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5.4 Ratios and Proportions

Comparing two quantities as a ratio, solving a proportion by cross multiplication, the constant of proportionality, and scaling maps and models.

Contemporary Mathematics, 5.4 Ratios and Proportions

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10 exercises

5.4 Exercise 1

The Euro (€) is the most common currency used in Europe. Twenty-two nations, including Italy, France, Germany, Spain, Portugal, and the Netherlands use it. On June 9, 2021, 1 U.S. dollar was worth 0.82 Euros. Write this comparison as a ratio.

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5.4 Exercise 3

The gravitational pull on various planetary bodies in our solar system varies. Because weight is the force of gravity acting upon a mass, the weights of objects is different on various planetary bodies than they are on Earth. For example, a person who weighs 200 pounds on Earth would weigh only 33 pounds on the moon! Write this comparison as a ratio.

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5.4 Exercise 5

You are going to take a trip to France. You have $520 U.S. dollars that you wish to convert to Euros. You know that 1 U.S. dollar is worth 0.82 Euros. How much money in Euros can you get in exchange for $520?

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5.4 Exercise 7

A person who weighs 170 pounds on Earth would weigh 64 pounds on Mars. How much would a typical racehorse (1,000 pounds) weigh on Mars? Round your answer to the nearest tenth.

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5.4 Exercise 9

A cookie recipe needs 2142 \frac{1}{4} cups of flour to make 60 cookies. Jackie is baking cookies for a large fundraiser; she is told she needs to bake 1,020 cookies! How many cups of flour will she need?

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5.4 Exercise 11

Isabelle has a part-time job. She kept track of her pay and the number of hours she worked on four different days, and recorded it in the table below. What is the constant of proportionality, or pay divided by hours? What does the constant of proportionality tell you in this situation?

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5.4 Exercise 13

Zac runs at a constant speed: 4 miles per hour (mph). One day, Zac left his house at exactly noon (12:00 PM) to begin running; when he returned, his clock said 4:30 PM. How many miles did he run?

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5.4 Exercise 15

Joe had a job where every time he filled a bucket with dirt, he was paid $2.50. One day Joe was paid $337.50. How many buckets did he fill that day?

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5.4 Exercise 17

While driving in Canada, Mabel quickly noticed the distances on the road signs were in kilometers, not miles. She knew the constant of proportionality for converting kilometers to miles was about 0.62—that is, there are about 0.62 miles in 1 kilometer. If the last road sign she saw stated that Montreal is 104 kilometers away, about how many more miles does Mabel have to drive? Round your answer to…

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5.4 Exercise 21

Die-cast NASCAR model cars are said to be built on a scale of 1:24 when compared to the actual car. If a model car is 9 inches long, how long is a real NASCAR automobile? Write your answer in feet.

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Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.