for given data is 21 Question 2. Another group in Ms. Li’s class added their pumpkin seed counts to the data set. Here is what they have all together: 20, 21, 23, 20, 22, 20, 23, 27, 28, 29, 28, 27. Make a dot plot for the combined data. Answer: Find these landmarks for this data set. Median: ___ Mode(s): __ Mean: ___ Answer: Median= If the total observations are even, then average of middle two numbers is median 20,20,20,21,22,23,23,27,27,28,28,29 middle numbers are 23,23 average = 23+23 /2 =23 Therefore, Median = 23. Mode= Most repeated observation in total observation. 20 is the most repeated observation (3 times) Therefore, Mode = 20. Mean= sum of observations / Total number of observations. = 20+20+20+21+22+23+23+27+27+28+28+29 /12 = 288/12 = 24 Therefore, Mean = 24 Question 3. If Ms. Li brought these packs every day for 20 days of class, about how many seeds would each student receive? Answer: Total number of students : 6+12 = 18 If each pack have 24 seeds, then for 20 days = 24*20 = 480 Number of seeds that each student receive =480/18 = 26.67 (approximately 27) Therefore, number of seeds each student receive is 27 Try This Question 4. If you were in charge of advertising these pumpkin seed packs, how many seeds would you advertise are in each pack ? Why? Answer: If I was the in charge of advertising these pumpkin seed packs, i will advertise 24 seeds in each pack. Because, it is the mean of majority group (12 members) total number of observations of seeds in pack. Practice Question 5. 4 ∗ 12 = __________________________ Answer: 48 Question 6. ___ 6 = 6 ∗ 12 Answer: Question 7. 15 ∗ 5 = ___ Answer: 75 Question 8. ___ = 13 ∗ 4 Answer: 52 ### Everyday Math Grade 6 Home Link 1.4 Answer Key Balancing Movies Sandy asked six students how many movies they watched last month, and then graphed the results. The mean number of movies watched was 4. Question 1. How likely is it that Sandy’s graph would look like the graph at the right? Explain. _______________________ ________________________ Answer: Given, Mean is 4 Therefore, Mean = Sum of Observations / Total number of observations Mean = 4+4+4+4+4+4 /6 = 24/6 = 4 Which is given Mean Hence, it is exact graph to represent the data. Question 2. Suppose that five students answered as shown. How many movies did the sixth student watch? ___ Plot the sixth point on the dot plot and explain how you know where to place it. Answer: Sixth student watched Six Movies. Explanation : Given, Mean is 4 Mean = sum of observations / total number of observations let, the movies watched by sixth member is x then, 2+4+4+4+4+4+x /6 =4 18+x /6 =4 x= 24-18 =6 Therefore, total number of movies watched is six (6) Each dot represents the person and the number represents rthe number of movies watched. Hence, there should be one dot at number six on number line. Question 3. Suppose that four students answered as shown. How many movies could the last two students watch? _______________ Answer : Given, Mean is 4 Mean = sum of observations / total number of observations let,the movies watched by two members be x+x = 2x 2+2+4+4+x+x /6 =4 12+2x =24 2x =12 x =6 Therefore, each student watched six movies. Plot the last two points on the dot plot and explain how you know where to place them. Answer : Each dot represents the person and the number represents rthe number of movies watched. Hence, there should be two dots at number six on number line. Try this Question 4. The data shown at the right is for four of six students surveyed. What two missing data points would make the mean 4? Answer : Given, Mean is 4 Mean = sum of observations / total number of observations let, movies watched by two members be x+x =2x 4+4+4+10+x+x /6 =4 22+2x =24 2x=2 x=1 Therefore, two students watched one movie each. Plot the points on the dot plot. Answer : Practice Solve. Question 5. 46 ÷ 2 = Answer: 23 Question 6. 80 ÷ 5 = Answer: 16 Question 7. 68 ÷ 2 = Answer: 34 ### Everyday Mathematics Grade 6 Home Link 1.5 Answers Measures of Center Math test scores (each out of 100 points) are shown below. Mia’s scores: 75, 75, 75, 85, 80, 95, 85, 90, 80, 80 Nico’s scores: 55, 80, 90, 100, 70, 80, 50, 80, 75, 80 Question 1. Find the median and mean scores for each student. Mia: Median Mean Nico: Median Mean Answer: Mia Scores : 75,75,75,80,80,80,85,85,90,95 Median = If the total observations are even, then average of middle two numbers is median. middle numbers are 80,80 average = 80+80 /2 = 80 Therefore, median= 80 Mean = sum of total observations / total number of observations = 75+75+75+80+80+80+85+85+90+95 /10 = 820/10 = 82 Therefore, Mean is 82 Nico scores : 50,55,70,75,80,80,80,80,90,100 Median = If the total observations are even, then average of middle two numbers is median middle numbers are 80,80 Average = 80+80 /2 = 80 Therefore, median = 80 Mean = sum of total observations / total number of observations = 50+55+70+75+80+80+80+80+90+100 /10 = 76 Therefore, Mean is 76 Question 2. Which better represents each student’s performance, the mean or median? Explain. Answer : Mia: Median = 80 Mean = 82 Nico: Median = 80 Mean = 76 Mean represents the better student’s performance because it is the average of all the scores they scored. Question 3. In their class, a score in the 80s is a B and a score in the 70s is a C. If their teacher uses the medians of their test scores to calculate grades, Mia and Nico would get the same grade. If the teacher uses the mean, Mia would get a B and Nico would get a C. Explain how Mia’s and Nico’s scores have the same median and different means. __________________________ ___________________________ ____________________________ Answer: Mia: Median = 80 Mean = 82 Nico: Median = 80 Mean = 76 So, Mia’s grade is B and Nico’s grade is C ( on basis on mean) Both Mia and Nico’s grade is B (on basis on Median) Question 4. If you were the teacher in Mia and Nico’s class, would you use the median or the mean to calculate students’ grades? Explain. _________________ ____________________ If i were the teacher I would like to use Mean to calculate students’ grades. Because, it gives the average scores for each student Practice Solve. Question 5. 25 ∗ 30 = _______________ Answer: 750 Question 6. ________ = 16 ∗ 400 Answer: 1/25 = 0.04 Question 7. 150 ∗ 600 = Answer: 1/4 = 0.25 Question 8. ____ = 90 ∗ 130 Answer: 11700 ### Everyday Math Grade 6 Home Link 1.6 Answer Key Analyzing Persuasive Graphs You are trying to convince your parents that you deserve an increase in your weekly allowance. You claim that during the past 10 weeks, the time you have spent doing jobs around the house (such as emptying the trash, mowing the lawn, and cleaning up after dinner) has increased. You have decided to present this information to your parents in the form of a graph. You have made two versions of the graph and need to decide which one to use. Question 1. How are Graph A and Graph B similar? Answer: Graph A and Graph B are similar because both are showing the work done during 3:00 to 4:00 in the past 10 weeks Question 2. How are Graph A and Graph B different? Answer: Graph A is showing the Hours on Y-axis from 0 to 7 where Graph b is showing hours on Y-axis only between 3:00 to 4:00 Question 3. Which graph, A or B, do you think will help you more as you try to convince your parents that you deserve a raise in your allowance? Why? Answer: Graph B, because it is showing exact display of the work done in the past 10 weeks. Analyzing Persuasive Home Link 1-6 Graphs Question 4. For the graph, describe what you plan to correct. Redraw the graph to give a more accurate picture of the data. Correction(s): ________ Answer: Describe how your corrections changed what you see in the graph. _______________________________________ _______________________________________ Answer: A Histogram contains no gaps between the vertical bars Practice Solve. Question 5. $$\frac{1}{12}$$ + $$\frac{7}{12}$$ = ___ Answer: 2/3 Explanation: = 1/12 + 7/12 = 8/12 = 2/3 Question 6. $$\frac{3}{10}$$ + $$\frac{7}{10}$$ = ___ Answer: 1 Explanation : = 3/10 +7/10 = 10/10 = 1 Question 7. $$\frac{1}{8}$$ + $$\frac{3}{8}$$ = ___ Answer: 1/2 0r 0.5 Explanation : = 1/8 + 3/8 = 4/8 = 1/2 0r 0.5 Question 8. 1$$\frac{1}{2}$$ + $$\frac{1}{2}$$ = ___ Answer: 1 Explanation: = 1/2 +1/2 = 2/2 = 1 ### Everyday Mathematics Grade 6 Home Link 1.7 Answers Exploring Bar Graphs and Histograms Question 1. Circle each graph that is a histogram. Answer: Question 2. Pick one of the graphs above and list two different questions you could answer with the graph . Do not use the same kind of question twice (even about a different graph). Answer: Question No.1 How many students did their homework between 6 to 8 hours (graph 1) ? Question No.2 What is the age group of highest number of siblings present ? Question 3. Describe features of a graph that make it a histogram. Answer: A histogram is used to display continuous data in categorical from. There is no gap between the bars in the histogram unlike a bar graph. ### Everyday Math Grade 6 Home Link 1.8 Answer Key Kentucky Derby Winners Use the graph of Kentucky Derby winners’ times for the problems below. Question 1. Describe the shape of this graph. Answer: Shape of the graph is histogram Question 2. Explain why the graph for this data might have this shape. Answer: Because, There is no gap between the bars in the histogram unlike a bar graph. Question 3. Draw a line on the graph approximately where you think the mean is. Approximately where are the median and the mode compared to the mean? Answer: Mean : 8.6 Median : 4 Mode : 0 Try This Question 4. Research and describe why the graph of Kentucky Derby winning times is this shape. ________________ Answer: Because, the data is displayed in histogram as there should be no gaps between the vertical bars. Practice Solve Question 5. ___ ∗ 50 = 350 Answer: 7 Explanation : 7*50 =350 Question 6. 60 * 40 = ____ Answer: 2400 Explanation : 60*40=2400 Question 7. 3,600 = 90 * ___ Answer: 40 Explanation : let the number be x Then, x = 3600/90 x=40 ### Everyday Mathematics Grade 6 Home Link 1.9 Answers Exploring Histograms Here are two histograms representing the lengths of the 20 longest rivers in the world. Question 1. Describe how the shapes of the graphs are different. Answer: The difference between the length of rivers in first histogram in X-axis is 300 miles. where as in second histogram, difference between the length of rivers in X-axis is 500 miles. First histogram ranges from 1,900 to 4,300 (miles) and there are only maximum of seven rivers in that range. second histogram ranges from 1,800 to 4,300 (miles) and there are only maximum of eleven rivers in that range. Question 2. These histograms represent the same set of data. Why do they look different? Answer: Because, the difference between the length of rivers in first histogram in X-axis is 300 miles. where as in second histogram, difference between the length of rivers in X-axis is 500 miles. So, even the histograms represent same det of data,they look different. Question 3. a. Based on the graphs, what is the largest the range can be? b. Explain how you figured out the largest possible range. Answer : a. Largest range is 500 b. The difference between two successive values gives the Range. in first Histogram Range is 300 Where as in second histogram, Range is 500 Question 4. a. Estimate the median for the lengths of the 20 longest rivers. b. Explain how you estimated the median. Answer: a. Median is 2.5 for first Histogram. Median is 3.5 for second Histogram. b. If there are even number of observations, then Median will be the average between two middle numbers. ### Everyday Math Grade 6 Home Link 1.10 Answer Key Plotting Numbers Question 1. Here is a list by month for the record low temperatures in Minneapolis, MN. Plot the letters for the temperatures on the number line below. A: January, -57°F B: February, -60°F C: March, -50°F D: April, -22°F E: May, 4°F F: June, 15°F G: July, 24°F H: August, 21°F I: September, 10°F J: October, -16°F K: November, -45°F L: December, -57°F Answer: Question 2. A tree has a trunk, branches, and leaves above ground (positive) and roots below ground (negative). Represent each height as a point on the number line. M: Lowest branch at 6 feet N: Deepest root at 5 feet P: Hole in trunk at 8 feet Q: Ground level R: Buried nuts at 3 feet Answer : Practice Solve. Question 3.$0.40 ∗ 5 =

