Ratios & Proportional Reasoning [PDF]

Mar 10, 2014 - Lesson 3 Skills Practice. Convert Unit Rates. 1. 660 ft/min = ft/s. 2. 25 mi/h ≈ ft/s. 3. 32 gal/min =

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Unit 5

Ratios & Proportional Reasoning

PRACTICE Name Period

Lesson 1 Skills Practice Rates Find each unit rate. Round to the nearest hundredth if necessary. 1. $112 in 8 hours

2. 150 miles in 6 gallons

3. 49 points in 7 games

4. 105 students in 3 classes

5. 120 problems in 5 hours

6. 3 accidents in 12 months

7. 6 eggs in 7 days

8. 8 batteries in 3 months

9. 122 patients in 4 weeks

10. 51 gallons in 14 minutes

11. $8.43 for 3 pounds

12. 357 miles in 6.3 hours

13. 25 letters in 4 days

14. $99 for 12 CDs

15. 5 breaks in 8 hours

16. 3 trips in 14 months

17. 2 pay raises in 3 years

18. 7 errors in 60 minutes

19. 15 pounds in 6 weeks

20. 8 commercials in 15 minutes

21. 8 glasses every 24 hours

22. 13 feet in 5 steps

Choose the lower unit price. 23. $4.99 for 6 cans or $7.99 for 10 cans 24. $21.50 for 4 pounds of lunch meat or $15.10 for 3 pounds of lunch meat

Lesson 2 Skills Practice Complex Fractions and Unit Rates Simplify. 1.

1

3.

4

5.

8

7.

9.

11.

13.

15.

17.

2 5

3 8

3 4

2 5 4 9

2.

4

4.

10

6.

8.

5 6

12 7 9

14

8 11 4 5

6 7

21 1 3 8 9

5 8

5 12

1 5 7 10

8 9

20

10.

12.

3 8 7 12

6 7 14 15

14.

30

16.

15

18.

5 7

5 9

2 3 24 25

Lesson 3 Skills Practice Convert Unit Rates Complete. Round to the nearest tenth if necessary. 1. 660 ft/min =

ft/s

2. 25 mi/h ≈

3. 32 gal/min =

qt/h

4. 425 ft/h =

5. 0.5 L/s =

7. 3.4 mi/h =

9. 5.6 lb/gal =

11. 42 cm/s =

13. 8 mi/h =

mL/h

ft/sec

oz/gal

m/min

ft/min

6. 60 ft/s ≈

8. 2.1 yd/min =

10. 4 m/h =

ft/s

in./min

mi/min

ft/s

cm/min

12. 4,500 ft/h =

ft/s

14. 900 cm/h =

cm/min

15. JOGGING Jarin jogs at a rate of 7.5 miles per hour. How many miles per minute does Jarin jog?

16. BUCKETS Alonzo fills buckets at a rate of 6 gallons per minute. What is the rate in pints per hour?

Lesson 4 Skills Practice Proportional and Nonproportional Relationships For Exercises 1–3, use the table of values. Write the ratios in the table to show the relationship between each set of values. 1. Number of Hours Total Amount Earned

1 $15

2 $30

3 $45

4 $60

1 $11

2 $20

3 $29

4 $38

1 24

2 48

3 72

4 92

Ratios 2. Number of Packages Total Cost Ratios 3. Number of Classrooms Total Students Ratios For Exercises 4–8 use the table of values. Write proportional or nonproportional. 4. Number of Hours Total Amount Earned

1 $0.99

2 $1.98

3 $2.97

4 $3.96

5. Number of Hours Total Amount Earned

1 $17.25

2 $35.50

3 $50.75

4 $70

1 37

2 73

3 109

4 145

1 $2.75

2 $5.50

3 $8.25

4 $11

6.

Number of Hours Number of Pages Read in Book

7. Number of Lunches Total Cost

8. Fred is ordering pies for a family reunion. Each pie costs $4.50. For orders smaller than a dozen pies, there is a $5 delivery charge. Is the cost proportional to the number of pies ordered? Use a table of values to explain your reasoning.

Lesson 5 Skills Practice Graph Proportional Relationships Determine whether the relationship between the two quantities shown in each table are proportional by graphing on the coordinate plane.

