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Converting Among Percents, Decimals, Fractions, and Percent Word Problems Study Guide

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Updated on Apr 25, 2014

Introduction to Converting Among Percents, Decimals, Fractions, and Percent Word Problems

It is a mathematical fact that fifty percent of all doctors graduate in the bottom half of their class.

—AUTHOR UNKNOWN

In this lesson, you will review converting among percents, decimals, and fractions, as well as how to apply percents in word problems.

A percent is the ratio of a number compared to 100. Percents are written with the percent symbol. For example, the ratio 12 out of 100 or is written as 12%.

It is helpful to know how to change values among percent form, fraction form, and decimal form.

Changing from a Percent to a Fraction

To change a percent to fraction form, write the percent as a number over 100. The percent 79% is equal to . The percent 15% is equal to in simplest form.

Changing from a Fraction to a Percent

To change a fraction to a percent, set the fraction equal to and cross multiply. The fraction can be changed to a percent by setting up the proportion . Cross multiply to get 25x = 400. Divide each side of the equation by 25.

  • x = 16

 

Tip:

Another way to change a fraction to a percent is to change the fraction to decimal form, and then multiply by 100. For example, to change to a percent, divide the numerator by the denominator: 1 ÷ 4 = 0.25. Next, multiply this decimal by 100 and write the percent symbol after the number: 0.25 × 100 = 25%.

Changing a Percent to a Decimal and a Decimal to a Percent

Percent to Decimal

To change a percent to a decimal, divide the percent by 100 and take away the percent symbol. For example, the percent 65% is equal to 65 ÷ 100 = 0.65. The percent 3% is equal to 3 ÷ 100 = 0.03.

Decimal to a Percent

To change a decimal to a percent, simply multiply the decimal by 100 and write the percent symbol after the number. The decimal 0.43 is equal to 0.43 × 100 = 43%. The decimal 2.34 is equal to 2.34 × 100 = 234%.

 

Tip:

Here's a quick way to convert between decimals and percents. When you are changing from a decimal to a percent, move the decimal point two places to the right: 0.45 = 45%.

When you are changing from a percent to a decimal, move the decimal point two places to the left: 64% = 0.64.

Percent Word Problems

Many percent word problems can be solved by using the proportion . When you are using these proportions, the number in the question with the percent symbol or the word percent is placed over 100. The number after the word of is the whole, or the denominator of the first fraction. The number that is usually closer to the word is is the part, or the numerator of the first fraction.

Read the following examples to help apply this strategy for certain percent word problems.

Example 1

What percent is 30 of 120?

Read and understand the question. This question is asking for the percent that one number is of another number.

Make a plan. Use the proportion . This question is looking for the percent, so place x over 100. The number after the word of is 120, so 120 is the whole. The number after the word is is 30, so 30 is the part.

Carry out the plan. Set up the proportion: . Cross multiply to get 120x = 3,000. Divide each side of the equation by 120.

  • x = 25%

Thirty out of 120 is equal to 25%.

Check your answer. Substitute the solution into the proportion to check this answer. The proportion is . The cross products are each 3,000, so this answer is checking.

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