Grade 7 Workbook — Chapter 5: Ratio Tables and Proportions

SOL 7.CE.2 (a–c) · Companion to Textbook Chapter 5

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Item numbers match the textbook, so one answer key serves both books.

PAGE 1 — Chapter opener

Chapter 5 · Ratio Tables and Proportions

Standard 7.CE.2 (a–c)

In this chapter you will:

• Build ratio tables and use them to find missing values
• Write proportions that match a situation, with the units lined up
• Solve proportions by scaling, by unit rate, and by cross multiplication
• Convert units of measurement using a conversion factor the problem gives you
• Decide whether a real situation is proportional before you set anything up

Words to know: ratio · proportional relationship · unit rate · constant of proportionality · ratio table · double number line · proportion · cross products · conversion factor · unit price · origin

Percent of a number is the other half of this standard. It gets its own book chapter — Chapter 6.

PAGE 2 — What a ratio table does

5.1 Ratio Tables and Missing Values

FIGURE: fig1-ratio-table-scaling.png (full width)

Fill in the blanks.

A ratio compares ______________ quantities.

In a proportional relationship, one quantity is always the same fixed number of ______________ the other.

To move from one column of a ratio table to another, you ______________ or ______________ both entries by the same number.

You may NOT ______________ the same number to both entries. Show why with the column $(1, 9)$:

Adding 4 to both gives ( ______ , ______ ), but $9 \times 5 =$ ______, so the ratio changed.

A unit rate is a rate whose second quantity is ______.

Six water bottles cost $4.50, so one bottle costs $4.50 \div 6 =$ $ ______.

PAGE 3 — Building tables

Complete Each Ratio Table

1. A theater charges $9 per ticket.

2. A printer prints 24 pages in 3 minutes.

Unit rate: ______ pages per minute

3. What number do you multiply the first column by to get the second?

Multiplier: ______

4. Seven pounds of rice cost $21. Unit price: $ ______ per pound. Cost of 4 pounds: $ ______

5. Explain. Why can $(3, 12)$ and $(6, 24)$ appear in the same ratio table, but $(3, 12)$ and $(6, 15)$ cannot?

PAGE 4 — Double number lines and more tables

Scaling Up and Scaling Down

FIGURE: fig2-double-number-line.png (full width)

6. One gallon of paint covers 35 square feet.

7. Six water bottles cost $4.50. Unit price: $ ______

8. Twelve sandwiches feed 18 people. Scale down.

9. Error hunt. One entry below is wrong.

Wrong entry: ______ How you know: _______________________________________________

Correct value: ______

PAGE 5 — Ratio tables in context

Using a Ratio Table to Answer a Question

10. A resting heart beats 210 times in 3 minutes. Unit rate: ______ beats per minute

11. Application. A car travels 180 miles on 6 gallons of gasoline. Build the table, then answer the question.

How far can the car travel on 11 gallons? ______ miles

12. Reasoning. Devon starts at $(2, 6)$ and fills his table by adding 3 to the top entry and 3 to the bottom entry each time.

Why is this not a ratio table? _______________________________________________

The correct third column should be ( ______ , ______ ).

PAGE 6 — Exit ticket 5.1

Exit Ticket · Lesson 5.1

Name: ________________________ Date: ____________

13. Four notebooks cost $10.

14. What number takes the column $(3, 21)$ to the column $(12, 84)$? ______

15. A faucet fills 8 liters in 2 minutes. How many liters in 7 minutes? ______

16. In your own words, what stays the same in every column of a ratio table?

PAGE 7 — What a proportion is

5.2 Writing a Proportion

A proportion says two ratios are equal.

$$\frac{a}{b} = \frac{c}{d}$$

Line up the units. Fill in the labels.

$$\frac{3 \text{ pounds}}{5.40 \text{ dollars}} = \frac{7 \text{ pounds}}{c \;\underline{\hspace{2cm}}}$$

Correct or incorrect? Circle one for each setup of "3 pounds cost $5.40; find the cost $c$ of 7 pounds."

Write the setup. Do not solve.

17. Three apples cost $2.10. Find the cost $c$ of 8 apples.

18. A runner covers 350 meters in 5 minutes. Find the distance $d$ in 12 minutes.

PAGE 8 — Cross products

The Cross-Product Test

FIGURE: fig5-cross-products.png (full width)

Why it works. Fill in the blanks.