$2 Question 4.$1.50 ∗ 3 =

$4.50 ### Everyday Mathematics Grade 6 Home Link 1.11 Answers Fractions on a Number Line Question 1. Find three rational numbers between each of the pairs of numbers below. a. $$\frac{1}{3}$$ and $$\frac{5}{6}$$ Answer: 7/6 Explanation : = 1/3+5/6 = 2(1/3)+5/6 = 2/6+5/6 = 7/6 b. $$\frac{1}{3}$$ and $$\frac{1}{5}$$ Answer: 8/15 Explanation : = 1/3+1/5 = LCM of 3,5 is 15 = 5/15+3/15 = 8/15 Question 2 a. Label the points on the number line . Answer : b. Find two fractions in the highlighted section of the number line. ____ Answer : Question 3. a. Fill in the missing labels on the number line. Answer : b. Find one fraction in the highlighted section of the number line. ___ Answer: Question 4. Nadjia created fraction strips to determine that $$\frac{4}{5}$$ is smaller than $$\frac{3}{4}$$. Here is a sketch of her strips and how she lined them up. What mistake did she make? Answer: The values of 4/5 is 0.8 and is always greater than 0.5. but, she included 4/5 in between 1/4 and 2/4 (from 0.25 to 0.5) Hence, 4/5 should be placed after 2/4. Practice Solve. Question 5. $$\frac{3}{4}$$ = Answer: 12 Explanation : Let the number be x = 3/4=x/16 = x=16*3 /4 = x=4*3 therefore, x= 12 Question 6. $$\frac{18}{20}$$ = Answer: 9 Explanation : let the number be x 18/20=x/10 x=18*10 /20 x= 9 therefore value of x is 9 Question 7. = $$\frac{3}{4}$$ Answer: 21/4 Explanation : let the value be x x/7=3/4 x=7*3 /4 x= 21/4 therefore value of x is 21/4 ### Everyday Math Grade 6 Home Link 1.12 Answer Key Zooming In on the Number Line Question 1. Maggie says there are no fractions between $$\frac{1}{4}$$ and $$\frac{1}{3}$$. Provide an example for Maggie and explain why you can always find another example. Answer: Question 2. One way to find fractions in between two fractions is to imagine zooming in on the number line. Insert the missing numbers for the number lines below. Answer: Question 3. Insert the missing numbers on the number line. Answer : List at least three fractions that are in the highlighted section of the number line. Answer: Practice Write an equivalent fraction. Question 4. 4$$\frac{1}{3}$$ = Answer: 13/3 Question 5. 5$$\frac{2}{9}$$ = Answer: 47/9 Question 6. 2$$\frac{5}{6}$$ = Answer: 17/6 ### Everyday Math Grade 6 Home Link 1.13 Answer Key Negative Numbers on a Number Line Question 1. Plot the following points. Answer: Question 2. a. On the vertical number line, label the topmost and bottommost tick marks as -4 and -5. Label the topmost tick mark with the greater value. b. Plot and label the following points as accurately as you can. -4$$\frac{1}{2}$$, -4$$\frac{1}{3}$$, -4$$\frac{2}{3}$$, -4$$\frac{1}{4}$$, -4$$\frac{2}{4}$$, -4$$\frac{3}{4}$$, -4$$\frac{1}{6}$$, -4$$\frac{2}{6}$$, -4$$\frac{3}{6}$$, -4$$\frac{4}{6}$$, -4$$\frac{5}{6}$$ Answer: Question 3. Of the points you plotted on the number line in Problem 2b, which has the greatest value? ___ Which has the least value?__ Answer: -4 1/6 has the greatest value -4 5/6 has the least value Question 4. How can you use a number line to compare values? Answer: As they are negative numbers, the values decreases from left side to right side. Hence, left side values are least when compared to right side. For Problems 5–6, you may draw a number line to help you. Question 5. Write two numbers that fit each description. a. Between -1 and -2 b. Less than -3 Answer: a. b. Question 6. Write the opposite of each number. a. -4 __ Answer : 4 b. 2$$\frac{1}{2}$$ ___ Answer : -2 1/2 c. –$$\frac{3}{4}$$ ___ Answer : 3/4 Practice Write the first three multiples of each number. Question 7. 9 ___ Answer: 9,18,27 Question 8. 7 ___ Answer: 7,14,21 Question 9. 21 __ Answer: 21,42,63 ### Everyday Math Grade 6 Home Link 1.14 Answer Key Plotting Points on a Coordinate Grid Question 1. Plot the following points on the coordinate grid. Label each with its letter. A: School: (8, 0) B : Library: (8, 5) C: Park: (1, -3) D: Grocery store: (- 4, -2) E: My house: (6, 3) F: Post office: (1, 9) G: Bank: (-5, 7) H: Friend’s house: (-4, 3) Answer: Question 2. You walk a straight line from your house to your friend’s house. Plot the point that is halfway between the two houses. Label this point M. Write the ordered pair for point M. __ Answer : Explanation: let A(0,0) be my house and B(8,0) be my friend’s house and the halfway between the two houses will be M(4,0) Question 3. Plot and label two points on the coordinate grid. Place your points in different quadrants. Letter: ___ Location : __ Ordered pair: ___ Letter: __ Location: __ Ordered pair: __ Answer : Letter: A Location : 1st Quadrant Ordered pair: (6,7) Letter: B Location: 3rd Quadrant Ordered pair: (-7,-6) Explanation : Question 4. Explain how to plot the point (- 3, 5). Explanation : Find number -3 on X-axis and draw a perpendicular line to the X-axis from that point. Find number 5 on Y-axis and draw a perpendicular line to the Y-axis from that point. Now, mark the point where both lines meet. It is (-3,5). Practice List all of the factors Question 5. 14 ________ Answer: 1,2,7,14 Question 6. 20 ________ Answer: 1,2,4,5,10,20 Question 7. 17 ________ Answer:1,17 Question 8. 32 ________ Answer: 1,2,4,8,16,32 ## Everyday Math Grade 5 Answers Unit 8 Applications of Measurement, Computation, and Graphing ## Everyday Mathematics 5th Grade Answer Key Unit 8 Applications of Measurement, Computation, and Graphing ### Everyday Mathematics Grade 5 Home Link 8.1 Answers Comparing Yard Sizes Question 1. Some neighbors are deciding where to hold the annual cookout and block party. They would like to have it in the largest backyard. Use the dimensions given to find the area of each neighbor’s backyard in square feet and square yards. Then answer the questions. Answer: Carson: area = 1584 sq ft, Dimensions = 22 x 8 yds, area in sq yds = 176. Flanigan: Dimensions in feet = 42 x 38 ft, Area in sq ft = 1596, Area in sq yds = 177(1/3). Salazar: Area in sq ft = 1520, Dimensions = 6(1/3) x 26(2/3), Area in sq yds = 168(8/9). De Marco: Dimensions in feet = 15 x 106 ft, Area in sq ft = 1590, Area in sq yds = 176(2/3). Explanation: In the above-given question, given that, Families neighbor’s backyard in square feet and square yards. area = l x w. where l = length, and w = width. area = 66 x 24. area = 1584. 1 feet = 0.333 yds. 66 x 0.333 = 21.978. 21.978 = 22. 24 x 8 = 7.992. 7.992 = 8 yds. area = 22 x 8 = 176. Flanigan: Dimensions in feet = 42 x 38 ft, Area in sq ft = 1596, Area in sq yds = 177(1/3). Salazar: Area in sq ft = 1520, Dimensions = 6(1/3) x 26(2/3), Area in sq yds = 168(8/9). De Marco: Dimensions in feet = 15 x 106 ft, Area in sq ft = 1590, Area in sq yds = 176(2/3). Question 2. a. Which family has the largest yard? b. Which family has the smallest yard? Answer: a. Flanigan family has the largest yard. b. Salazar family has the smallest yard. Explanation: In the above-given question, given that, a. Flanigan dimensions = 14 x 12(2/3). area = l x w. where l = 14. w = 38/3. area = 14 x 12(2/3). area = 177(1/3) sq yds. b. Salazar dimensions = 19 x 80. area = l x b. where l = 19. b = 80. area = 1520. Question 3. Look at the number of square feet and the number of square yards in each family’s yard. What number could you multiply the number of square yards by to get the number of square feet? Explain why this makes sense. Answer: 9. Explanation: In the above-given question, given that, There are 9 square feet in 1 square yard. so it makes sense that an area in square feet would be 9 times the area in square yards. Practice Question 4. $$\frac{3}{4}$$ ∗ 7 = ______ Answer: $$\frac{3}{4}$$ ∗ 7 = 21/4. Explanation: In the above-given question, given that, multiply. $$\frac{3}{4}$$ ∗ 7. 3/4 x 7. 7 x 3/4 = 21/4. $$\frac{3}{4}$$ ∗ 7 = 21/4. Question 5. 17 ∗ $$\frac{2}{5}$$ = ________ Answer: 17 ∗ $$\frac{2}{5}$$ = 34/5. Explanation: In the above-given question, given that, multiply. $$\frac{2}{5}$$ ∗ 17. 2/5 x 17. 17 x 2/5 = 34/5. $$\frac{2}{5}$$ ∗ 17 = 34/5. Question 6. 9 ∗ $$\frac{11}{12}$$ = ______ Answer: 9 ∗ $$\frac{11}{12}$$ = 99/12. Explanation: In the above-given question, given that, multiply. $$\frac{11}{12}$$ ∗ 9. 11/12 x 9. 9 x 11/12 = 99/12. $$\frac{11}{12}$$ ∗ 9 = 99/12. Question 7. $$\frac{15}{16}$$ ∗ 5 = _________ Answer: $$\frac{15}{16}$$ ∗ 5 = 75/16. Explanation: In the above-given question, given that, multiply. $$\frac{15}{16}$$ ∗ 5. 15/16 x 5. 5 x 15/16 = 75/16. $$\frac{15}{16}$$ ∗ 5 = 75/16. ### Everyday Math Grade 5 Home Link 8.2 Answer Key Finding Area with the Rectangle Method Use the rectangle method to find the area of each figure. To use the rectangle method: • Draw one or more rectangles around the figure or parts of the figure. • Use the area of the rectangle(s) to determine the area of the original figure. Answer: 1: 5, 2: 8(1/4), 3: 9, 4: 6(3/4). Explanation: In the above-given question, given that, area of the triangle = 1/2 x b x h. where b = base and h = height. 1.area = 1/2 x 5 x 2.5. area = 5. where 2 and 2.5 get canceled. 2.area = 1/2 x 5.5 x 3. area = 5.5 x 3/2. area = 8(1/4). 3.area = 1/2 x 3 x 4. area = 12/2. area = 6. Practice Solve. Show your work on the back of this page. Question 5. 0.14 ∗ 8 = ______ Answer: 0.14 x 8 = 1.12. Explanation: In the above-given question, given that, multiply. 0.14 x 8. 1.12. Question 6. 2.75 ∗ 4.3 = ________ Answer: 2.75 x 4.3 = 11.825. Explanation: In the above-given question, given that, multiply. 2.75 x 4.3. 11.825. ### Everyday Mathematics Grade 5 Home Link 8.3 Answers Solving Remodeling Problems Therese is remodeling her bedroom. A drawing of her bedroom is shown below. Solve Therese’s remodeling problems. Show your work. Question 1. How many square feet of carpet should Therese buy to cover the entire floor of her room? ________ ft2 Answer: The Therese buy to cover the entire floor of her room = 102 sq ft. Explanation: In the above-given question, given that, area of the rectangle 1 = b x h. where b = base, h = height. area = 7(1/2) x 9. area = 63/2. area of the rectangle 2 = b x h. area = 4 x 9. area = 36. area of the rectangle 3 = b x h. area = 6 x 9. area = 54. the total area of all the rectangles = areas of rectangle 1+ 2 + 3. 63 + 36 + 54. 90 + 12 = 102 sq ft. so therese buy to cover the entire floor of her room = 102 sq ft. Question 2. Which air conditioner should Therese buy for her room? The Coolmax: Cools up to 800 cubic feet The Ice Storm: Cools up to 1,500 cubic feet The Polar Extreme: Cools up to 2,500 cubic feet Explain your choice. Answer: The Ice Storm should Therese buy for her room. Explanation: In the above-given question, given that, CoolMax cools up to 800 cubic feet. Ice storm cools up to 1500 cubic feet. Polar Extreme cools up to 2500 cubic feet. so Therese buys medium temperature. Practice Solve. Show your work on the back of this page. Question 3. 4 $$\frac{3}{4}$$ ∗ $$\frac{1}{2}$$ = __________ Answer: 4 $$\frac{3}{4}$$ ∗ $$\frac{1}{2}$$ = 19/8. Explanation: In the above-given question, given that, 4 x 3/4 = 4 x 4. 4 x 4 = 16. 16 + 3/4 x 1/2. 4 x 2 = 8. 19/8. 4 $$\frac{3}{4}$$ ∗ $$\frac{1}{2}$$ = 19/8. Question 4. $$\frac{2}{3}$$ ∗ 10 $$\frac{1}{5}$$ = _________ Answer: $$\frac{2}{3}$$ ∗ 10 $$\frac{1}{5}$$ = 6(12/15). Explanation: In the above-given question, given that, 2/3 x 10(1/5). 10 x 5 = 50. 50 + 1/5 = 51/5. 5 x 3 = 15. 51 x 1/2 = 102/15. ### Everyday Math Grade 5 Home Link 8.4 Answer Key Milk Carton Volume Myles poured milk from a carton into glasses for his family for breakfast on Monday and Tuesday. Each day he poured 200 cubic centimeters of milk for each of his 2 sisters and himself. He also poured 300 cubic centimeters of milk for his mom and the same amount for his dad. The milk carton is a rectangular prism. The length is 15 centimeters and the width is 10 centimeters. Question 1. What is the minimum height of the milk carton if all of the milk for both days came from one carton? Show your work and explain your answer. Answer: The minimum height of the milk carton if all of the milk for both days came from one carton = 16 cms. Explanation: In the above-given question, given that, Myles poured milk from a carton into glasses for his family for breakfast on Monday and Tuesday. Each day he poured 200 cubic centimeters of milk for each of his 2 sisters and himself. He also poured 300 cubic centimeters of milk for his mom and the same amount for his dad. the milk carton is a rectangular prism. The length is 15 centimeters and the width is 10 cms. 8 x 2 = 16. so the minimum height of the milk carton if all of the milk for both days came from one carton = 16 cms. Practice Solve. Show your work on the back of this page. Question 2. 36.4 ÷ 1.3 = _______ Answer: 36.4 ÷ 1.3 = 28. Explanation: In the above-given question, given that, divide. 36.4 ÷ 1.3. 28. 36.4 ÷ 1.3 = 28. Question 3. 33.66 ÷ 0.55 = ________ Answer: 33.66 ÷ 0.55 = 61.2 Explanation: In the above-given question, given that, divide. 33.66 ÷ 0.55. 61.2. 33.66 ÷ 0.55 = 61.2. ### Everyday Mathematics Grade 5 Home Link 8.5 Answers Spending$500

