middle school math solution · c01_sp_m02_t01.indd 36 1/16/19 3:23 pm module 2: relating...

Middle School

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ISBN: 978-1-60972-886-1Skills Practice

Printed in the United States of America1 2 3 4 5 6 7 8 9 CC 21 20 19 18 17


Table of Contents

Module 1: Composing and Decomposing

Topic 2: Positive Rational Numbers .................................14

Module 2: Relating Quantities

Topic 1: Ratios ................................................................35

Module 3: Determining Unknown Quantities

Topic 2: Equations ..........................................................76

FM-3


Odd-number Ansed wers ............................................139

I. Representing Fraction DivisionA. Write a number sentence that describes each model using multiplication.

2. 1 whole 1 whole

34

34 of 3

423

4.

of 59

45

1 whole

59

6. 1 whole

25

25

25

15

1. 11 whole 1 whole 4

34

34

34

3. 1 whole

23

23

13

5. 1 whole 1 whole 1 whole

112 11

2 of12 11

2

34

Topic 2

Positive Rational Numbers

Name Date

14 • MODULE 1: Composing and Decomposing

C01_SP_M01_T02.indd 14C01_SP_M01_T02.indd 14 1/16/19 3:23 PM1/16/19 3:23 PM

Module 1: Composing & Decomposing

Topic 2

POSITIVE RATIONAL NUMBERS

POSITIVE RATIONAL NUMBERS: Skills Practice • 15

Name Date

2. 18

18

18

34

18

18

18

1. 16

16

32

16

16

16

16

16

16

16

B. Write a number sentence that describes each model using division.

4. 3. 16

16

16

23

16

6. 5. of13

13

45

25

13

5

of32

32

32

13

32

3

34

34

34

34



Topic 2



2. Cheyenne is making friendship braceletsfor all of her friends. Each braceletrequires 2 __ 3 meter of thread. If Cheyennehas 2 1 __ 3 meters of thread, how manycomplete friendship bracelets canshe make?

1. Tara buys clay in a tube that is 2 feet long.She is making clay fl owers and each fl owerrequires 3 __ 4 foot of clay. How many wholefl owers can Tara make from the tube ofclay? Tara used the following model tohelp her solve the problem.

6. Kelly is making sandwiches to sell at thefootball game’s concession stand. She has4 3 __ 8 ounces of roast beef. Each sandwichhas 3 __ 4 ounce of roast beef. How manysandwiches can Kelly make?

5. Derek is making puppets to sell at histown’s annual craft fair. He is using yarn tomake the hair for the puppets. He has atotal of 3 yards of yarn, and each puppetrequires 4 __ 5 yard of yarn to make the hair.How many puppets can Derek make?

4. Mary has a pet ferret. She bought a bag offerret food that contains 1 1 __ 4 cups of food.The maker of the ferret food suggestsfeeding a ferret only 3 __ 8 cup of food a day.If Mary follows the suggestion, for howmany days can she feed her ferret fromthe bag of food before she needs to opena new bag?

3. Kayla works at a bookstore. One of herjobs is to take books that arrive and placethem on bookshelves in the store. She hasfour shelves for a shipment of 1 4 __ 5 boxes ofthe latest novel by one of Kayla’s favoriteauthors. Will Kayla be able to stock allthe books if each shelf can hold 2 __ 5 boxof books? Use a model to explain yourreasoning.

II. Interpreting Remainders Using ModelsA. Solve each problem. Draw a model to help you.

2

34

34 of 3

423



Topic 2



Name Date

III. Developing the Fraction Division AlgorithmA. Determine the fraction that makes each product 1.

2. 2 __ 3 3 5 11. 3 3 __ 1 5 1

4. 1 ___ 11 3 5 13. 3 5 __ 4 5 1

6. 3 9 __ 4 5 15. 3 __ 5 3 5 1

7. 1 __ 7 3 _____ 5 1 8. 3 1 ___ 23 5 1

9. 3 8 __ 9 5 1 10. 3 __ 7 3 5 1



Topic 2



2. 24 ___ 5 4 7 __ 2 5 ?1. 7 __ 4 4 11 ___ 7 5 ?

4. 1 __ 2 4 4 5 ?

