## Percent

**Percent**

A percent is a ratio of a number to 100. Percent means “per hundred.” Thus, 20 percent, or 20%, means . A percent can be written as a fraction or a decimal.

To change a fraction to a percent, find an equivalent fraction with a denominator of 100. To change a percent to a fraction, use the given percent as the numerator of a fraction and 100 as the denominator and then reduce the fraction.

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To change a percent to a decimal, use the given percent as the numerator of a fraction and 100 as the denominator and then write the fraction as a decimal. To change a decimal to a percent, write the decimal as a fraction with 100 as the denominator and then write the fraction as a percent.

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Another way to change a percent to a decimal is to write the percent amount and move the decimal point 2 places to the left. To change a decimal to a percent, write the decimal, move the decimal point 2 places to the right, and add the percent sign.

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Sometimes a zero must be appended to change a percent to a decimal or to change a decimal to a percent.

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Another way to change a fraction to a percent is to divide the numerator by the denominator and then change the resulting decimal to a percent.

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Comparisons of fractions, decimals, and percents can be made in several ways including locating each on a number line, rewriting each as a fraction with a common denominator, or rewriting each as a decimal or as a percent.

To find a percent of a number, first change the percent to either a fraction or a decimal and then multiply the given number by that fraction or decimal. The percent of a number can also be found by writing the percent as a fraction and then finding an equivalent fraction with the given number as the denominator.

To find what percent one number is of another number, write the two numbers as a fraction, with the whole as the denominator. Then find an equivalent ratio with a denominator of 100 and write that ratio as a percent. Equivalent ratios are also used to compare ratios.

In later grades, students will learn to use the percent equation, which is usually set up as “whole × percent = part.” Since a percent can be written either as a fraction or as a decimal this equation can have two general forms, where n is the percent amount, x is the part, and w is the whole. w × 0.01n = x or w × = x.

**Teaching Model 19.3:** Compare Fractions, Decimals, and Percents