Y ou are planning a camping trip for yourself and two friends. After saving money for a few months, you and your friends have $500 to spend on the trip. Question 1. Use the prices above to plan how you will spend$500. Round each unit cost to find approximate total costs. Write a number sentence in the last column to show how you estimated. Spend as clos e to $500 as yo u can. Answer: Campsite in 1 night =$522.
6 – person tent (no rain protection) = $654. 8 – person tent (with rain protection) =$729.
Meals (1 day) = $522.04. Single kayak (2-hour rental) =$529.99.
Mountain bike rental (1 day) = $540.59. Explanation: In the above-given question, given that, Campsite in 1 night =$22.
6 – person tent (no rain protection) = $154.99. 8 – person tent (with rain protection) =$229.99.
Meals (1 day) = $22.04. Single kayak (2-hour rental) =$29.99.
Mountain bike rental (1 day) = $40.59. Question 2. On the back of this page, explain one decision you made as you planned. Answer: Campsite in 1 night =$522.
6 – person tent (no rain protection) = $654. 8 – person tent (with rain protection) =$729.
Meals (1 day) = $522.04. Single kayak (2-hour rental) =$529.99.
Mountain bike rental (1 day) = $540.59. Explanation: In the above-given question, given that, Campsite in 1 night =$22.
6 – person tent (no rain protection) = $154.99. 8 – person tent (with rain protection) =$229.99.
Meals (1 day) = $22.04. Single kayak (2-hour rental) =$29.99.
Mountain bike rental (1 day) = $40.59. Practice Question 3. 6 $$\frac{2}{3}$$ ∗ 4 $$\frac{7}{8}$$ = ________ Answer: 6 $$\frac{2}{3}$$ ∗ 4 $$\frac{7}{8}$$ =780/24. Explanation: In the above-given question, given that, 6 $$\frac{2}{3}$$ ∗ 4 $$\frac{7}{8}$$. 6 x 3 = 18. 18 + 2/3 = 20/3. 4 x 8 = 32. 32 + 7/8 = 39/8. 20/3 x 39/8 = 780/24. Question 4. 10$$\frac{5}{6}$$ ∗ 5 $$\frac{3}{4}$$ = ________ Answer: 10$$\frac{5}{6}$$ ∗ 5 $$\frac{3}{4}$$ = 1495/24. Explanation: In the above-given question, given that, 10 $$\frac{5}{6}$$ ∗ 5 $$\frac{3}{4}$$. 10 x 6 = 60. 60 + 5/6 = 65/6. 5 x 4 = 20. 20 + 3/4 = 23/4. 65/6 x 23/4 = 1495/24. ### Everyday Math Grade 5 Home Link 8.6 Answer Key Calculating Earnings Solve. Show your work. Write a number model to show how you solved. Question 1. Jeremiah mows his neighbor’s lawn to earn money. His neighbor pays him$50 per month. It takes Jeremiah 1 hour and 15 minutes to mow the lawn once. He mows the lawn 4 times per month.
a. How many hours does Jeremiah spend mowing the lawn each month?
Number model: __________

The number of hours does Jeremiah spends mowing the lawn each month = 5 hours.

Explanation:
In the above-given question,
given that,
Jeremiah mows his neighbor’s lawn to earn money.
His neighbor pays him $50 per month. It takes Jeremiah 1 hour and 15 minutes to mow the lawn once. He mows the lawn 4 times per month. 1 + 1 + 1 + 1 = 4. 15 + 15 + 15 + 15 = 60. 4 hours 60 minutes = 5 hours. b. How much money does Jeremiah earn per hour? Number model: __________ Answer: The money does Jeremiah earns per hour =$10.

Explanation:
In the above-given question,
given that,
Jeremiah mows his neighbor’s lawn to earn money.
His neighbor pays him $50 per month. It takes Jeremiah 1 hour and 15 minutes to mow the lawn once. He mows the lawn 4 times per month.$10 + $10 +$10 + $10 =$40.
so the money does Jeremiah earns per hour = $10. c. How long would it take Jeremiah to earn$1,000? Give your answer in both months and hours.
Number model(s): __________
Jeremiah would have to work for __________ months, or __________ hours.

The number of months would it take Jeremiah to earn $1,000 = 20 months. Explanation: In the above-given question, given that, Jeremiah mows his neighbor’s lawn to earn money. His neighbor pays him$50 per month.
It takes Jeremiah 1 hour and 15 minutes to mow the lawn once.
He mows the lawn 4 times per month.
for 1 month = $100. 100 x 100 = 1000. so the number of months would it take Jeremiah to earn$1000 = 20 months.
Practice
Solve using common denominators. Show your work.
Question 2.
8 ÷ $$\frac{1}{5}$$ = ?
8 ÷ $$\frac{1}{5}$$ = ________

8 ÷ $$\frac{1}{5}$$ = 40.