Start with $\dfrac{a}{b} = \dfrac{c}{d}$. Multiply both sides by ______ $\times$ ______.

On the left the $b$'s cancel, leaving ______. On the right the $d$'s cancel, leaving ______.

So $a \times d =$ ______ $\times$ ______.

Test each pair. Show both products.

19. $\tfrac{4}{6}$ and $\tfrac{14}{21}$ → $4 \times 21 =$ ______ and $6 \times 14 =$ ______ → proportion? ______

20. $\tfrac{3}{8}$ and $\tfrac{12}{30}$ → $3 \times 30 =$ ______ and $8 \times 12 =$ ______ → proportion? ______

21. Copy and label: in $\dfrac{9 \text{ tiles}}{12 \text{ square feet}} = \dfrac{t}{40 \text{ square feet}}$, the letter $t$ stands for

PAGE 9 — Setting up proportions

Practice Writing Proportions

22. Test each pair with cross products.

23. Nine tiles cover 12 square feet. Write a proportion for the number of tiles $t$ needed for 40 square feet. Do not solve.

24. Four pounds of dog food last 10 days. Write two different correct proportions for the number of days $d$ that 15 pounds will last.

25. On a map, 2 inches represents 35 miles. Write a proportion for the distance $m$ shown by 7 inches. Do not solve.

26. A student writes $\dfrac{6 \text{ hours}}{270 \text{ miles}} = \dfrac{450 \text{ miles}}{h}$. What is wrong?

Correct setup: _______________________

PAGE 10 — Application and reasoning

Think It Through

27. Application. A 15-ounce box of cereal costs $3.60. Write a proportion for the cost $c$ of a 25-ounce box, assuming price is proportional to weight.

Why might a real store not price it that way?

28. Reasoning. Explain why $\dfrac{3}{5} = \dfrac{x}{20}$ and $\dfrac{5}{3} = \dfrac{20}{x}$ describe the same relationship.

Will they give the same value of $x$? ______ What is it? ______

PAGE 11 — Exit ticket 5.2

Exit Ticket · Lesson 5.2

Name: ________________________ Date: ____________

29. Do $\tfrac{8}{14}$ and $\tfrac{20}{35}$ form a proportion?

$8 \times 35 =$ ______ $14 \times 20 =$ ______ Answer: ______

30. Seven buses carry 336 students. Write a proportion for the number of students $s$ in 10 buses. Do not solve.

31. Circle the correct setup for "3 gallons cover 240 square feet; how many gallons $g$ cover 400 square feet?"

a) $\dfrac{3}{240} = \dfrac{400}{g}$ b) $\dfrac{3}{240} = \dfrac{g}{400}$

32. Why must the units line up in the same positions on both sides?

PAGE 12 — Four ways to solve

5.3 Solving a Proportion

One proportion, four strategies. Complete each column for $\dfrac{x}{4} = \dfrac{15}{12}$.

Cross multiplication, step by step.

1. Multiply each numerator by the other ______________.
2. Set the two products ______________.
3. ______________ both sides by the number in front of the variable.
4. ______________ your answer by comparing cross products.

Solve. Show the cross products and the division step.

33. $\dfrac{x}{4} = \dfrac{15}{12}$

34. $\dfrac{3}{7} = \dfrac{12}{y}$

35. $\dfrac{n}{9} = \dfrac{8}{6}$

36. $\dfrac{5}{8} = \dfrac{m}{40}$

37. $\dfrac{2.5}{1} = \dfrac{w}{6}$

PAGE 13 — Solving practice

Solve Each Proportion

38.

39. Solve $\dfrac{4}{5} = \dfrac{t}{45}$ two ways.

By scaling: _______________________________________________

By cross multiplication: _______________________________________________

40. $\dfrac{9}{x} = \dfrac{6}{8}$ $x =$ ______

41. $\dfrac{5}{7} = \dfrac{9}{k}$ Exact answer: $k =$ ______

PAGE 14 — Proportions in context

Set It Up, Then Solve

42. Application. Three pounds of grapes cost $5.40. Find the cost of 7 pounds.

Setup: _______________________

Solve: _______________________________________________

Answer: $ ______

43. Application. A typist enters 84 words in 2 minutes. How many words in 5 minutes at the same rate?

Setup: _______________________

Answer: ______ words

44. Reasoning. Explain why cross multiplication works. Use $\dfrac{a}{b} = \dfrac{c}{d}$ and the fact that you may multiply both sides of an equation by the same nonzero number.