1. Volume of a Cube Side Length Volume (ft) (ft3) 1 1 2 8 3 27

2. DVD Rental Number of Cost ($) DVDs 1 7 2 9 3 11

3. Gallons of Gas Used Per Hour Number of Gallons Hours of Gas 3 15 4 20 5 25

Lesson 6 Skills Practice Solve Proportional Relationships Determine whether each pair of ratios form a proportion. 5 2 8 3

7 14 3 6

1. , 4.

16 11 , 9 6

5.

5 15 9 27

7. , 10.

6 9 8 12

2. ,

8.

9 13 , 13 17

3. ,

55 12 , 10 2

6 15 8 20

6. ,

3 11 , 18 66

11.

9.

3 5 , 42 70

7 15 , 11 23 6 36 7 49

12. ,

Solve each proportion. 13.

16.

19.

22.

25.

28.

4 12

=

𝑦 9

5 10

=

8 𝑤

5 9

=

6 𝑟

𝑦 5

=

13 10

14.

17.

20.

1.2 𝑚

=

3 5

6.3 𝑋

=

18 5

23.

26.

29.

6 18

4 𝑐

=

𝑥 9

=

4 15

8 𝑛

=

10 7

2 28

=

𝑝 35

0.9 0.5

=

𝑎 10

3.6 9

=

𝑏 0.5

15.

18.

21.

24.

27.

30.

7 𝑧

=

6 20 𝑑 5

𝑦 5

= =

11 𝑡 3 7

84 12

12 80 100 11

= =

14 1.5

𝑘 4.2

=

4.2 𝑦

Lesson 7 Skills Practice Constant Rate of Change Find the constant rate of change for each table. 1.

3.

2.

Time

Temperature (°F)

10

9:00

60

3

30

10:00

62

5

50

11:00

64

7

70

12:00

66

Time Spent Mowing (h)

Money Earned ($)

1

4.

Number of Trees

Number of Apples

100

5

100

15

150

10

200

20

200

15

300

25

250

20

400

Number of Students

Number of Magazines Sold

10

Find the constant rate of change for each graph. 5. 85 80 75 70 65 60 55 50 0

6.

Meat Consumption

Pound of Meat

Temperature (°F)

Temperature Change

1 2 3 4 5 6 7 8

Hours

16 14 12 10 8 6 4 2 0

1 2 3 4 5 6 7 8

Number of People

Lesson 8 Skills Practice Slope Graph the data. Then find the slope Explain what the slope represents.

Wages ($)

1

2

3

4

11

22

33

44

Wages ($)

44

1. Hours

33 22 11

0

1

2

3

4

2.

Temperature (°F)

70

78

86

94

Number of People on Beach

24

40

56

72

Number of People

Hours 80 70 60 50 40 30 20 10 0

66 70 74 78 82 86 90 94

Temperature

1

3. SWIMMING Latonya swims 50 meters in 2 minute. Meters

400 350 300 250 200 150 100 50 0

1

2

3

4

4. SONGS Find the slope of the line on the graph showing the cost to download songs.

Cost to Download ($)

Minutes

2.00 1.50 1.00 0.50

0

1 2 3 4 5 6 7

8

Number of Songs

Lesson 9 Skills Practice Direct Variation Determine whether each linear function is a direct variation. If so, state the constant of proportionality. Speed, x

25

30

35

40

Distance, y

100

120

140

160

2. Price, x Tax, y 3.

$5

$8

$11

$14

$0.50

$0.80

$1.10

$1.40

Seconds, x Number of Sit-ups, y

15

30

45

60

5

10

15

20

4. DISHES The number of place settings of dishes varies directly with the number of boxes. How many place settings are in each box?

16

Place Settings

1.

12 8 4

0

1

2

3

4

3

4

Boxes 40

Figurines

5. FIGURINES Kentish is arranging figurines on shelves. The number of figurines varies directly with the number of shelves. What is the constant of proportionality?

30 20 10

0

1

2

Shelves

6. CAT FOOD Loretta paid $6.70 for 5 cans of cat food and $10.72 for 8 cans of cat food. How much did 1 can of cat food cost? 7. PILLOWS You need 2 yards of fabric to cover 3 pillows and 6 yards to cover 9 pillows. How much fabric do you need to cover 15 pillows? 8. READING The number of pages read varies directly as the number of minutes. If you can read 20 pages in 45 minutes, how many pages can you read in 18 minutes?

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