6. 15 ___ 8 4 4 __ 3 5 ?

3. 8 __ 3 4 2 __ 5 5 ?

5. 9 4 3 __ 5 5 ?

B. Calculate each quotient by rewriting it as a multiplication problem.

7. 10 ___ 3 4 1 __ 6 5 ? 8. 5 4 7 __ 9 5 ?

9. 2 ___ 11 4 3 5 ? 10. 6 __ 5 4 8 __ 7 5 ?



Topic 2



Name Date

IV. Multiplying and Dividing Rational NumbersA. Calculate each quotient. Simplify your answer.

1. 5 __ 6 4 1__2

3. 7 __ 8 4 1__4

5. 15 ___ 16 4 3__4

7. 9 1 __ 3 4 2 1__3

2. 8 __ 9 4 2__3

4. 3 __ 4 4 1__6

6. 7 ___ 12 4 1__3

8. 10 1 __ 5 4 3 2__5

9. 19 4 6 1__4 10. 12 1 __ 2 4 2 1__

3



Topic 2



11. 7 3 __ 4 4 1 1__4 12. 15 2 __ 3 4 4 5__

6

13. 5 1 __ 2 4 1 1__4 14. 6 1 __ 2 4 2 1__

2

15. 7 1 __ 3 4 1 2__3 16. 5 3 __ 4 4 1 1__

8

17. 6 4 2 1__3 18. 7 3 __ 4 4 3 1__

4



RATIOS: Skills Practice • 35

Topic 1

Ratios

Name Date

1. strawberry bars to blueberry bars

3. strawberry bars to total bars

5. blueberry bars to total bars

2. apple bars to blueberry bars

4. apple bars to total bars

6. apple bars to strawberry bars

I. Understanding Ratio RelationshipsA. Determine whether each statement represents additive reasoning or multiplicative reasoning.

B. Nina buys a variety box of cereal bars. The box contains 5 blueberry bars, 3 strawberrybars, and 2 apple bars. Write the ratio that represents each relationship in words, in colonform, and in fractional form.

2. Juan has 7 apples, and Latanya has4 times as many, or 28 apples.

4. Tim ran 15 laps, which was 3 times asmany laps as Nathan ran.

6. The temperature was 70 degreesFahrenheit. It rose 3 degrees in one hour.

1. Ellie’s plant has grown a total of 8 inches,and Lin’s plant has grown a total of9 inches. Lin’s has grown more than Ellie’s.

3. Melanie is 8 years old, and Justin is 4 yearsolder than Melanie.

5. The Hawks scored 20 points in the fi rsthalf of the game. The team scored twiceas many points in the second half of thegame.



36 • MODULE 2: Relating Quantities

Topic 1

RATIOS

6. Juanita received a bouquet of 2 dozenroses. In the bouquet, 12 were red and12 were pink.

5. Kata’s movie collection consists of45 action movies and 31 comedy movies.

8. Of the 31 students surveyed, 19 preferwhite bread. The remaining studentsprefer wheat bread.

10. Emilio’s vegetable garden consists of8 tomato plants and 3 zucchini plants.

7. Wei planted 15 daffodils and 14 day-liliesin her garden.

9. Of the 400 students surveyed, 139 packedlunch and 261 bought lunch from theschool cafeteria.

4. Of the 100 students surveyed, 42 preferto play basketball and 28 prefer to playhockey.

3. Of the 100 students surveyed, 53 preferto watch football and 42 prefer to watchbaseball.

C. Write a part-to-part and a part-to-whole ratio for each problem situation.

2. Serena’s book collection contains23 fi ction books and 4 non-fi ction books.

1. Of the 200 students surveyed in 5thgrade, 120 prefer bananas and 80 preferapples.




Topic 1

RATIOS

II. Problem Solving with Equivalent Ratios and Rates using Double

Number LinesA. Use a double number line to answer each question.

2. Teresa is mixing red paint and blue paintto create a shade of purple paint. Thedouble number line shows the ratio redpaint : blue paint. If Teresa has 75 ouncesof red paint, how much blue paint doesshe need?

1. Yuko is making pancakes. The doublenumber line shows the ratio fl our : eggs.If Yuko accidentally uses 3 eggs instead of2 eggs, how much fl our should he use?

