Common Fraction and Decimal Equivalents in Business Math
How to Increase and Reduce the Terms of Fractions
How to Convert an Improper Fraction to a Mixed Number

Ratios and Proportions

A ratio is a mathematical comparison of two numbers, based on division. For example, suppose you bring 2 scarves and 3 caps with you on a ski vacation. Here are a few ways to express the ratio of scarves to caps:

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The simplest way to work with a ratio is to turn it into a fraction. Be sure to keep the order the same: The first number goes on top of the fraction, and the second number goes on the bottom.

In practice, a ratio is most useful when used to set up a proportion — that is, an equation involving two ratios. Typically, a proportion looks like a word equation, as follows:

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For example, suppose you know that both you and your friend Andrew brought the same proportion of scarves to caps. If you also know that Andrew brought 8 scarves, you can use this proportion to find out how many caps he brought. Just increase the terms of the fraction

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so that the numerator becomes 8. Do this in two steps:

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As you can see, the ratio 8:12 is equivalent to the ratio 2:3 because the fractions

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are equal. Therefore, Andrew brought 12 caps.

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