PAGE 15 — Exit ticket 5.3

Exit Ticket · Lesson 5.3

Name: ________________________ Date: ____________

45. Solve $\dfrac{x}{6} = \dfrac{20}{15}$. $x =$ ______

46. Solve $\dfrac{7}{4} = \dfrac{35}{y}$. $y =$ ______

47. Five concert tickets cost $62.50. Write and solve a proportion for the cost of 8 tickets.

Setup: _______________________ Answer: $ ______

48. Name a strategy other than cross multiplication for $\dfrac{3}{4} = \dfrac{x}{20}$, and use it.

PAGE 16 — Conversion factors

5.4 Converting Units with a Given Conversion Factor

FIGURE: fig6-conversion-double-line.png (full width)

A conversion factor is a ______________ of two measurements of the same amount in different units.

The problem will always give you the factor. You are not expected to memorize it.

Direction check. Circle the right word.

Converting a big unit to a small unit (miles → feet) gives ( more / fewer ) of the smaller unit.

Converting a small unit to a big unit (quarts → gallons) gives ( more / fewer ) of the bigger unit.

Convert. Show the setup.

49. 1 mile = 5,280 feet. 3 miles = ______ feet

50. 1 kilogram = 2.2 pounds. 15 kg = ______ pounds

51. 1 gallon = 4 quarts. 26 quarts = ______ gallons

52. 1 inch = 2.54 centimeters. 12 inches = ______ cm

53. 1 hour = 3,600 seconds. 2.5 hours = ______ seconds

PAGE 17 — Conversion practice

Convert Each Measurement

54.

55. 1 mile = 1.609 kilometers. 8 miles = ______ km (round to the nearest tenth)

56. 1 cup = 8 fluid ounces. 60 fl oz = ______ cups

57. 1 meter = 100 centimeters. 3.4 m = ______ cm

58. Application. A bag of flour weighs 2.5 pounds. 1 pound = 453.6 grams. Weight in grams: ______

59. Application. A student exchanges 250 euros. 1 euro = 1.08 dollars. Dollars received: $ ______

60. Reasoning. A classmate converts 48 inches to feet using 1 foot = 12 inches and gets 576 feet. How can you tell it is wrong without redoing the arithmetic?

Correct answer: ______ feet

PAGE 18 — Exit ticket 5.4

Exit Ticket · Lesson 5.4

Name: ________________________ Date: ____________

61. 1 foot = 12 inches. 7.5 feet = ______ inches

62. 1 kilogram = 1,000 grams. 4,750 g = ______ kg

63. 1 gallon = 3.785 liters. 6 gallons = ______ liters (round to the nearest tenth)

64. How does checking whether the unit gets bigger or smaller help you catch a backward setup?

PAGE 19 — Unit prices and ratio totals

5.5 Proportional Reasoning in Context

FIGURE: fig3-tape-diagram.png (full width)

A unit price is the cost of ONE unit. Divide the cost by the number of units.

65. A 12-ounce jar costs $3.00. A 20-ounce jar costs $4.60.

Better buy: _______________

66. A soup recipe serving 6 uses 2.5 cups of broth. Broth for 15 servings: ______ cups

67. On a floor plan, 1 inch represents 12 feet. A wall measures 4.5 inches. Actual length: ______ feet

68. A car travels 150 miles in 3 hours at a steady speed. Distance in 7 hours: ______ miles

69. Twenty-four stickers are shared in the ratio 1 to 3.

Number of equal parts in all: ______ One part: ______ The two shares: ______ and ______

PAGE 20 — Comparing, splitting, graphing

Put the Tools Together

FIGURE: fig4-proportional-graph.png (right half of page)

70. Find each unit price, then order the bags from least to greatest cost per ounce.

Order: _______________________

71. Eight gallons of fertilizer treat 2,000 square feet. Gallons for 4,500 square feet: ______

72. Forty marbles are shared in the ratio 3 blue to 5 green.

Blue: ______ Green: ______ Show the ratio still holds: _______________________

73. A printing service charges $0.12 per page with no other fees.

How would the graph of this relationship look? _______________________________________________

