3 0–A R I T H M E T I C–RATIOSA RATIOIS A COMPARISON OF TWO OR MORE NUMBERS WITH THE SAME UNIT LABEL

15.3 0

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A R I T H M E T I C

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RatiosA ratiois a comparison of two or more numbers with the same unit label. A ratio can be written in three ways:a:bato b

a

or

b

A rateis similar to a ratio except that the unit labels are different. For example, the expression 50 milesper hour is a rate—50 miles/1 hour.ProportionTwo ratios set equal to each other is called a proportion. To solve a proportion, cross-multiply.

4

5

¹⁰

x

Cross multiply to get:4x50

4x

4

⁵⁰

4

x12

¹

2

PercentA ratio that compares a number to 100 is called a percent.To change a decimal to a percent, move the decimal two places to the right..25 = 25%.105 = 10.5%.3 = 30%To change a percent to a decimal, move the decimal two places to the left.36% = .36125% = 1.258% = .08Some word problems that use percents are commission and rate-of-change problems, which includesales and interest problems. The general proportion that can be set up to solve this type of word problem is

Part

, although more specific proportions will also be shown.

Whole

100

^%

3 3 2

C

^OMMISSION

John earns 4.5% commission on all of his sales. What is his commission if his sales total $235.12?To find the part of the sales John earns, set up a proportion:partoriginal cost %whole change100

x