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# Percents as Fractions

## Write percents as fractions and simplify.

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Percents as Fractions

### License: CC BY-NC 3.0 [Figure1]

Shane’s favorite store is having a blowout sale. The sign says everything is 60% off. He finds a jacket that was originally 150. What fraction of the price will he need to pay if he wants to buy it? How much is the jacket? In this concept, you will learn how to convert percents as fractions. ### Writing Percents as Fractions Percents and fractions are parts of a whole. A percentage is a quantity out of 100. A fraction can also represent a quantity out of 100. Compare 44% and 44100\begin{align*}\frac{44}{100}\end{align*}. 44% is 44 out of 100. The faction 44100\begin{align*}\frac{44}{100}\end{align*} also is the ratio of 44 out of 100. Both ratios compare the number 44 to 100. A percent can be converted to a fraction by writing the number over 100. The number is placed in the numerator and 100 is the denominator. Let’s look at 7%. 7 percent is the ratio of 7 out of 100. First, remember that a percent is written as a quantity over 100. Then, write 7 in the numerator and 100 in the denominator. 7100\begin{align*}\frac{7}{100}\end{align*} 7% is written as 7100\begin{align*}\frac{7}{100}\end{align*}. ### Examples #### Example 1 Earlier, you were given a problem about Shane at the blowout sale. He wants a150 jacket that is 60% off. To find the fraction of the price he needs to pay, he has to first fine the percentage he needs to pay and convert it to a fraction.

First, find the percentage that he needs to pay. Subtract 60% from 100%.

100%60%=40%\begin{align*}100\% - 60\%=40\%\end{align*}

Then, convert 40% to a fraction. 40% is the same as 40 out of 100. The numerator is 40 and the denominator is 100.

40100\begin{align*}\frac{40}{100}\end{align*}

If Shane wants to buy the jacket, he will need to pay 40100\begin{align*}\frac{40}{100}\end{align*} of the original price. To find the sale price, multiply the original price by the fraction 40100\begin{align*}\frac{40}{100}\end{align*}.

150×40100=sale price\begin{align*}\150 \times \frac{40}{100} = \text{sale price}\end{align*} But first, look at the fraction 40100\begin{align*}\frac{40}{100}\end{align*}. It can be simplified by dividing the numerator and denominator by 20 to find an equivalent ratio that is easier to multiply. Remember, equivalent ratios have the same value. 40÷20100÷20=25\begin{align*}\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\end{align*} Now, find the sale price. Multiply the original price by 25\begin{align*}\frac{2}{5}\end{align*}.150×25=60\begin{align*}\150 \times \frac{2}{5} = \ 60\end{align*} The sale price of the jacket is60.

#### Example 2

Write 95% as a fraction.

First, think of 95% as “95 out of 100.” 95 is the part out of 100.

Then, write 95 as the numerator over the denominator 100.

95100\begin{align*}\frac{95}{100}\end{align*}

95% is written as 95100\begin{align*}\frac{95}{100}\end{align*}.

Write the following percents as a fraction.

#### Example 3

Write 68% as a fraction.

First, think of 68% as “68 out of 100.” 68 is the part out of 100.

Then, write 68 as the numerator over the denominator 100.

68100\begin{align*}\frac{68}{100}\end{align*}

68% is written as 68100\begin{align*}\frac{68}{100}\end{align*}.

#### Example 4

Write 13% as a fraction.

First, think of 13% as “13 out of 100.” 13 is the part out of 100.

Then, write 13 as the numerator over the denominator 100.

13100\begin{align*}\frac{13}{100}\end{align*}

13% is written as 13100\begin{align*}\frac{13}{100}\end{align*}.

#### Example 5

Write 21% as a fraction.

First, think of 21% as “21 out of 100.” 21 is the part out of 100.

Then, write 21 as the numerator over the denominator 100.

21100\begin{align*}\frac{21}{100}\end{align*}

21% is written as 21100\begin{align*}\frac{21}{100}\end{align*}.

### Review

Write the following percents as a fraction.

1. 54%
2. 11%
3. 6%
4. 12%
5. 89%
6. 83%
7. 19%
8. 4%
9. 9%
10. 18%
11. 89%
12. 100%
13. 23%
14. 77%
15. 98%
16. 2%

To see the Review answers, open this PDF file and look for section 8.12.

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### Vocabulary Language: English

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

Percent

Percent means out of 100. It is a quantity written with a % sign.