4. Ling is conducting a survey outside ofa grocery store. The double numberline shows the ratio of customers usingreusable shopping bags to customersusing plastic bags on a typical day. If thereare 50 customers that use plastic bags,how many use reusable shopping bags?

3. Pedro is going on a school fi eld trip.The double number line shows the ratiostudents : chaperones. If 32 studentsare going on the fi eld trip, how manychaperones must also go on the trip?

12. Raul collected the mail from his mailbox.It contains 3 catalogues and 2 bills.

11. Of the 250 students surveyed, 142 prefercarrots and 97 prefer peas.

2

3Flour (cups)

Eggs

3

24Students

Chaperones

8

12Red Paint(oz)

Blue Paint(oz)

3

15Plastic Bags

Reusable Bags

Name Date




Topic 1

RATIOS

III. Problem Solving with Equivalent Ratios and Rates using TablesA. Complete each ratio table. Show your calculations.

2. 1. Yellow paint (oz) 8 16

Blue paint (oz) 4 8 16

Red paint (oz) 1 50 100

Blue paint (oz) 20 400

Yellow paint (oz) 1 2 10

Red paint (oz) 6 60

4. 3.

6. 5.

6. Marcus is exercising. The double numberline shows the ratio of calories burned totime. If Marcus exercises for 45 minutes,how many calories will he burn?

5. Aiko is planting a fl ower garden. Thedouble number Iine shows the ratioof daisies to blue bells. If Aiko plants16 daisies, how many blue bells will sheplant?

9

12Daisies

Blue Bells20

112CaloriesBurned

Time(minutes)

Green paint (oz) 15 30

White paint (oz) 5 25 75

White paint (oz) 2 6 8

Red paint (oz) 3 36

White paint (oz) 1 3

Purple paint (oz) 30 40 60




Topic 1

RATIOS

B. Complete the ratio table to answer each question. Show your calculations.

1. Alberto is in charge of making lunch ata summer camp. He knows that 3 tunacasseroles will serve 15 campers. Howmany tuna casseroles should Alberto maketo serve 35 campers?

3. Perry is responsible for distributing soccerballs to the kids at soccer camp. Duringpractice, Perry would like each group of5 children to share two soccer balls. Howmany soccer balls does Perry need if 25kids attend camp?

5. Eva is planting fl owers in her garden. Eachvariety pack of bulbs contains 4 lilies and 6dahlias. How many dahlias will Eva plant ifshe plants 12 lilies?

2. Shawna is mixing red and white paint tocreate a shade of pink to paint her room.After experimenting, Shawna decides thatthe perfect shade of pink is created bymixing 3 ounces of red paint and 1 ounceof white paint. How much red and whitepaint does Shawna need to make 1 gallonof pink paint? (1 gallon 5 128 fl uid ounces)

4. Leon is bringing boxes of fruit snacks toclass for a holiday party at school. Leonknows that 2 boxes of fruit snacks willserve 11 students. How many boxes offruit snacks does Leon need to serve 33students?

6. Olivia is celebrating her birthday at amovie theater. She invites 12 friends fora movie and popcorn. She is told that 1large bucket of popcorn can be shared by3 people. How many buckets of popcorndoes Olivia need?

Pink Paint (oz) 128

Red Paint (oz) 3

White Paint (oz) 1

Casseroles 1 3

Campers 15 30 35

Soccer balls 2

Children 5 20 25

Lilies 4 8 12

Dahlias 6

Boxes 2

Students 11 22 33

Buckets of popcorn 1

People 3 9 12

Name Date




Topic 1

RATIOS

IV. Problem Solving with Equivalent Ratios and Rates using GraphsA. Create a graph that represents the values shown in each ratio table.