Explanation:
In the above-given question,
given that,
8 ÷ $$\frac{1}{5}$$.
8 ÷ 1/5.
8 x 5 = 40.
8 ÷ $$\frac{1}{5}$$ = 40.

Question 3.
$$\frac{1}{4}$$ ÷ 12 = ?
$$\frac{1}{4}$$ ÷ 12 = ________

$$\frac{1}{4}$$ ÷ 12 =1/48.

Explanation:
In the above-given question,
given that,
$$\frac{1}{4}$$ ÷ 12.
12 x 4 = 48.
1 x 1/48 = 1/48.

Paying Off Debts

Solve Problems 1–3. Write a number model to show how you solved.
Question 1.
Kendall lent Kel $40 to buy a game. Kel is earning money by washing cars. He charges$7 per car. How many cars will Kel need to wash in order to pay Kendall back?
Number model: ___________

The number of cars will Kel need to wash in order to pay Kendall back = 6 cars.

Explanation:
In the above-given question,
given that,
Kendall lent Kel $40 to buy a game. Kel is earning money by washing cars. He charges$7 per car.
6 x $7 = 42. so the The number of cars will Kel need to wash in order to pay Kendall back = 6 cars. Question 2. Josie borrowed$65 from her mom for a class trip to Washington, D.C. When she returns from the trip, Josie will start working for her neighbors. She will make $8.50 each time she walks their dogs. a. How many times will Josie have to walk the dogs in order to repay her debt? Number model: ______________ Answer: The number of times will Josie have to walk the dogs in order to repay her debt = 8 times. Explanation: In the above-given question, given that, Josie borrowed$65 from her mom for a class trip to Washington, D.C.
When she returns from the trip Josie will start working for her neighbors.
She will make $8.50 each time she walks their dogs.$8.50 x $8.50 =$65.
8 x 8 = 64.
$50 +$50 = $100. 64 + 1 = 65. so the number of times will Josie have to walk the dogs in order to repay her debt = 8 times. b. If Josie walks 3 miles each time she takes the dogs out, how many miles will she have walked by the time she repays her debt? Number model: ______________ Answer: The number of miles she walked by the time she repays her debt = 24 miles. Explanation: In the above-given question, given that, If Josie walks 3 miles each time she takes the dogs out. 3 x 8 = 24 miles. so the number of miles she walked by the time she repays her debt = 24 miles. Question 3. Langdon earns$23 an hour at a law office. He works about 55 hours per week.
a. If there are about 4 weeks in one month, how much money does Langdon earn each month?
Number model: ______________

The money does Langdon earn a month = $5060 Explanation: In the above-given question, given that, Langdon earns$23 an hour at a law office.
He works about 55 hours per week.
$23 x 55 = 1265. 1265 x 4 = 5060. so the money does Langdon earn a month =$5060.

b. Langdon took out a $5,000 loan to help pay for college. Would one month’s earnings pay off his loan? Answer: Yes. Explanation: In the above-given question, given that, Langdon took out a$5,000 loan to help pay for college.
the money does Langdon earns a month = $5060. so the money he earns for 1 month is enough to pay the loan. Practice Question 4. 4.53 ∗ 103 = ________ Answer: 4.53 ∗ 103 = 4530. Explanation: In the above-given question, given that, multiply. 4.53 x 10 x 10 x 10. 10 x 10 x 10 = 1000. 4.53 x 1000 = 4530. Question 5. 62.8 ÷ 104 = ________ Answer: 62.8 ÷ 104 = 0.00628. Explanation: In the above-given question, given that, divide. 6.28 ÷ 104. 6.28 x 10 x 10 x 10 x 10. 6.28 x 10000. 0.00628. Question 6. 29.1 ∗ 106 = ________ Answer: 29.1 ∗ 106 = 29,100.000. Explanation: In the above-given question, given that, multiply. 29.1 x 10 x 10 x 10 x 10 x 10 x 10. 29.1 x 1000000. 29,100.000. Question 7. 7,354.2 ÷ 102 = __________ Answer: 7,354.2 ÷ 102 = 73.542. Explanation: In the above-given question, given that, divide. 7354.2 ÷ 10 x 10. 7354.2 ÷ 100. 73.542. ### Everyday Math Grade 5 Home Link 8.8 Answer Key Hiking a New Zealand Trail Use the information from journal page 300 to fill in the blank. Length of one footstep: About ________ feet A group of hikers in New Zealand is walking to a campsite. They will hike from Wellington to Ruapehu, a distance of about 200 miles. Then they will follow a trail for another 12 miles to their campsite. (The campsite is not shown on the map.) Use your class information about step length to solve the problems. Reminder: 1 mile = 5,280 feet Question 1. About how many total miles is it from Wellington to the campsite? About ________ miles Answer: The number of total miles is it from wellington to the campsite = 212 miles. Explanation: In the above-given question, given that, They will hike from Wellington to Ruapehu, a distance of about 200 miles. 1 inch represents = 400 miles. 200 + 12 = 212. so the number of total miles is it from wellington to the campsite = 212 miles. Question 2. About how many steps would a hiker take to walk from Wellington to the campsite? Show your work below. About ________ miles Answer: The number of steps would a hiker take to walk from wellington to the campsite = 11,19,360 feet. Explanation: In the above-given question, given that, They will hike from Wellington to Ruapehu, a distance of about 200 miles. 1 inch represents = 400 miles. 200 + 12 = 212. 1 mile = 5280 feet. 212 x 5280 = 11,19,360 feet. so number of steps would a hiker take to walk from wellington to the campsite = 11,19,360 feet. Practice Question 3. 2 $$\frac{2}{3}$$ ∗ 4 $$\frac{1}{5}$$ = ? 2 $$\frac{2}{3}$$ ∗ 4 $$\frac{1}{5}$$ = __________ Answer: 2 $$\frac{2}{3}$$ ∗ 4 $$\frac{1}{5}$$ =168/15. Explanation: In the above-given question, given that, multiply. 2 x 3 = 6. 6 + 2/3 = 8/3. 4 x 5 = 20. 20 + 1/5 = 21/5. 5 x 3 = 15. 8/3 x 21/5 = 168/15. Question 4. 9 $$\frac{1}{2}$$ ∗ 3 $$\frac{5}{6}$$ = ? 2 $$\frac{2}{3}$$ ∗ 4 $$\frac{1}{5}$$ = ________ Answer: 9 $$\frac{1}{2}$$ ∗ 3 $$\frac{5}{6}$$ = 437/12. Explanation: In the above-given question, given that, multiply. 9 x 2 = 18. 18 + 1/2 = 19/2. 3 x 6 = 18. 18 + 5/6 = 23/6. 6 x 2 = 12. 19/2 x 23/6 = 437/12. ### Everyday Mathematics Grade 5 Home Link 8.9 Answers How Many Blueberries? Question 1. Fill in the blanks. 1 pint = __________ cups 1 quart = __________ pints Answer: 1 pint = 2 cups. 1 quart = 2 pints. Explanation: In the above-given question, given that, 1 pint = 2 cups. 1 quart = 2 pints. Question 2. About 75 blueberries fill a 1-cup container. Use this information and your answers to Problem 1 to help you complete the table. Hint: If 75 blueberries are in 1 cup, how can you find how many are in 2 cups? Answer: The number of blueberries = 75. the number of blueberries in 1 pint = 150. the number of blueberries in 1 quart = 300. Explanation: In the above-given question, given that, About 75 blueberries fill a 1-cup container. 1 pint = 2 cups. 1 quart = 2 pints. 75 = 75. 75 x 2 = 150. 150 x 2 = 300. The number of blueberries = 75. the number of blueberries in 1 pint = 150. the number of blueberries in 1 quart = 300. Question 3. One blueberry plant can produce 4 quarts of blueberries in 1 year. How many blueberries does one plant produce in 1 year? Explain how you know. Answer: The number of blueberries does one plant can produce in 1 year = 1200. Explanation: In the above-given question, given that, One blueberry plant can produce 4 quarts of blueberries in 1 year. 300 x 4 = 1200. so the number of blueberries does one plant can produce in 1 year = 1200. Question 4. A farmer can fit about 1,100 blueberry plants in a 1-acre field. About how many blueberries would a well-tended blueberry field produce in 1 year? About __________ blueberries Answer: The number of blueberries would a well-tended blueberry field produces in 1 year = 1320000 blueberries. Explanation: In the above-given question, given that, A farmer can fit about 1,100 blueberry plants in a 1-acre field. 1100 x 1200. 1320,000. so the number of blueberries would a well-tended blueberry field produces in 1 year = 1320000 blueberries. Question 5. With proper maintenance, a blueberry plant can live for 20 years. a. Suppose you have one blueberry plant in your backyard. About how many blueberries would it produce in its lifetime? About __________ blueberries Answer: The number of blueberries would it produce in its lifetime = 24000. Explanation: In the above-given question, given that, a blueberry plant can live for 20 years. 12 x 20 = 24000. so the number of blueberries would it produce in its lifetime = 24000. b. Suppose a farmer had a 1-acre blueberry field. About how many blueberries would the field produce in the plants’ lifetime? About __________ blueberries Answer: The number of blueberries would the field produces in the plant’s lifetime = 26,400,000. Explanation: In the above-given question, given that, suppose a farmer had a 1-acre blueberry field. 300 x 1200 = 26,400,000. so the number of blueberries would the field produces in the plant’s lifetime = 26,400,000. Practice Estimate. Then multiply. Show your work on the back of this page. Question 6. 23.3 ∗ 1.28 = _______ Estimate: _________ Answer: 23.3 x 1.28 = 29.824. Explanation: In the above-given question, given that, multiply. 23.3 x 1.28. 29.824. 23.3 x 1.28 = 29.824. Question 7. 326.2 ∗ 0.52 = __________ Estimate: __________ Answer: 326.2 x 0.52 = 169.624. Explanation: In the above-given question, given that, multiply. 326.2 x 0.52. 169.624. 326.2 x 0.52 = 169.624. ### Everyday Math Grade 5 Home Link 8.10 Answer Key Cardiac Output Today you learned that cardiac output is the amount of blood a heart pumps in 1 minute. You can find your cardiac output using your heart rate and the amount of blood your heart pumps with each heartbeat. Cardiac output = heart rate ∗ amount of blood pumped with each heartbeat Question 1. The typical resting heart rate for a healthy adult is about 72 beats per minute. A healthy adult heart pumps about 2.4 fluid ounces of blood per heartbeat. a. What is the cardiac output of a healthy adult? __________ beats per minute ∗ __________ fluid ounces of blood per heartbeat = __________ fluid ounces of blood per minute Answer: The number of beats per minute = 72. A healthy adult heart pumps about 2.4 fluid ounces of blood per heartbeat = 2.4. The number of fluid ounces of blood per minute = 172.8. Explanation: In the above-given question, given that, The typical resting heart rate for a healthy adult is about 72 beats per minute. A healthy adult heart pumps about 2.4 fluid ounces of blood per heartbeat. 72 x 2.4 = 172.8. so the number of fluid ounces of blood per minute = 172.8. b. How many fluid ounces of blood will a healthy adult’s heart pump in one hour? About ________ fluid ounces Answer: The healthy adult’s heart pump in one hour = 10.368. Explanation: In the above-given question, given that, The typical resting heart rate for a healthy adult is about 72 beats per minute. A healthy adult heart pumps about 2.4 fluid ounces of blood per heartbeat. 72 x 2.4 = 172.8. so the number of fluid ounces of blood per minute = 172.8. 1 hour = 60 minutes. 172.8 x 60 = 10.368. so the healthy adult’s heart pump in one hour = 10.368. c. How many cups of blood is that? About ________ cups Answer: The number of cups = 1296. Explanation: In the above-given question, given that, 1 pint = 2 cups. 1 quart = 2 pints. 172.8 x 2 = 1296. so the number of cups = 1296. Question 2. A newborn baby’s heart beats about 135 times per minute, but it pumps only about 0.25 fluid ounce of blood per heartbeat. a. What is the cardiac output of a newborn baby? __________ beats per minute ∗ __________ fluid ounces of blood per heartbeat = __________ fluid ounces of blood per minute Answer: The number of fluid ounces of blood per minute = 33.75. Explanation: In the above-given question, given that, A newborn baby’s heart beats about 135 times per minute, but it pumps only about 0.25 fluid ounce of blood per heartbeat. 135 x 0.25 = 33.75. so The number of fluid ounces of blood per minute = 33.75. b. How many fluid ounces of blood will a newborn baby’s heart pump in one hour? About __________ fluid ounces Answer: The newborn baby’s heart pump in one hour = 2.025. Explanation: In the above-given question, given that, A newborn baby’s heart beats about 135 times per minute, but it pumps only about 0.25 fluid ounces of blood per heartbeat. 135 x 0.25 = 33.75. so The number of fluid ounces of blood per minute = 33.75. 1 hour = 60 minutes. 33.75 x 60 = 2.025. c. How many cups of blood is that? About __________ cups Answer: The number of cups of blood is = 253. Explanation: In the above-given question, given that, A newborn baby’s heart beats about 135 times per minute, but it pumps only about 0.25 fluid ounces of blood per heartbeat. 135 x 0.25 = 33.75. so The number of fluid ounces of blood per minute = 33.75. 1 hour = 60 minutes. 33.75 x 60 = 2.025. 1 pint = 2 cups. 1 quart = 2 pints. so the number of cups of blood = 253. Practice Estimate. Then divide. Show your work. Question 3. 361.2 ÷ 14 = ? Estimate: _________ 361.2 ÷ 14 = _________ Answer: 361.2 ÷ 14 = 25.8. Explanation: In the above-given question, given that, divide. 361.2 ÷ 14. 25.8. Question 4. 7.28 ÷ 0.8 = ? Estimate: _________ 7.28 ÷ 0.8 = ________ Answer: 7.28 ÷ 0.8 = 9.1. Explanation: In the above-given question, given that, divide. 7.28 ÷ 0.8. 9.1. ### Everyday Mathematics Grade 5 Home Link 8.11 Answers Latitude and Temperature Latitude is a measure of how far north or south a location is from the equator. This table shows the approximate latitude and average high temperature in April for five cities. Question 1. Write the data as ordered pairs. The latitudes are the x-coordinates. The average high temperatures for April are the y-coordinates. Graph the points and use line segments to connect them. Answer: The ordered pairs are (1,89), (17, 87), (30,83), (52, 53), (60, 43). Explanation: In the above-given question, given that, Latitude is a measure of how far north or south a location is from the equator. The latitudes are the x-coordinates. The average high temperatures for April are the y-coordinates. the city of Singapore = 1 and 89. Acapulco and Mexico = 17 and 87. Cairo and Egypt = 30 and 83. Amsterdam and Netherlands = 52 and 53. so they can be written in ordered pairs are (1,89), (17, 87), (30,83), (52, 53), (60, 43). Question 2. The city of Nassau, Bahamas, is located at latitude 25°N. Based on your graph, what would you predict for the average high temperature in Nassau in April? Answer: About 84°F. Explanation: In the above-given question, given that, The city of Nassau, Bahamas, is located at latitude 25°N. by seeing the graph we can notice the temperature of Nassau. so the average temperature in Nassau in April is 84°F. Question 3. Does latitude seem to have an effect on average high temperature? Explain your answer. Answer: Yes. Explanation: In the above-given question, given that, As the latitude increases, the average temperature seems to go down. I can tell because as you move to the right on the graph, the point gets lower. yes, the latitude seems to have an effect on average high temperature. ### Everyday Math Grade 5 Home Link 8.12 Answer Key The Boiling Point The boiling point of water is the temperature at which it boils. The graphs show how altitude and salt affect