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5.6 Ratios and Rate

Comparing two quantities as a fraction, rates that pair unlike units, unit rates scaled to one, and unit price for comparing package sizes.

Prealgebra 2e, 5.6 Ratios and Rate

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79 exercises

5.6 Exercise 1

Before you get started, take this readiness quiz.

Simplify: 1624.\frac{16}{24} .
If you missed this problem, review the reference.

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5.6 Exercise 2

Divide: 2.76÷11.5.2.76 \div 11.5 .
If you missed this problem, review the reference.

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5.6 Exercise 3

Simplify: 112234.\frac{1 \frac{1}{2}}{2 \frac{3}{4}} .
If you missed this problem, review the reference.

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5.6 Exercise 4

Write each ratio as a fraction: ⓐ 15to2715 \text{to} 27ⓑ 45to18.45 \text{to} 18 .

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5.6 Exercise 5

Write each ratio as a fraction: ⓐ 21to5621 \text{to} 56ⓑ 48to32.48 \text{to} 32 .

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5.6 Exercise 6

Write each ratio as a fraction: ⓐ 27to7227 \text{to} 72ⓑ 51to34.51 \text{to} 34 .

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5.6 Exercise 7

Write each ratio as a fraction of whole numbers:

  1. ⓐ 4.8to11.24.8 \text{to} 11.2
  2. ⓑ 2.7to0.542.7 \text{to} 0.54
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5.6 Exercise 8

Write each ratio as a fraction: ⓐ 4.6to11.54.6 \text{to} 11.5ⓑ 2.3to0.69.2.3 \text{to} 0.69 .

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5.6 Exercise 9

Write each ratio as a fraction: ⓐ 3.4to15.33.4 \text{to} 15.3ⓑ 3.4to0.68.3.4 \text{to} 0.68 .

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5.6 Exercise 10

Write the ratio of 114to2381 \frac{1}{4} \text{to} 2 \frac{3}{8} as a fraction.

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5.6 Exercise 11

Write each ratio as a fraction: 134to258.1 \frac{3}{4} \text{to} 2 \frac{5}{8} .

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5.6 Exercise 12

Write each ratio as a fraction: 118to234.1 \frac{1}{8} \text{to} 2 \frac{3}{4} .

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5.6 Exercise 13

Hector's total cholesterol is 249249 mg/dl and his HDL cholesterol is 3939 mg/dl. ⓐ Find the ratio of his total cholesterol to his HDL cholesterol. ⓑ Assuming that a ratio less than 55 to 11 is considered good, what would you suggest to Hector?

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5.6 Exercise 14

Find the patient's ratio of total cholesterol to HDL cholesterol using the given information.

Total cholesterol is 185185 mg/dL and HDL cholesterol is 4040 mg/dL.

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5.6 Exercise 15

Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information.

Total cholesterol is 204204 mg/dL and HDL cholesterol is 3838 mg/dL.

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5.6 Exercise 16

The Americans with Disabilities Act (ADA) Guidelines for wheel chair ramps require a maximum vertical rise of 11 inch for every 11 foot of horizontal run. What is the ratio of the rise to the run?

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5.6 Exercise 17

Find the ratio of the first length to the second length: 3232 inches to 11 foot.

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5.6 Exercise 18

Find the ratio of the first length to the second length: 11 foot to 5454 inches.

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5.6 Exercise 19

Bob drove his car 525525 miles in 99 hours. Write this rate as a fraction.

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5.6 Exercise 20

Write the rate as a fraction: 492492 miles in 88 hours.

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5.6 Exercise 21

Write the rate as a fraction: 242242 miles in 66 hours.

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5.6 Exercise 22

Anita was paid $384\$\text{384} last week for working 32 hours.\text{32 hours} . What is Anita’s hourly pay rate?

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5.6 Exercise 23

Find the unit rate: $630\$\text{630} for 3535 hours.

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5.6 Exercise 24

Find the unit rate: $684\$\text{684} for 3636 hours.

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5.6 Exercise 25

Sven drives his car 455455 miles, using 1414 gallons of gasoline. How many miles per gallon does his car get?