2. 1. Weight (pounds) 1 2 4 5

Cost (dollars) 3 6 12 15

Distance (miles) 25 75 125 175

Time (hours) 1 3 5 7

4. 3. Calories 80 160 240 320

Time (minutes) 15 30 45 60

Data (Mb) 10 100 150 200

Time (seconds) 1 10 15 20




Topic 1

RATIOS

6. 5. Distance (miles) 1.5 3 4.5 6


Height (feet) 6 30 36 60


Dis

tanc

e (m

iles)

Time (hours)

200

0

50

100

150

x

y

642 8 10

Distance Traveled by Serena

Cal

orie

s B

urne

d

Time (minutes)

Calories Burned Exercising200

0

50

100

150

x

y

3015 45 60

B. Use the given graph to answer each question.

1. Serena is driving to the mountains for asummer camping trip. She is traveling ata constant rate of 45 miles per hour. Thegraph shows the ratio time : distance. Howfar has Serena traveled after 4 hours?

2. Cisco is exercising. The graph shows theratio calories burned : time for Cisco.How many calories did Cisco burn in30 minutes?

Name Date




Topic 1

RATIOS

Cos

t (d

olla

rs)

Weight (pounds)

Cost of Oranges5

0

2

1

4

3

x

y

21 3 54

Dis

tanc

e C

limb

ed (f

eet)

Time (minutes)

Distance Climbed by Jose100

0

25

75

50

x

y

105 15 20

Cos

t (d

olla

rs)

Weight (pounds)

Cost of Bananas4

0

2

1

3

x

y

21 3 54

3. Manuel is biking at a constant rate.The graph shows the ratio time : distance.How long did it take Manuel to bike 4miles?

4. Jose is climbing a challenging section ofa mountain. The graph shows the ratiotime : distance climbed. How far did Joseclimb after 10 minutes?

5. Sofi a is grocery shopping. Oranges areon sale. The graph shows the ratiocost : weight. How much will it cost Sofi ato purchase 4 pounds of oranges?

6. Hector is grocery shopping. Bananasare on sale. The graph shows the ratiocost : weight. If Hector wants to spend$2, how many pounds of bananas can hepurchase?

Dis

tanc

e (m

iles)

Time (minutes)

Distance Biked by Manuel10

0

2

4

8

6

x

y

3015 45 60



Topic 2

Equations

Name Date

1. 2x 5 18

3. 6 5 x 1 3

2. x 5 4x

4. 15 5 5 ∙ x

II. Identifying the Number of Solutions to EquationsA. Determine whether each equation has one solution, no solutions, or an infi nite number of

solutions.

I. Using Substitution to Identify Solutions to EquationsA. Use substitution to determine which of the given values is the solution to each equation.

2. {18, 34, 36, 100}

2b 5 36

4. {1, 3, 5, 7, 9, 11}

d 2 7 5 1 1 3

6. {2, 6, 12, 18, 36}

3 5 g__6

1. {4, 9, 13, 21, 25}

a 1 0 5 13

3. {17, 24, 37, 81, 220}

c 5 110(2)

5. {0, 4, 9, 13, 15}

2 1 f 5 13 2 2

76 • MODULE 3: Determining Unknown Quantities



Topic 2

EQUATIONS

Name Date

5. x 1 9 5 9 1 x

7. 20 2 x 5 7

6. x 2 1 5 x 1 1

8. x 5 1x

III. Graphing Inequalities with Positive Rational NumbersA. Write the inequality represented by the given graph.

2. 1.

4.

6.

3.

5.

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

EQUATIONS: Skills Practice • 77



Topic 2

EQUATIONS


B. Grap h the solution set for each given inequality.

C. Determine what value each variable represents.

2. x $ 7.51. x , 6

4. x . 8.25

6. x , 9

3. 3 1 __ 2 $ x

5. 1.8 # x

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

2. 3 1 a 5 1 1 6

4. 6 1 5 5 b 1 5

6. x 1 3 5 2 1 6

1. p 1 2 5 4 1 4

3. 5 5 0 1 q

5. 4 1 1 5 1 1 c



Topic 2

EQUATIONS

Name Date

D. Determine what value each variable represents.

2. 3a 5 6

4. 6 1 6 5 2b

6. 2z 5 5 1 5

1. 2p 5 4

3. 6 1 2 5 4q

5. 3 1 3 5 1c

2. 40 5 10 1 x1. x 1 12 5 18

4. 48 5 x 1 233. 7.5 1 x 5 13

IV. Solving One-Step Equations with a Bar ModelA. Create a bar model to solve each addition equation.




Topic 2

EQUATIONS


6. x 1 9.3 5 11.45. 3 __ 4 5 1 __ 2 1 x

V. Solving One-Step Equations with a BalanceA. Determine what will balance 1 rectangle in each.

2. 1.

4.3.



Topic 2

EQUATIONS

Name Date

6. 5.

8. 7.

10. 9.




Topic 2

EQUATIONS


12. 11.

B. Create a bar model to solve each multiplication equation.

2. 10 5 4x

4. 5 5 x__4

1. 3x 5 15

3. x __ 2 5 4

6. 6 5 2 __ 3 x5. 3 __ 4 x 5 3



Topic 2

EQUATIONS

Name Date

VI. Solving One-Step Equations with Addition and SubtractionA. Solve each equation.

2. z 2 2 5 10

4. y 1 2 5 5

6. g 2 5 5 9

8. 5 5 a 2 5

10. m 2 9 5 7

12. 1 1 t 5 2

1. 8 5 6 1 w

3. 4 5 2 1 x

5. 4 5 p 2 8

7. 7 1 x 5 7

9. 4 5 d 1 1

11. 8 5 y 2 10




Topic 2

EQUATIONS


VII. Solving One-Step Equations with Multiplication and DivisionA. Solve each equation.

2. y ___ 10 5 8

4. 5p 5 20

6. 12 5 2a

8. b 4 7 5 1

10. 15 5 3x

12. 6y 5 6

1. 8 5 4w

3. 6 5 z 4 2

5. 2 5 x__5

7. 9t 5 54

9. s __ 3 5 10

11. 4 5 m 4 4




Topic 2

EQUATIONS

Name Date

1. The equation P 5 4s is used to calculatethe perimeter, P, of a square with a sidelength, s. Calculate the perimeter of asquare with side lengths that are each 12meters long.

3. The equation A 5 bh is used to calculatethe area, A, of a parallelogram with base,b, and height, h. Calculate the area of aparallelogram with a base of 15 inches anda height of 9 inches.

5. The equation C 5 F 2 32 ______ 1.8 is used toconvert a temperature in degrees Fahrenheit, F, to a temperature in degrees Celsius, C. Calculate the temperature, in degrees Celsius, when the temperature is 86 degrees Fahrenheit.

2. Use the equation P 5 4s to calculate theside lengths of a square with a perimeterof 28 feet.

4. Use the equation A 5 bh to calculate theheight of a parallelogram with an area of36 square inches and a base of 9 inches.

6. The equation P 5 a 1 b 1 c is used tocalculate the perimeter, P, of a trianglewith side lengths a, b, and c. Calculate theunknown side length for a triangle witha perimeter of 25 meters and two sidesmeasuring 7 meters each.

VIII. Using Literal Equations to Solve ProblemsA. Determine each answer using the given equation.



I. A.

I. B.

1. 3 3 3 __ 4 5 2 1__

4 3. 2 3 2 __ 3 5 1 1__

3 5. 2 1 __ 2 3 1 1 __ 2 5 3 3__4

1. 3 __ 2 4 1 __ 6 5 9 3. 2 __ 3 4 1 __ 6 5 4 5. 4 __ 5 4 1 __ 3 5 2 2__5

Topic 2

Positive Rational Numbers

II. A.

1.

2

34

34 of 3

423

Tara can make 2 whole fl owers. She can only make 2 __ 3 of another fl ower with theleftover clay.

3. 25

25

25

1 45

25 of 2

512

Kayla will not be able to stock all the books on the shelves. She will need another 1 __ 2 of a shelf to stock all the books.

POSITIVE RATIONAL NUMBERS: Skills Practice Answers • 143

C01_SP_AK_ODD.indd 143C01_SP_AK_ODD.indd 143 1/16/19 3:22 PM1/16/19 3:22 PM

Answer Key


5. 45

45

45

3

45of3

4

Derek can make 3 puppets. He will have yarn left over that will not be enough to make hair on another puppet.