the boiling point of water. (Altitude is the measure of how high a location is.) Study the graphs. Then use the m to answer the questions. Question 1. What would you expect the boiling point of water to be at an altitude of 2,500 feet above sea level? About _________ Answer: The boiling point of water to be at an altitude of 2500 feet above sea level = 207°F. Explanation: In the above-given graph, given that, by seeing the above graph we can notice that the boiling point of water to be at an altitude of 2000 feet above sea level = 208. so the boiling point of water to be at an altitude of 2500 feet above sea level = 207°F. Question 2. What would you expect the boiling point of a quart of water to be if it contained $$\frac{1}{2}$$ tablespoon of salt? About _________ Answer: The boiling point of a quart of water to be if it contained 1/2 tablespoon of salt = 214°F. Explanation: In the above-given graph, given that, by seeing the above graph we can notice that the boiling point of water to be at an altitude of salt = 214. so the boiling point of a quart of water to be if it contained 1/2 tablespoon of salt = 214°F. Question 3. How does altitude affect the boiling point of water? Answer: The altitude affects the boiling point of water decreases. Explanation: In the above-given graph, given that, On x-axis altitude. on y-axis boiling point. so the altitude affects the boiling point of water decreases. Question 4. How does salt affect the boiling point of water ? Answer: The salt affects the boiling point of water increases. Explanation: In the above-given graph, given that, On x-axis amount of salt. on y-axis boiling point. so the salt affects the boiling point of water increases. Practice Divide using the common denominator method. Show your work on the back of this page. Question 5. $$\frac{1}{4}$$ ÷ 6 = ________ Answer: 6 ÷ $$\frac{1}{4}$$ = 1/24. Explanation: In the above-given question, given that, 6 ÷ $$\frac{1}{4}$$. 6 ÷ 1/4. 6 x 4 = 24. 6 ÷ $$\frac{1}{4}$$ = 1/24. Question 6. 5 ÷ $$\frac{1}{10}$$= ________ Answer: 5 ÷ $$\frac{1}{10}$$ = 50. Explanation: In the above-given question, given that, 5 ÷ $$\frac{1}{10}$$. 5 ÷ 1/10. 10 x 5 = 50. 5 ÷ $$\frac{1}{10}$$ = 50. ## Everyday Math Grade 5 Answers Unit 7 Multiplication of Mixed Numbers; Geometry; Graphs ## Everyday Mathematics 5th Grade Answer Key Unit 7 Multiplication of Mixed Numbers; Geometry; Graphs ### Everyday Mathematics Grade 5 Home Link 7.1 Answers Mixed-Number Multiplication For Problems 1 and 2: • Use the rectangle to make an area model. Label the sides. The model in Problem 1 has been started for you. • Find and list the partial products. Label the partial products in the area model. • Add the partial products to find your answer. You may need to rename fractions with a common denominator . Question 1. 4$$\frac{3}{8}$$ ∗ 5 = ? Partial products: 4$$\frac{3}{8}$$ ∗ 5 = _________ Answer: 20 x 15/8. Explanation: In the above-given question, given that, the length of the large rectangle = 4. the length of the small rectangle = 3/8. the width of the larger rectangle = 5. the width of the smaller rectangle = 5. area = l x w. where l = length, and w = width. area = 3/8 x 5. area = 15/8. area = 5 x 4. area = 20. area = 20(15/8). Question 2. 2$$\frac{3}{5}$$ ∗ 3$$\frac{1}{3}$$ = ? Partial products: 2$$\frac{3}{5}$$ ∗ 3$$\frac{1}{3}$$ = _________ Area Model: Answer: 8(10/15). Explanation: In the above-given question, given that, the length of the large rectangle = 4. the length of the small rectangle = 5/5. the width of the larger rectangle = 2. the width of the smaller rectangle =2/3 . area = l x w. where l = length, and w = width. area = 4 x 2. area = 8. area = 5/5 x 2/3. area = 10/15. 8(10/15). Question 3. Write a number story that matches Problem 1. Answer: 20 x 15/8. Explanation: In the above-given question, given that, the length of the large rectangle = 4. the length of the small rectangle = 3/8. the width of the larger rectangle = 5. the width of the smaller rectangle = 5. area = l x w. where l = length, and w = width. area = 3/8 x 5. area = 15/8. area = 5 x 4. area = 20. Practice Solve. Question 4. $$\frac{2}{3}$$ + $$\frac{5}{8}$$ = _________ Answer: 2/3 + 5/8 = 31/24. Explanation: In the above-given question, given that, $$\frac{2}{3}$$ + $$\frac{5}{8}$$. 8 x 3 = 24. 24 + 2 = 26. 26 + 5 = 31. 2/3 + 5/8 = 31/24. Question 5. $$\frac{1}{16}$$ + $$\frac{3}{4}$$ = ___________ Answer: 1/16 + 3/4 = 13/16. Explanation: In the above-given question, given that, $$\frac{1}{16}$$ + $$\frac{3}{4}$$. 4 x 4 = 16. 4 x 3 = 12. 12 + 1 = 13. 1/16 + 3/4 = 13/16. ### Everyday Math Grade 5 Home Link 7.2 Answer Key More Mixed-Number Multiplication Solve Problems 1 and 2 using the method in the example below. Show your work. Example: 2$$\frac{1}{5}$$ ∗ 1$$\frac{3}{4}$$ • Rename any mixed or whole numbers as fractions: 2$$\frac{1}{5}$$ = $$\frac{11}{5}$$; 1$$\frac{3}{4}$$ = $$\frac{7}{4}$$ • Rewrite the problem using the fractions as factors: $$\frac{11}{5}$$ * $$\frac{7}{4}$$ • Multiply using a fraction multiplication algorithm: $$\frac{(11 * 7)}{(5 * 4)}=\frac{77}{20}$$, or 3$$\frac{17}{20}$$ Question 1. 1$$\frac{3}{5}$$ ∗ 6 = ? 1$$\frac{3}{5}$$ ∗ 6 = __________ Answer: 48/5. Explanation: In the above-given question, given that, 1$$\frac{3}{5}$$ ∗ 6. 1$$\frac{3}{5}$$ = $$\frac{8}{5}$$. 8/5 x 6. 6 x 8 = 48. 48/5. Question 2. 4$$\frac{1}{2}$$ ∗ 1$$\frac{5}{6}$$ = ? 4$$\frac{1}{2}$$ ∗ 1$$\frac{5}{6}$$ = __________ Answer: 99/12. Explanation: In the above-given question, given that, 4$$\frac{1}{2}$$ ∗ 1$$\frac{5}{6}$$. $$\frac{9}{2}$$ ∗ $$\frac{11}{6}$$. latex]\frac{(11 * 9)}{(6 * 2)}=\frac{99}{12}[/latex] 99/12. Solve Problems 3 and 4 using the method of your choice. Question 3. What is the area of a table that is 1$$\frac{1}{4}$$ m long and 2$$\frac{1}{3}$$ m wide? Write a number model with a letter for the unknown. Then solve. Show your work. Number model: _________________ The area of the table is _________________ m2. Answer: The area of the table is 35/12 sq m. Explanation: In the above-given question, given that, 1$$\frac{1}{4}$$ ∗ 2$$\frac{1}{3}$$. $$\frac{5}{4}$$ ∗ $$\frac{7}{3}$$. latex]\frac{(5 * 7)}{(6 * 2)}=\frac{35}{12}[/latex] 5 x 7 = 35. 4 x 3 = 12. 35/12. so the area of the table is 35/12 sq m. Question 4. Write a number story that can be solved by multiplying 2$$\frac{3}{4}$$ and $$\frac{1}{2}$$. Then solve the problem. Show your work on the back of this page. Number story: Answer: 11/8. Explanation: In the above-given question, given that, 2$$\frac{3}{4}$$ ∗ $$\frac{1}{2}$$. $$\frac{11}{4}$$ ∗ $$\frac{1}{2}$$. latex]\frac{(11 * 1)}{(4 * 2)}=\frac{11}{8}[/latex] Practice Question 5. $$\frac{11}{12}$$ – $$\frac{3}{4}$$ = ________ Answer: $$\frac{11}{12}$$ – $$\frac{3}{4}$$ = 2/12. Explanation: In the above-given question, given that, $$\frac{11}{12}$$ – $$\frac{3}{4}$$. 14 – 2/12. 2/12 = 1/6. Question 6. $$\frac{7}{8}$$ – $$\frac{1}{6}$$ = _________ Answer: $$\frac{7}{8}$$ – $$\frac{1}{6}$$ = 17/24. Explanation: In the above-given question, given that, $$\frac{7}{8}$$ – $$\frac{1}{6}$$. lcm of 6 and 8 = 24. 7 x 3 = 21. 1 x 4 = 4. 21 – 4 = 17. 17/24. ### Everyday Mathematics Grade 5 Home Link 7.3 Answers Solving More Area Problems Solve. Sho w your work. Write a number model to summarize each solution. Question 1. The cover of Martina’s book measures 7$$\frac{1}{4}$$ inches by 9 inches. What is the area of the book cover? Area: ____________ Number Model: ____________ Answer: The area of the book cover = 65(1/4) sq in. Explanation: In the above-given question, given that, The cover of Martina’s book measures 7(1/4) inches by 9 inches. 7(1/4) = 7 x 4 = 28. 28 + 1 = 29. 29 x 9 = 261. 261/4. so the area of the book cover = 261/4 sq in. Question 2. The hallway floor in Ryan’s school is covered with square tiles that are $$\frac{1}{2}$$ foot by $$\frac{1}{2}$$ foot. Ryan counted and found that the hallway is 15 tiles wide and 60 tiles long. a. How many tiles cover the hallway floor? b. What is the area of the hallway floor? Area: ____________ Number Model: ____________ Answer: a.The number of tiles cover the hallway floor = 900 tiles. b. The area of the hallway floor = 225 sq ft. Explanation: In the above-given question, given that, The hallway floor in Ryan’s school is covered with square tiles that are 1/2 foot by 1/2. Ryan counted and found that the hallway is 15 tiles wide and 60 tiles long. 60 x 15. 60 x 15 = 900. so no of tiles = 900 tiles. area = 15 x 15. area = 225 sq ft. Question 3. An artist made a stained-glass window that is 3$$\frac{1}{2}$$ feet by 2 $$\frac{3}{4}$$ feet. a. What is the area of the window? Area: ____________ Number Model: ____________ Answer: The area of the window = 77/8 sq ft. Explanation: In the above-given question, given that, An artist made a stained-glass window that is 3(1/2) feet by 2(3/4). 3 x 2 = 6. 6 + 1/2 = 7/2. 4 x 2 = 8. 8 + 3/4 = 11/4. 7/2 x 11/4. 11 x 7 = 77. 4 x 2 = 8. 77/8. so the area of the window = 77/8 sq ft. b. The artist’s design used squares of colored glass that measure $$\frac{1}{4}$$ foot by $$\frac{1}{4}$$ foot. How many colored squares did the artist use? Area: ____________ Number Model: ____________ Answer: The number of colored squares did the artist use = 154 tiles. Explanation: In the above-given question, given that, The artist’s design used squares of colored glass that measure 1/4 foot by 1/4. 4 x 4 = 16. 16 x 9 = 144. 144 + 10 = 154. so the number of colored squares did the artist use = 154 tiles. Practice Question 4. 3$$\frac{1}{8}$$ + 4$$\frac{2}{3}$$ = _________ Answer: 3$$\frac{1}{8}$$ + 4$$\frac{2}{3}$$ = 187. Explanation: In the above-given question, given that, 3$$\frac{1}{8}$$ + 4$$\frac{2}{3}$$. 3(1/8) + 4(2/3). 3 x 8 = 24. 24 + 1/8 = 25/8. 4 x 3 = 12. 12 + 2/3 = 14/3. lcm of 8 and 3 = 24. 25 x 3 = 75. 14 x 8 = 112. 112 + 75 = 187. Question 5. 2$$\frac{1}{6}$$ + 1$$\frac{5}{8}$$ = __________ Answer: 2$$\frac{1}{6}$$ + 1$$\frac{5}{8}$$ = 62/18. Explanation: In the above-given question, given that, 2$$\frac{1}{6}$$ + 1$$\frac{5}{8}$$. 2(1/6) + 1(5/8). 6 x 2 = 12. 12 + 1/6 = 13/6. 8 x 1 = 8. 8 + 5/8 = 13/8. lcm of 6 and 8 = 18. 13 + 3 = 16. 16/18 + 46/18 = 62/18. ### Everyday Math Grade 5 Home Link 7.4 Answer Key Solving Fraction Division Problems Using Common Denominators to Divide 210 One way to divide fractions is to use common denominators. This method can be used to divide whole numbers by fractions and fractions by whole numbers. Step 1 Rename the dividend and divisor as fractions with a common denominator Step 2 Divide the numerators Example: $$\frac{1}{3}$$ ÷ 4 = $$\frac{1}{3}$$ ÷ $$\frac{12}{3}$$ 1 ÷ 12 = $$\frac{1}{12}$$ Solve Problems 1–4. Show your work. Use multiplication to check your answer. Question 1. 5 ÷ $$\frac{1}{3}$$= ? Check: _______ Answer: $$\frac{1}{15}$$ Explanation: In the above-given question, given that, 5 ÷ $$\frac{1}{3}$$. $$\frac{1}{3}$$ ÷ $$\frac{15}{3}$$. 1 ÷ 15. $$\frac{1}{15}$$. Question 2. 4 ÷ $$\frac{1}{8}$$ = ? Check: _______ Answer: $$\frac{1}{32}$$. Explanation: In the above-given question, given that, 4 ÷ $$\frac{1}{8}$$. $$\frac{1}{8}$$ ÷ $$\frac{32}{8}$$. 1 ÷ 32. $$\frac{1}{32}$$. Question 3. $$\frac{1}{6}$$ 4 = ? Check: _______ Answer: $$\frac{1}{24}$$. Explanation: In the above-given question, given that, 4 ÷ $$\frac{1}{6}$$. $$\frac{1}{6}$$ ÷ $$\frac{24}{6}$$. 1 ÷ 24. $$\frac{1}{24}$$. Question 4. $$\frac{1}{5}$$ 6 = ? Check: _________ Answer: $$\frac{1}{30}$$. Explanation: In the above-given question, given that, 6 ÷ $$\frac{1}{5}$$. $$\frac{1}{5}$$ ÷ $$\frac{30}{6}$$. 1 ÷ 30. $$\frac{1}{30}$$. Question 5. Write a number story to match Problem 2. Answer: $$\frac{1}{32}$$. Explanation: In the above-given question, given that, 4 ÷ $$\frac{1}{8}$$. $$\frac{1}{8}$$ ÷ $$\frac{32}{8}$$. 1 ÷ 32. $$\frac{1}{32}$$. Practice Question 6. 4$$\frac{1}{2}$$ – 1$$\frac{3}{4}$$ = _________ Answer: 4$$\frac{1}{2}$$ – 1$$\frac{3}{4}$$ = 11/4. Explanation: In the above-given question, given that, 4$$\frac{1}{2}$$ – 1$$\frac{3}{4}$$. 4(1/2) – 1(3/4). 4 x 2 = 8. 8 + 1/2 = 9/2. 1 x 4 = 4. 4 + 3/4 = 7/4. lcm of 2 and 4 is 4. 9 x 2 = 18. 18 – 7 = 11/4. Question 7. 2$$\frac{7}{8}$$ – 1$$\frac{1}{3}$$ = __________ Answer: 2$$\frac{7}{8}$$ – 1$$\frac{1}{3}$$ = 37/24. Explanation: In the above-given question, given that, 2$$\frac{7}{8}$$ – 1$$\frac{1}{3}$$. 2(7/8) – 1(1/3). 8 x 2 = 16. 16 + 7/8 = 23/8. 1 x 3 = 3. 3 + 1/3 = 4/3. lcm of 8 and 3 is 24. 23 + 3/8 = 26/8. 4 + 8 = 12/8. 