Ratios and Proportions

A ratio is a comparison of two quantities by division. You can write equal ratios by multiplying or dividing each quantity by the same nonzero number.

Ways to Write a Ratio

Example 1

Write 3 1 3 : 1 2 3 , and 1 third , colon , 1 half as a ratio in simplest form.

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A rate is a ratio that compares different types of quantities. In simplest form for a rate, the second quantity is one unit.

Example 2

Write 247 mi in 5.2 h as a rate in simplest form.

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A proportion is a statement that two ratios are equal. You can find a missing term in a proportion by using the cross products.

Cross Products of a Proportion

Example 3

The Copy Center charges $2.52 for 63 copies. At that rate, how much will the Copy Center charge for 140 copies?

Exercises

Write each ratio or rate in simplest form.

1. 15 to 20
2. 85 : 34
3. 38 g in 4 oz
4. 375 mi in 4.3 h
5. 84 30 84 over 30

Solve each proportion. Round your answer to the nearest tenth, if necessary.

6. a 5 = 12 15 eh over 5 , equals , 12 over 15
7. 21 12 = 1 4 x 21 over 12 , equals , fraction 1 4 , over x end fraction
8. 8 : 15 = n : 25 8 colon 15 equals n colon 25
9. 2 . 4 : c = 4 : 3 2 . 4 colon c equals 4 colon 3
10. 17 8 = n 20 17 over 8 , equals , n over 20
11. 13 n = 20 3 13 over n , equals , 20 over 3
12. 5 : 7 = y : 5 5 colon 7 equals y colon 5
13. 0.4 3.5 = 5.2 x 0.4 over 3.5 , equals , 5.2 over x
14. 4 x = 7 6 4 over x , equals , 7 sixths
15. 4 : n = n : 9 4 colon n equals n colon 9
16. A canary's heart beats 130 times in 12 s. Use a proportion to find about how many times its heart beats in 50 s.

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