III. A.

III. B.

1. 1__3 3. 4__

5 5. 5__3 7. 7__

1 9. 9__8

1. 7 __ 4 3 7 ___ 11 5 49 ___ 44 3. 8 __ 3 3 5 __ 2 5 40___6 5. 9 3 5 __ 3 5 45___

3 7. 10 ___ 3 3 6 __ 1 5 60___3 9. 2 ___ 11 3 1 __ 3 5 2 ___

33

IV. A.

1. 5 __ 6 4 1 __ 2 5 5 __ 6 3 2__1

5 10___6

5 1 4__6

5 1 2__3

5. 15 ___ 16 4 3 __ 4 5 15 ___ 16 3 4__3

5 60___48

5 1 12___48

5 1 1__4

9. 19 4 6 1 __ 4 5 19 ___ 1 4 25___4

5 19 ___ 1 3 4 ___25

5 76 ___ 25 5 3 1 ___25

13. 5 1 __ 2 4 1 1 __ 4 5 11 ___ 2 4 5__4

5 11 ___ 2 3 4__5

5 4 2__5

3. 7 __ 8 4 1 __ 4 5 7 __ 8 3 4__1

5 28___8

5 3 4__8

5 3 1__2

7. 9 1 __ 3 4 2 1 __ 3 5 28 ___ 3 4 7__3

5 28 ___ 3 3 3__7

5 4 __ 1 5 4

11. 7 3 __ 4 4 1 1 __ 4 5 31 ___ 4 4 5__4

5 31 ___ 4 3 4__5

5 6 1__5

15. 7 1 __ 3 4 1 2 __ 3 5 22 ___ 3 4 5__3

5 22 ___ 3 3 3__5

5 4 2__5

17. 6 4 2 1 __ 3 5 6 __ 1 4 7__3

5 6 __ 1 3 3__7

5 18 ___ 7 5 2 4__7

Topic 2



RATIOS: Skills Practice Answers • 147

3. additive 5. multiplicative

MODULE 2

Topic 1

Ratios

I. A.

1. additive

I. B.

1. 3 strawberry bars to 5 blueberry bars3 strawberry bars: 5 blueberry bars3 strawberry bars______________5 blueberry bars

5. 5 blueberry bars to 10 total bars5 blueberry bars: 10 total bars

5 blueberry bars

_____________ 10 total bars

3. 3 strawberry bars to 10 total bars3 strawberry bars: 10 total bars

3 strawberry bars

______________ 10 total bars

I. C.

1. part-to-part: 120 prefer bananas

_______________ 80 prefer apples or 80 prefer apples

_______________ 120 prefer bananas

part-to-whole: 120 prefer bananas

_______________ 200 total students or 80 prefer apples

______________ 200 total students

3. part-to-part: 53 prefer football

______________ 42 prefer baseball or 42 prefer baseball

______________ 53 prefer football

part-to-whole: 53 prefer football

______________ 100 total students or 42 prefer baseball

______________ 100 total students

Topic 1

RATIOS


5. part-to-part: 45 action movies _______________ 31 comedy movies or 31 comedy movies

_______________ 45 action movies

part-to-whole: 45 action movies _____________ 76 total movies or 31 comedy movies

_______________ 76 total movies

7. part-to-part: 15 daffodils __________ 14 day-lilies or 14 day-lilies__________15 daffodils

part-to-whole: 15 daffodils ____________ 29 total fl owers or 14 day-lilies

____________ 29 total fl owers

9. part-to-part: 139 packed

__________ 261 bought or 261 bought__________139 packed

part-to-whole: 139 packed

______________ 400 total students or 261 bought

______________ 400 total students

11. part-to-part: 142 prefer carrots

______________ 97 prefer peas or 97 prefer peas

______________ 142 prefer carrots

part-to-whole: 142 prefer carrots

______________ 250 total students or 97 prefer peas

______________ 250 total students

II. A.

1.

2

3Flour (cups)

Eggs3

1.5 4.5

1

Yuko should use 4.5 cups of fl our.

5.

9

12Daisies

Blue Bells

4

12

16

3

If Aiko plants 16 daisies, she will plant 12 blue bells.

3.

3

24Students

Chaperones

8

4

32

1

If 32 students go on the fi eld trip, 4 chaperones must also go on the trip.


Topic 1

RATIOS



III. A.

1.

Yellow paint (oz) 2 4 8 16

Blue paint (oz) 4 8 16 32

44

44

42

42

32

32

3.

Red paint (oz) 1 5 50 100

Blue paint (oz) 4 20 200 400

42

4204100

42

4204100

5.

