5.5: Ratios and Proportions
- Page ID
- 129556
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After completing this section, you should be able to:
- Construct ratios to express comparison of two quantities.
- Use and apply proportional relationships to solve problems.
- Determine and apply a constant of proportionality.
- Use proportions to solve scaling problems.
Ratios and proportions are used in a wide variety of situations to make comparisons. For example, using the information from Figure 5.15, we can see that the number of Facebook users compared to the number of Twitter users is 2,006 M to 328 M. Note that the "M" stands for million, so 2,006 million is actually 2,006,000,000 and 328 million is 328,000,000. Similarly, the number of Qzone users compared to the number of Pinterest users is in a ratio of 632 million to 175 million. These types of comparisons are ratios.
Constructing Ratios to Express Comparison of Two Quantities
Note there are three different ways to write a ratio, which is a comparison of two numbers that can be written as: /**/(\$ 1 =0.82\,{€})/**/, how many dollars should you receive? Round to the nearest cent if necessary.
Example 5.31
Solving a Proportion Involving Weights on Different Planets
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.
- Answer
Step 1: Set up the two ratios into a proportion. Notice the Earth weights are both in the numerator and the Mars weights are both in the denominator.
Step 2: Cross multiply, and then divide to solve.
So the 1,000-pound horse would weigh about 376.5 pounds on Mars.
Your Turn 5.31
Example 5.32
Solving a Proportion Involving Baking
A cookie recipe needs /**/1{\text{ inch}} =/**/ how many miles). Then use that scale to determine the approximate lengths of the other borders of the state of Wyoming.
Example 5.38
Solving a Scaling Problem Involving Model Cars
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.
- Answer
The scale tells us that 1 inch of the model car is equal to 24 inches (2 feet) on the real automobile. So set up the two ratios into a proportion. Notice that the model lengths are both in the numerator and the NASCAR automobile lengths are both in the denominator.
This amount (216) is in inches. To convert to feet, divide by 12, because there are 12 inches in a foot (this conversion from inches to feet is really another proportion!). The final answer is:
The NASCAR automobile is 18 feet long.
Your Turn 5.38
Check Your Understanding
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625 | 6,250 | 3,456 | 345.6 | None of these |
Section 5.4 Exercises
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Receipt | 1 | 2 | 3 | 4 |
Ounces | 128 | 460 | /**/b/**/ | 541 |
Cost | $163.84 | /**/a/**/ | $277.76 | /**/c/**/ |