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# Converting Among Percents, Decimals, Fractions, and Percent Word Problems Study Guide (page 2)

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Updated on Apr 25, 2014

#### Example 2

What number is 10% of 80?

Read and understand the question. This question is looking for 10% of a number.

Make a plan. Use the proportion . This question gives the value 10%, so place 10 over 100. The number after the word of is 80, so 80 is the whole. The phrase what number appears before the word is, so x is the part.

Carry out the plan. Set up the proportion. . Cross multiply to get 100x = 800. Divide each side of the equation by 100.

• x = 8

Eight is 10% of 80.

Check your answer. Substitute the solution into the proportion to check this answer. The proportion is . The cross products are each 800, so this answer is checking.

#### Tip:

Another quick way to find the percent of a number is to change the percent to a decimal, and then multiply by the number. For example, to find 20% of 30, change 20% to a decimal and multiply: 0.20 × 30 = 6; 20% of 30 is 6.

#### Example 3

54 is 90% of what number?

Read and understand the question. This question is asking for a number when the part of the number is given.

Make a plan. Use the proportion . This question is looking for the whole (the number after the word of) so place x in the denominator of the first fraction. The number before the word is is 54, so 54 is the part, or the numerator of the first fraction. The percent given in the question is 90%, so place 90 over 100 in the proportion.

Carry out the plan. Set up the proportion. . Cross multiply to get 90x = 5,400. Divide each side of the equation by 90.

• x = 60

54 is 90% of 60.

Check your answer. Check this solution by finding 90% of 60. This is equal to 0.90 × 60 = 54, so this problem is checking.

Find practice problems and solutions for these concepts at Converting Among Percents, Decimals, Fractions, and Percent Word Problems Practice Questions.

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