26 + 11 = 37/24. ### Everyday Mathematics Grade 5 Home Link 7.5 Answers Using a Hierarchy A pentagon is a shape with 5 sides. The shape below is a pentagon. An equilateral pentagon is a pentagon with 5 sides that are all the same length. The shape below is an equilateral pentagon. Consider the pentagon hierarchy below. Use it to answer the questions. Question 1. Answer Parts a–c to classify this shape on the hierarchy. a. Can this shape go in the top category, Pentagons? How do you know? Answer: Yes. Explanation: In the above-given question, given that, pentagons are in the above diagrams. so the shape belongs to this category. b. Can this shape go in the first subcategory, Equilateral pentagons? How do you know? Answer: No. Explanation: In the above-given question, given that, Equilateral pentagons are in the second subcategory. so the shape does not belong to the 1st category. c. Can this shape go into the second subcategory, Equilateral pentagons with at least one right angle? How do you know? Answer: No. Explanation: In the above-given question, given that, Equilateral pentagons with at least one right angle are in the third subcategory. so the shape does not belong to the second subcategory. Question 2. Describe how you would classify the shape below on the hierarchy. Start at the top and describe how you know if the shape fits in each category and subcategory. Answer: The shape fits the Equilateral pentagon. Explanation: In the above-given question, given that, Equilateral pentagons are in the second subcategory. so the shape does not belong to the 1st category. ### Everyday Math Grade 5 Home Link 7.6 Answer Key The Quadrilateral Hierarchy The quadrilateral hierarchy you used in class is below. Use it to answer the questions. Question 1. Fill in the blanks a. All trapezoids are quadrilaterals, but not all quadrilaterals are trapezoids . b. All __________ are __________, but not all __________ are __________. c. All __________are __________, but not all __________ are __________ Answer: a.Yes. b. All parallelograms are rhombuses, but not all rectangles are squares. Explanation: In the above-given question, given that, All quadrilaterals are trapezoids and kites. All trapezoids are parallelograms. All parallelograms are rectangles. All parallelograms are rhombuses. All rhombuses are squares. Question 2. a. All parallelograms have two pairs of parallel sides. Does this mean that all rectangles have two pairs of parallel sides? Explain how you can tell by looking at the hierarchy. Answer: Yes. Explanation: In the above-given question, given that, All parallelograms have two pairs of parallel sides. Yes, it means that all rectangles have two pairs of parallel sides. b. All trapezoids have at least one pair of parallel sides. Which other shapes have at least one pair of parallel sides? Explain how you can tell by looking at the hierarchy. Answer: Yes, All trapezoids have at least one pair of parallel sides. Rhombuses have at least one pair of parallel sides. All rectangles are squares. Explanation: In the above-given question, given that, Yes, All trapezoids have at least one pair of parallel sides. Rhombuses have at least one pair of parallel sides. All rectangles are squares. Practice Question 3. $$\frac{1}{4}$$ ÷ 8 = ________ Answer: $$\frac{1}{4}$$ ÷ 8 = 1/32. Explanation: In the above-given question, given that, $$\frac{1}{4}$$ ÷ 8. 1/4 ÷ 8. 8 x 4 = 32. 1/32. $$\frac{1}{4}$$ ÷ 8 = 1/32. Question 4. $$\frac{1}{10}$$ ÷ 3 = __________ Answer: $$\frac{1}{10}$$ ÷ 3 = 1/30. Explanation: In the above-given question, given that, $$\frac{1}{10}$$ ÷ 3. 1/10 ÷ 3. 10 x 3 = 30. 1/30. $$\frac{1}{10}$$ ÷ 3 = 1/30. Question 5. $$\frac{1}{6}$$ ÷ 2 = ___________ Answer: $$\frac{1}{6}$$ ÷ 2 = 1/12. Explanation: In the above-given question, given that, $$\frac{1}{6}$$ ÷ 2. 1/6 ÷ 2. 6 x 2 = 12. 1/12. $$\frac{1}{6}$$ ÷ 2 = 1/12. Question 6. $$\frac{1}{5}$$ ÷ 12 = _________ Answer: $$\frac{1}{5}$$ ÷ 12 = 1/60. Explanation: In the above-given question, given that, $$\frac{1}{5}$$ ÷ 12. 1/5 ÷ 12. 12 x 5 = 60. 1/60. $$\frac{1}{5}$$ ÷ 12 = 1/60. ### Everyday Mathematics Grade 5 Home Link 7.7 Answers Property Pandemonium Question 1. Imagine that you are playing Property Pandemonium. You already chose all of your cards and filled in the Property and Quadrilateral columns. Complete the Drawing, Additional Names, and Points columns for each round. Then find your total score. Answer: The total score = 8. Explanation: In the above-given question, given that, 2 pairs of parallel sides = rhombus. 2 pairs of adjacent sides equal in length = parallelogram. 4 right angles = kite. 2 + 2 + 4 = 8. the total number of points = 8. Practice Divide. Question 2. 9 ÷ $$\frac{1}{3}$$ = _______ Answer: 9 ÷ $$\frac{1}{3}$$ = 27. Explanation: In the above-given question, given that, 9 ÷ $$\frac{1}{3}$$. 9 x 3 = 27. 9 ÷ $$\frac{1}{3}$$ = 27. Question 3. 4 ÷ $$\frac{1}{5}$$ = _________ Answer: 4 ÷ $$\frac{1}{5}$$ = 20. Explanation: In the above-given question, given that, 4 ÷ $$\frac{1}{5}$$. 5 x 4 = 20. 4 ÷ $$\frac{1}{5}$$ = 20. Question 4. 2 ÷ $$\frac{1}{10}$$ = _________ Answer: 2 ÷ $$\frac{1}{10}$$ = 20. Explanation: In the above-given question, given that, 2 ÷ $$\frac{1}{10}$$. 10 x 2 = 20. 2 ÷ $$\frac{1}{10}$$ = 20. Question 5. 12 ÷ $$\frac{1}{4}$$ = __________ Answer: 12 ÷ $$\frac{1}{4}$$ = 48. Explanation: In the above-given question, given that, 12 ÷ $$\frac{1}{4}$$. 12 x 4 = 48. 12 ÷ $$\frac{1}{4}$$ = 48. ### Everyday Math Grade 5 Home Link 7.8 Answer Key Classifying Polygons Question 1. Draw the 12 shapes above in the correct categories on the hierarchy. Answer: The shapes that have at least 1 right angle = rhombus. The shapes that have exactly 4 right angles = 90 degrees. The shapes that have at least 1 obtuse angle = trapezoid, rhombus, acute angle, diamond shape. The shapes that have exactly all obtuse angles = hexagon, pentagon, octagon, parallelogram. Explanation: In the above-given question, given that, the shapes. The shapes that have at least 1 right angle = rhombus. The shapes that have exactly 4 right angles = 90 degrees. The shapes that have at least 1 obtuse angle = trapezoid, rhombus, acute angle, diamond shapes. Question 2. Explain how you decided where to place the hexagon. Answer: Hexagon is placed in all obtuse angles. Explanation: In the above-given question, given that, The shape Hexagon has all the sides 120 degrees. so hexagon is placed in all obtuse angles. Practice Solve. Question 3. 6.8 ∗ 103 = ________ Answer: 6.8 x 103 = 6800. Explanation: In the above-given question, given that, Multiply. 6.8 x 103. 6.8 x 10 x 10 x 10. 6.8 x 1000. 6800. Question 4. 12.7 ÷ 104 = __________ Answer: 12.7 ÷ 104 = 0.00127. Explanation: In the above-given question, given that, Divide. 12.7 ÷ 104. 12.7 ÷ 10 x 10 x 10 x 10. 0.00127. Question 5. 0.4 ∗ _________ = 4,000 Answer: 0.4 x 104. = 4000. Explanation: In the above-given question, given that, Multiply. 0.4 x 104.. 0.4 x 10 x 10 x 10 x 10. 4000. Question 6. 64.3 ÷ ________ = 0.643 Answer: 64.3 x 10 x 10 = 0.643. Explanation: In the above-given question, given that, Divide. 64.3 x 10 x 10. 64.3 x 100. 0.643. ### Everyday Mathematics Grade 5 Home Link 7.9 Answers Plotting and Interpreting Line-Plot Data Marisela and her class are finding their finger-stretch measurements. The finger stretch is measured from the tip of the pinkie to the tip of the index finger with an outstretched hand. Below are the measurements for Marisela and her classmates to the nearest $$\frac{1}{2}$$ inch. Question 1. Plot the data on the line plot. Answer: The fingers on 4 inches = 1. 4.5 in = 2, 5 in = 4, 5.5 in = 7, 6 in = 4, 6.5 = 3, 7 = 1. Explanation: In the above-given question, given that, The finger length in inches. fingers on 4 inches = 1. 4.5 in = 2. on 5 in = 4. on 5.5 in = 7. on 6 in = 4. on 6.5 in = 3. on 7 in = 1. Question 2. Marisela wants to find the total length of all the 6 $$\frac{1}{2}$$inch finger stretches. Write a number model using addition to help her find the total, then solve. Number model: __________ ________ inches Answer: The total length of all 6-inch finger stretches = 39/2. Explanation: In the above-given question, given that, Marisela wants to find the total length of all the 6(1/2) inch finger stretches. 6 x 2 = 12. 6 x 5 = 30. 30 + 9/2 = 39/2. so the total length of all 6-inch finger stretches = 39/2. Question 3. Now Marisela wants to use multiplication to find the total length of all the 5 $$\frac{1}{2}$$ inch finger stretches. Write a number model. Then solve. Number model: __________ __________ inches Answer: The total length of all the 5(1/2) inch finger stretches = 77/2. Explanation: In the above-given question, given that, Now Marisela wants to use multiplication to find the total length of all the 5(1/2) inch finger stretches. 5 x 2 = 10. 10 + 1/2 = 11/2. 11 x 7/2 = 77/2. Question 4. Find the total length of all the finger stretches in Marisela’s class. __________ inches Answer: The total length of all the finger stretches in Marisela’s class = 122. Explanation: In the above-given question, given that, Now Marisela wants to use multiplication to find the total length of all the 5(1/2) inch finger stretches. 5 x 2 = 10. 10 + 1 = 11. 11 x 12 = 120. 120 + 2 = 122. so the total length of all the finger stretches in Marisela’s class = 122. Practice Question 5. 4 $$\frac{1}{5}$$ ∗ $$\frac{1}{3}$$ = ________ Answer: 4 $$\frac{1}{5}$$ ∗ $$\frac{1}{3}$$ = 21/15. Explanation: In the above-given question, given that, 4 $$\frac{1}{5}$$ ∗ $$\frac{1}{3}$$ . 4(1/5) x 1/3. 5 x 4 = 20. 20 + 1/5 = 21/5. 21/5 x 1/3. 5 x 3 = 15. 4(1/5) x 1/3 = 21/15. Question 6. 2 $$\frac{5}{6}$$ ∗ 7 $$\frac{1}{4}$$ = ________ Answer: 2 $$\frac{5}{6}$$ ∗ 7 $$\frac{1}{4}$$ = 493/24. Explanation: In the above-given question, given that, 2 $$\frac{5}{6}$$ ∗ 7 $$\frac{1}{4}$$ . 2(5/6) x 7 (1/4). 6 x 2 = 12. 12 + 5/6 = 17/6. 7 x 4 = 28. 28 + 1/4 = 29/4. lcm of 6 and 4 is 24. 17 + 4 = 21. 29 + 6 = 31. 493/24. ### Everyday Math Grade 5 Home Link 7.10 Answer Key Identifying Patterns Question 1. a. Each column in the table below has a rule at the top. Use the rules to fill in the columns. Answer: In (x) = 2, 4, 6, 8, and 10. In (Y) = 8, 6, 4, 2, and 0. Explanation: In the above-given question, given that, in (x) Rule: 0 + 2 = 2. 2 + 2 = 4. 4 + 2 = 6. 6 + 2 = 8. 8 + 2 = 10. in (Y) Rule: 10 – 2 = 8. 8 – 2 = 6. 6 – 2 = 4. 4 – 2 = 2. 2 – 2 = 0. b. What rule relates the numbers in the in column to the numbers in the out column? Hint: What happens when you add the numbers in each row? Answer: Subtract the numbers in from 10 to get out. Explanation: In the above-given question, given that, when we add the numbers in each row is to subtract the numbers in from 10 to get out. c. Write the numbers from the table as ordered pairs. Graph the ordered pairs on the grid. Draw a line to connect the points. Ordered pairs: Answer: The order pairs are (2,8), (6, 4), (8, 2), (10, 0). Explanation: In the above-given question, given that, write the numbers from the table as ordered pairs. the ordered pairs are (2,8), (6, 4), (8, 2), (10, 0). Question 2. How does your graph in Problem 1c show the + 2 rule from the in column? Answer: The graph shows the problem + 2 rule. Explanation: In the above-given question, given that, in (x) Rule: 0 + 2 = 2. 2 + 2 = 4. 4 + 2 = 6. 6 + 2 = 8. 8 + 2 = 10. in (Y) Rule: 10 – 2 = 8. 8 – 2 = 6. 6 – 2 = 4. 4 – 2 = 2. 2 – 2 = 0. Practice The digits in each product or quotient are given. Use an estimate to place the decimal point. Write a number sentence to show how you estimated. Question 3. 42.96 ÷ 1.2 = 3 5 8 Number sentence: ___________ Answer: 42.96 ÷ 1.2 = 35.8. Explanation: In the above-given question, given that, Divide. 42.96 ÷ 1.2. 35.8. Question 4. 19.2 ∗ 8.8 = 1 6 8 9 6 Number sentence: ___________ Answer: 19.2 ∗ 8.8 = 168.96. Explanation: In the above-given question, given that, Multiplication. 19.2 x 8.8. 168.96. ### Everyday Mathematics Grade 5 Home Link 7.11 Answers Working with Rules, Tables, and Graphs Use the rule to complete the table. Write ordered pairs to represent the data. Then graph the ordered pairs and answer the questions. Question 1. Cherry tomatoes cost$2.50 per p ound.
Rule: Cost = $2.50 ∗ weight in pounds a. Answer: The weight in pounds 1 =$2.50, 3 = $7.50, 6 =$15, 10 = $25.00. Explanation: In the above-given question, given that, Cherry tomatoes cost$2.50 per pound.
2.50 + 2.50 + 2.50 = 7.50.
2.50 x 6 = $15. 2.50 x 10 =$25.00.

