7
Ratio and
Proportion
Functions
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.”
3
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.
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Example 4
Express the ratio
in lowest terms.
5
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:
6
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.
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