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# Fractions as Percents

## Convert fractions to percents.

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Fractions as Percents

Sam is on his way to the Grand Canyon. He calculates that the Grand Canyon is about 500 miles from his house. He takes a break at a rest stop and checks the odometer in his car. So far he has traveled 325 miles. What percent of the total trip to the Grand Canyon has Sam traveled so far?

In this concept, you will learn to convert fractions to percents.

### Guidance

A percent is part of a whole where the whole is 100. Percents can be written as fractions by removing the percent symbol and writing the number over the denominator of 100.

To write 14% as a fraction, take the number and write it as the quantity over a fraction with the denominator 100.

14% is 14100\begin{align*}\frac{14}{100}\end{align*}.

Fractions with a denominator of 100 can also be written as a percent by doing the reverse.

Write 47100\begin{align*}\frac{47}{100}\end{align*} as a percent.

Remove the fraction bar and denominator and add the percent symbol.

47%

47100\begin{align*}\frac{47}{100}\end{align*} is written as 47%.

Fractions with a denominator other than 100 can still be written as a percent. A fraction can be rewritten with a denominator of 100 using equivalent fractions. The equivalent fraction can then be converted to a percent.

Let’s write 25\begin{align*}\frac{2}{5}\end{align*} as a percent.

First, write a proportion to find the equivalent fraction of 25\begin{align*}\frac{2}{5}\end{align*} with the denominator of 100.

25=100

Next, cross-multiply or use mental math to find the unknown numerator.

Think, “100 divided by 5 is 2. I can multiply 2 by 20 to get the equivalent numerator.”

2×2025==4040100

Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.

40%

25\begin{align*}\frac{2}{5}\end{align*} is written as 40%.

One special fraction remember is 13\begin{align*}\frac{1}{3}\end{align*}.

13=100

Converting 13\begin{align*}\frac{1}{3}\end{align*} to a percent is a little tricky because 3 does not divide evenly into 100. The result is a repeating decimal.

100÷3=0.3333333

Instead, remember that 13\begin{align*}\frac{1}{3}\end{align*} is written as 3313%\begin{align*}33\frac{1}{3}\%\end{align*}, read as “thirty three and one-third percent.”

### Guided Practice

Write the fraction as a percent.

2350

First, write a proportion to find the equivalent fraction of 2350\begin{align*}\frac{23}{50}\end{align*} with the denominator of 100.

2350=100

Then, find the unknown numerator.

Think, “50 is half of 100. 23 is half of 46.”

2350=46100

Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.

46%

2350\begin{align*}\frac{23}{50}\end{align*} is written as 46%.

### Examples

Write the following fractions as a percent.

#### Example 1

48100

Remove the fraction bar and denominator and add the percent symbol.

The answer is 48100\begin{align*}\frac{48}{100}\end{align*} is 48%.

#### Example 2

82100

Remove the fraction bar and denominator and add the percent symbol.

The answer is 82100\begin{align*}\frac{82}{100}\end{align*} is 82%.

#### Example 3

91100

Remove the fraction bar and denominator and add the percent symbol.

The answer is 91100\begin{align*}\frac{91}{100}\end{align*} is 91%.

Remember Sam on his way to the Grand Canyon?

Sam has traveled 325 miles on a 500 mile journey to the Grand Canyon. To find the percent he has traveled so far, Sam can write the ratio of the miles traveled to the total miles as a percent.

First, write a proportion to find the equivalent fraction of 325500\begin{align*}\frac{325}{500}\end{align*} with the denominator of 100.

325500=100

Next, solve the proportion to find the unknown quantity. Divide the numerator and denominator by 5.

500÷5325÷5325500===1006565100

Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.

65%

Sam has traveled 65% of the total trip.

### Explore More

Write each fraction as a percent.

1. 4100\begin{align*}\frac{4}{100}\end{align*}
2. 24100\begin{align*}\frac{24}{100}\end{align*}
3. 20100\begin{align*}\frac{20}{100}\end{align*}
4. 76100\begin{align*}\frac{76}{100}\end{align*}
5. 61100\begin{align*}\frac{61}{100}\end{align*}
6. 14\begin{align*}\frac{1}{4}\end{align*}
7. \begin{align*}\frac{3}{4}\end{align*}
8. \begin{align*}\frac{3}{6}\end{align*}
9. \begin{align*}\frac{2}{5}\end{align*}
10. \begin{align*}\frac{4}{5}\end{align*}
11. \begin{align*}\frac{8}{10}\end{align*}
12. \begin{align*}\frac{6}{10}\end{align*}
13. \begin{align*}\frac{6}{50}\end{align*}
14. \begin{align*}\frac{3}{25}\end{align*}
15. \begin{align*}\frac{20}{50}\end{align*}

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 8.14.

### Vocabulary Language: English

Decimal

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).
Equivalent

Equivalent

Equivalent means equal in value or meaning.
fraction

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

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

1. [1]^ License: CC BY-NC 3.0
2. [2]^ License: CC BY-NC 3.0

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