b. Ordered pairs:
___________ ___________ ___________ ___________

The ordered pairs are (1, 2.50), (3, 7.50), (6, 15.00), (10, 25.00).

Explanation:
In the above-given question,
given that,
Cherry tomatoes cost $2.50 per pound. 2.50 + 2.50 + 2.50 = 7.50. 2.50 x 6 =$15.
2.50 x 10 = $25.00. The ordered pairs are (1, 2.50), (3, 7.50), (6, 15.00), (10, 25.00). c. Answer: d. Plot a point to show the cost of 8 pounds of cherry tomatoes. What is the cost? Answer: The cost of 8 pounds of cherry tomatoes =$20.00.

Explanation:
In the above-given question,
given that,
Cherry tomatoes cost $2.50 per pound. 2.50 + 2.50 + 2.50 = 7.50. 2.50 x 8 = 20.00. so the cost of 8 pounds of cherry tomatoes =$20.00.

e. Julius has $12.00. Does he have enough money to buy 5 pounds of cherry tomatoes? Explain. Answer: No. Explanation: In the above-given question, given that, Julius has$12.00.
2.50 x 5 = $12.5. so he does not have enough money. f. Would you use the graph, the table, or the rule to find out how much 50 pounds of cherry tomatoes would cost? Explain. Answer: 50 x 2.50 =$125.

Explanation:
In the above-given question,
given that,
50 x 2.50 = \$125.

Practice
Question 2.
29.5 ∗ 62.3 = ___________

29.5 x 62.3 = 1837.85.

Explanation:
In the above-given question,
given that,
Multiply.
29.5 x 62.3.
1837.85.

Question 3.
4.1 ∗ 250.8 = ___________

4.1 x 250.8 = 1028.28.

Explanation:
In the above-given question,
given that,
Multiply.
4.1 x 250.8.
1028.28.

Interpreting Tables and Graphs

Ami runs 6 yards per second. Derek runs 5 yards per second. Ami challenged Derek to an 80-yard race. She told him he could have a 12-yard head start.

• Complete the tables to show the distances Ami and Derek are from the starting line during the first 5 seconds of the race.
• Write 3 ordered pairs each for Ami and Derek.
• Graph the ordered pairs you wrote and connect them with a line. Extend each line to the 80-yard mark to find out who wins. Label each line.

Question 1.
Who wins the race? How do you know?

Ami wins the race.

Explanation:
In the above-given question,
given that,
Ami run in seconds 1 = 6 yards.
2 = 12 yds.
3 = 18 yds.
4 = 24 yds.
5 = 30 yds.
Derex run in seconds 0 = 12 yds.
1 = 17 yds.
2 = 22 yds.
4 = 32 yds.
5 = 37 yds.

Practice
Write an equivalent problem with a whole-number divisor. Then solve.
Question 2.
68 ÷ 0.5 = ________

68 ÷ 0.5 = 136.

Explanation:
In the above-given question,
given that,
Equivalent problems.
680 ÷ 5.
136.
68 ÷ 0.5 = 136.

Question 3.
7.92 ÷ 0.22 = _________

7.92 ÷ 0.22 = 36.

Explanation:
In the above-given question,
given that,
Equivalent problems.
7.92 ÷ 0.22.
36.
7.92 ÷ 0.22 = 36.

Analyzing Patterns and Relationships

Question 1.
Use the given rules to complete each column of the table.

In Rule 1: 2, 3, 4, and 5.
In Rule 2: 17, 23, 29, and 35.

Explanation:
In the above-given question,
given that,
In rule 1 adding 1 to the other number.
In rule 2 adding 6 to the other number.
In Rule 1: 2, 3, 4, and 5.
In Rule 2: 17, 23, 29, and 35.

Question 2.
Find a rule that relates the in numbers to the corresponding out numbers.
Rule: ______________

In number x 6 + 5 = out number.

Explanation:
In the above-given question,
given that,
1 x 6 + 5 = 11.
in rule 1 = rule 11.
in number x 6 + 5 = out number.

Question 3.
Write the numbers in the table as ordered pairs.

The numbers in ordered pairs are (0,5), (1, 11), (2, 17), (3, 23), (4, 29), (5, 35).

Explanation:
In the above-given question,
given that,
In rule 1 adding 1 to the other number.
In rule 2 adding 6 to the other number.
In Rule 1: 2, 3, 4, and 5.
In Rule 2: 17, 23, 29, and 35.

Question 4.
Graph the ordered pairs on the grid.

The numbers in ordered pairs are (0,5), (1, 11), (2, 17), (3, 23), (4, 29), (5, 35).

Explanation:
In the above-given question,
given that,
In rule 1 adding 1 to the other number.
In rule 2 adding 6 to the other number.
In Rule 1: 2, 3, 4, and 5.
In Rule 2: 17, 23, 29, and 35.

Question 5.
a. When the in number is 8, what is the out number? ___________
b. When y is 64, about how much is x? About __________

5a = 53.
5b = 10.

Explanation:
In the above-given question,
given that,
The In number is 8.
8 x 6 + 5 = 53.
48 + 5 = 53.
x x 6 + 5 = 5.
4 + 60 = x.
x = 64.

Practice
Question 6.
3 $$\frac{1}{5}$$ ∗ 2 $$\frac{2}{3}$$ = ________

3 $$\frac{1}{5}$$ ∗ 2 $$\frac{2}{3}$$ =128/15.

Explanation:
In the above-given question,
given that,
3 $$\frac{1}{5}$$ ∗ 2 $$\frac{2}{3}$$.
3(1/5) x 2 (2/3).
3 x 5 = 15.
15 + 1/5 = 16/5.
2 x 3 = 6.
6 + 2/3 = 8/3.
lcm of 3 and 5 = 15.
16 x 3 = 48.
8 x 5 = 40.
80 + 48 = 128/15.

Question 7.
8 $$\frac{1}{2}$$ ∗ 12 = _________

8 $$\frac{1}{2}$$ ∗ 12 = 204/2.

Explanation:
In the above-given question,
given that,
8 x 2 = 16.
16 + 1/2 = 17/2.
17/2 x 12 = 204/2.

Question 8.
9 ∗ 5 $$\frac{1}{7}$$ = __________

9 ∗ 5 $$\frac{1}{7}$$ = 324/7.