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5.6 Exercise 26

Find the unit rate: 423423 miles to 1818 gallons of gas.

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5.6 Exercise 27

Find the unit rate: 406406 miles to 14.514.5 gallons of gas.

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5.6 Exercise 28

The grocery store charges $3.99\$\text{3}.\text{99} for a case of 2424 bottles of water. What is the unit price?

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5.6 Exercise 29

Find the unit price. Round your answer to the nearest cent if necessary.

24-pack\text{24}-\text{pack} of juice boxes for $6.99\$\text{6}.\text{99}

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5.6 Exercise 30

Find the unit price. Round your answer to the nearest cent if necessary.

24-pack\text{24}-\text{pack} of bottles of ice tea for $12.72\$\text{12}.\text{72}

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5.6 Exercise 31

Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at $14.99\$\text{14}.\text{99} for 6464 loads of laundry and the same brand of powder detergent is priced at $15.99\$\text{15}.\text{99} for 8080 loads.

Which detergent has the lowest cost per load?

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5.6 Exercise 32

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand A Storage Bags, $4.59\$\text{4}.\text{59} for 4040 count, or Brand B Storage Bags, $3.99\$\text{3}.\text{99} for 3030 count

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5.6 Exercise 33

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand C Chicken Noodle Soup, $1.89\$\text{1}.\text{89} for 2626 ounces, or Brand D Chicken Noodle Soup, $0.95\$\text{0}.\text{95} for 10.7510.75 ounces

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5.6 Exercise 34

Translate the word phrase into an algebraic expression:

  1. ⓐ 427427 miles per hh hours
  2. ⓑ xx students to 33 teachers
  3. ⓒ yy dollars for 1818 hours
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5.6 Exercise 35

Translate the word phrase into an algebraic expression.

ⓐ 689689 miles per hh hours ⓑ yy parents to 2222 students ⓒ dd dollars for 99 minutes

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5.6 Exercise 36

Translate the word phrase into an algebraic expression.

ⓐ mm miles per 99 hours ⓑ xx students to 88 buses ⓒ yy dollars for 4040 hours

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5.6 Exercise 37

Write each ratio as a fraction.

2020 to 3636

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5.6 Exercise 39

Write each ratio as a fraction.

4242 to 4848

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5.6 Exercise 41

Write each ratio as a fraction.

4949 to 2121

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5.6 Exercise 43

Write each ratio as a fraction.

8484 to 3636

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5.6 Exercise 45

Write each ratio as a fraction.

0.560.56 to 2.82.8

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5.6 Exercise 47

Write each ratio as a fraction.

1231 \frac{2}{3} to 2562 \frac{5}{6}

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5.6 Exercise 49

Write each ratio as a fraction.

4164 \frac{1}{6} to 3133 \frac{1}{3}

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5.6 Exercise 51

Write each ratio as a fraction.

$18\$\text{18} to $63\$\text{63}

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5.6 Exercise 53

Write each ratio as a fraction.

$1.21\$\text{1}.\text{21} to $0.44\$\text{0}.\text{44}

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5.6 Exercise 55

Write each ratio as a fraction.

2828 ounces to 8484 ounces

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5.6 Exercise 57

Write each ratio as a fraction.

1212 feet to 4646 feet

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5.6 Exercise 59

Write each ratio as a fraction.

246246 milligrams to 4545 milligrams

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5.6 Exercise 61

Write each ratio as a fraction.

total cholesterol of 175175 to HDL cholesterol of 4545

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5.6 Exercise 63

Write each ratio as a fraction.

2727 inches to 11 foot

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5.6 Exercise 65

Write each rate as a fraction.

140140 calories per 1212 ounces

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5.6 Exercise 67

Write each rate as a fraction.

8.28.2 pounds per 33 square inches

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5.6 Exercise 69

Write each rate as a fraction.

488488 miles in 77 hours

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5.6 Exercise 71

Write each rate as a fraction.

$595\$\text{595} for 4040 hours

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5.6 Exercise 73

Find the unit rate. Round to two decimal places, if necessary.

140140 calories per 1212 ounces

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5.6 Exercise 75

Find the unit rate. Round to two decimal places, if necessary.

