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Copyright © Cengage Learning. All rights reserved. 7 Ratio and Proportion Functions Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved. 7.1 Ratio Copyright © Cengage Learning. All rights reserved.

Ratio The comparison of two numbers is a very important concept, and one of the most important of all comparisons is the ratio. The ratio of two numbers, a and b, is the first number divided by the second number. Ratios may be written in several different ways. For example, the ratio of 3 to 4 may be written as , 3/4, 3 : 4, or 3  4. Each form is read “the ratio of 3 to 4.”

Ratio If the quantities to be compared include units, the units should be the same whenever possible. To find the ratio of 1 ft to 15 in., first express both quantities in inches and then find the ratio: Ratios are usually given in lowest terms. To find the ratio of two fractions, use the technique for dividing fractions.

Example 4 Express the ratio in lowest terms.

Ratio In a ratio, we compare like or related quantities; for example, A ratio simplified into its lowest terms is a pair of unitless numbers. Suppose you drive 75 miles and use 3 gallons of gasoline. Your mileage would be found as follows:

Ratio We say that your mileage is 25 miles per gallon. Note that each of these two fractions compares unlike quantities: miles and gallons. A rate is the comparison of two unlike quantities whose units do not cancel.