White paint (oz) 2 6 8 24

Red paint (oz) 3 9 12 36

33

33

add

add

312

312

Topic 1

RATIOS


III. B.

1.

Casseroles 1 3 6 7

Campers 5 15 30 35

add

43 32

Alberto will need 7 tuna casseroles to serve 35 campers.

3.

Perry needs 10 soccer balls.

Soccer balls 2 8 10

Children 5 20 25

34

add

Eva will plant 18 dahlias.

5.

Lilies 4 8 12

Dahlias 6 12 18

32

add


Topic 1

RATIOS



IV. A.

1.

Cos

t ($

)

Weight (lb)

20

0

5

10

15

8x

y

2 4 6

3.

Cal

orie

s

Time (minutes)

400

0

100

200

300

x

y

3015 45 60

5.

Dis

tanc

e (m

iles)

Time (minutes)

10

0

2

4

6

8

x

y

3015 45 60

Topic 1

RATIOS


IV. B.

1.

Dis

tanc

e (m

iles)

Time (hours)

200

0

50

100

150

x

y

642 8 10

Distance Traveled by Serena

After 4 hours, Serena has traveled 180 miles.

3.

Dis

tanc

e (m

iles)

Time (minutes)

Distance Biked by Manuel10

0

2

4

8

6

x

y

3015 45 60

It took Manuel 30 minutes to bike 4 miles.

5.

Cos

t (d

olla

rs)

Weight (pounds)

Cost of Oranges5

0

2

1

4

3

x

y

21 3 54

It will cost Sofi a $3 to purchase 4 pounds of oranges.


Topic 1

RATIOS


EQUATIONS: Skills Practice Answers • 159

Topic 2

Equations

1. p 5 6 3. 5 5 q 5. 4 5 c

III. C.

I. A.

1. a 5 13 3. c 5 220 5. f 5 9

II. A.

1. one solution

5. infi nite number of solutions

3. one solution

7. one solution

III. A.

1. x . 7 3. x , 2 5. x # 1

III. B.

1. x , 6

0 1 2 3 4 5 6 7 8 9

5. 1.8 # x

0 1 2 3 4 5 6 7 8 9

3. 3 1 __ 2 $ x

0 1 2 3 4 5 6 7 8 9

III. D.

1. p 5 2 3. 2 5 q 5. 6 5 c

Topic 2

EQUATIONS



IV. A.Answers may vary. Sample models provided.

1. x 5 6

x

x 1 12

18

6

12

12

3. x 5 5.5

7.5

7.5 1 x

13

7.5

x

5.5

5. 1 __ 4 5 x

1__2

3__4

1 __ 2 1 x

1__2

1__4

x

V. A.

1. Eight squares will balance 1 rectangle.

5. Five squares will balance 1 rectangle.

9. Two squares will balance 1 rectangle.

3. Six squares will balance 1 rectangle.

7. Seven squares will balance 1 rectangle.

11. Twelve squares will balance 1 rectangle.

Topic 2

EQUATIONS

V. B.Answers may vary. Sample models provided.

1. x 5 5

1x

3x

15

5

1x 1x

5 5

3. x 5 8

( 1 __ 2 ) x

4

( 1 __ 2 ) x

4

8

1x5. x 5 4

( 3 __ 4 ) x

3

( 1 __ 4 ) x

1

1x

4


VI. A.

1. 2 5 w7. x 5 0

3. 2 5 x9. 3 5 d

5. 12 5 p11. 18 5 y

VII. A.

1. 2 5 w7. t 5 6

3. 12 5 z9. s 5 30

5. 10 5 x11. 16 5 m


VIII. A.

1. P 5 4(12)P 5 48The perimeter of the square is 48 meters.

3. A 5 15(9)A 5 135The area of the parallelogram is135 square inches.

5. C 5 86 2 32_______1.8

C 5 54 ___ 1.8 5 30The temperature is 30 degrees Celsius.

Topic 2

EQUATIONS

GRAPHING QUANTITATIVE RELATIONSHIPS: Skills Practice Answers • 161


middle school math solution · c01_sp_m02_t01.indd 36 1/16/19 3:23 pm module 2: relating...

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