8.28.2 pounds per 33 square inches

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5.6 Exercise 77

Find the unit rate. Round to two decimal places, if necessary.

488488 miles in 77 hours

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5.6 Exercise 79

Find the unit rate. Round to two decimal places, if necessary.

$595\$\text{595} for 4040 hours

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5.6 Exercise 81

Find the unit rate. Round to two decimal places, if necessary.

576576 miles on 1818 gallons of gas

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5.6 Exercise 83

Find the unit rate. Round to two decimal places, if necessary.

4343 pounds in 1616 weeks

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5.6 Exercise 85

Find the unit rate. Round to two decimal places, if necessary.

4646 beats in 0.50.5 minute

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5.6 Exercise 87

Find the unit rate. Round to two decimal places, if necessary.

The bindery at a printing plant assembles 96,00096,000 magazines in 1212 hours. How many magazines are assembled in one hour?

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5.6 Exercise 89

Find the unit price. Round to the nearest cent.

Soap bars at 88 for $8.69\$\text{8}.\text{69}

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5.6 Exercise 91

Find the unit price. Round to the nearest cent.

Women’s sports socks at 66 pairs for $7.99\$\text{7}.\text{99}

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5.6 Exercise 93

Find the unit price. Round to the nearest cent.

Snack packs of cookies at 1212 for $5.79\$\text{5}.\text{79}

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5.6 Exercise 95

Find the unit price. Round to the nearest cent.

CD-RW discs at 2525 for $14.99\$\text{14}.\text{99}

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5.6 Exercise 97

Find the unit price. Round to the nearest cent.

The grocery store has a special on macaroni and cheese. The price is $3.87\$\text{3}.\text{87} for 33 boxes. How much does each box cost?

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5.6 Exercise 99

Find each unit price and then identify the better buy. Round to three decimal places.

Mouthwash, 50.7-ounce\text{50}.\text{7}-\text{ounce} size for $6.99\$\text{6}.\text{99} or 33.8-ounce\text{33}.\text{8}-\text{ounce} size for $4.79\$\text{4}.\text{79}

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5.6 Exercise 101

Find each unit price and then identify the better buy. Round to three decimal places.

Breakfast cereal, 1818 ounces for $3.99\$\text{3}.\text{99} or 1414 ounces for $3.29\$\text{3}.\text{29}

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5.6 Exercise 103

Find each unit price and then identify the better buy. Round to three decimal places.

Ketchup, 40-ounce\text{40}-\text{ounce} regular bottle for $2.99\$\text{2}.\text{99} or 64-ounce\text{64}-\text{ounce} squeeze bottle for $4.39\$\text{4}.\text{39}

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5.6 Exercise 105

Find each unit price and then identify the better buy. Round to three decimal places.

Cheese $6.49\$\text{6}.\text{49} for 11 lb. block or $3.39\$\text{3}.\text{39} for 12\frac{1}{2} lb. block

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5.6 Exercise 107

Translate the English phrase into an algebraic expression.

793793 miles per pp hours

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5.6 Exercise 109

Translate the English phrase into an algebraic expression.

$3\$\text{3} for 0.50.5 lbs.

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5.6 Exercise 111

Translate the English phrase into an algebraic expression.

105105 calories in xx ounces

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5.6 Exercise 113

Translate the English phrase into an algebraic expression.

the ratio of yy and 5x5 x

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5.6 Exercise 115

One elementary school in Ohio has 684684 students and 4545 teachers. Write the student-to-teacher ratio as a unit rate.

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5.6 Exercise 117

A popular fast food burger weighs 7.57.5 ounces and contains 540540 calories, 2929 grams of fat, 4343 grams of carbohydrates, and 2525 grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce. Round to two decimal places.

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5.6 Exercise 119

Would you prefer the ratio of your income to your friend’s income to be 3/1\text{3}/\text{1} or 1/3?1/3 ? Explain your reasoning.

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5.6 Exercise 121

Kathryn ate a 4-ounce4-ounce cup of frozen yogurt and then went for a swim. The frozen yogurt had 115115 calories. Swimming burns 422422 calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.