PAGE 21 — Multi-step and non-proportional

Two Steps, and a Trap

74. Application. A cyclist rides 42 km in 3 hours at a steady speed. 1 kilometer = 0.621 miles.

Kilometers in 5 hours: ______ Miles in 5 hours (nearest tenth): ______

75. Application. A tree grows 18 inches in 2 years at a steady rate. 1 foot = 12 inches.

Inches in 8 years: ______ Feet in 8 years: ______

76. Reasoning. A phone plan costs $20 per month plus $0.10 per gigabyte of data.

Cost for 10 GB: $ ______ Cost for 20 GB: $ ______

Doubling the data did not double the cost. What feature of the plan breaks the proportionality?

PAGE 22 — Exit ticket 5.5

Exit Ticket · Lesson 5.5

Name: ________________________ Date: ____________

77. A 6-pack of juice costs $4.50; a 10-pack costs $7.00.

Unit prices: $ ______ and $ ______ Better buy: _______________

78. A recipe for 4 servings uses 3 cups of rice. Rice for 10 servings: ______ cups

79. A model is built so 1 inch represents 8 feet. A 2.5-inch model car represents a real length of ______ feet

80. A pool service charges a $40 visit fee plus $12 per hour. Why is the total cost not proportional to the number of hours?

PAGE 23 — Chapter 5 review, part 1

Chapter 5 Review

Part A · Ratio tables (7.CE.2a)

81. Muffins cost $2.75 each.

82. A machine seals 96 envelopes in 4 minutes. Unit rate: ______ per minute

83. One entry is wrong.

Wrong entry: ______ Correct value: ______

84. What number takes $(6, 15)$ to $(18, 45)$? ______

PAGE 24 — Chapter 5 review, part 2

Chapter 5 Review (continued)

Part B · Writing and solving proportions (7.CE.2b)

85. Do $\tfrac{9}{15}$ and $\tfrac{21}{35}$ form a proportion? $9 \times 35 =$ ______, $15 \times 21 =$ ______, answer ______

86. Solve: a) $\dfrac{x}{8} = \dfrac{21}{24}$ ______ b) $\dfrac{5}{6} = \dfrac{n}{42}$ ______ c) $\dfrac{12}{p} = \dfrac{8}{10}$ ______

87. Four pounds of birdseed cost $7.00. Cost of 10 pounds: setup _______________ answer $ ______

88. A student writes $\dfrac{4 \text{ cups}}{6 \text{ servings}} = \dfrac{s}{10 \text{ cups}}$. Explain the error and write a correct proportion.

89. Solve $\dfrac{7}{2} = \dfrac{x}{9}$ exactly. $x =$ ______

Part C · Converting units (7.CE.2c)

90. 1 pound = 16 ounces. 3.75 lb = ______ oz

91. 1 meter = 3.28 feet. 25 m = ______ ft

92. 1 gallon = 4 quarts. 34 qt = ______ gal

93. 1 kilometer = 0.621 miles. 12 km = ______ mi (nearest tenth)

PAGE 25 — Chapter 5 review, part 3

Chapter 5 Review (continued)

Part D · Mixed application and reasoning

94. A 9-ounce bag of nuts costs $4.05; a 15-ounce bag costs $6.60.

Unit prices: $ ______ and $ ______ Better buy: _______________

95. A hiker walks 3 miles in 50 minutes at a steady pace. 1 hour = 60 minutes.

Minutes in 2 hours: ______ Miles in 2 hours: ______

96. One streaming service charges a $10 signup fee plus $8 per month. A second charges $9 per month with no signup fee.

Which cost is proportional to the number of months? _______________

Describe how each would look when graphed.

Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Ratio tables: set every table on a 0.5 in row height so students have room to write inside a cell; keep the shaded label column at 1.2 in wide
• Figure widths: fig1, fig2, fig3, fig5, and fig6 run full width; fig4-proportional-graph.png is close to square, so place it at half width beside the page-20 tables
• Money: every dollar amount is typed with the dollar sign in the text, not as math, so it renders literally
• Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow