Fractions as Percents

Convert fractions to percents.

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Fractions as Percents
Credit: Moyan Brenn
Source: https://www.flickr.com/photos/aigle_dore/5824868343

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.

Writing Fractions as Percents

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

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

\begin{align*}47\%\end{align*}

\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 \begin{align*}\frac{2}{5}\end{align*} as a percent.

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

\begin{align*}\frac{2}{5} = \frac{}{100}\end{align*}

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.”

\begin{align*}\begin{array}{rcl} 2 \times 20 & = & 40\\ \frac{2}{5} & = & \frac{40}{100} \end{array}\end{align*}

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

\begin{align*}40\%\end{align*}

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

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

\begin{align*}\frac{1}{3} = \frac{}{100}\end{align*}

Converting \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.

\begin{align*}100 \div 3 = 0.3333333\ldots\end{align*}

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

Examples

Example 1

Earlier, you were given a problem about 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 \begin{align*}\frac{325}{500}\end{align*} with the denominator of 100.

\begin{align*}\frac{325}{500} = \frac{}{100}\end{align*}

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

\begin{align*}\begin{array}{rcl} 500 \div 5 & = & 100\\ 325 \div 5 & = & 65\\ \frac{325}{500} & = & \frac{65}{100} \end{array}\end{align*}

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

\begin{align*}65\%\end{align*}

Sam has traveled 65% of the total trip.

Example 2

Write the fraction as a percent.

\begin{align*}\frac{23}{50}\end{align*}

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

\begin{align*}\frac{23}{50}=\frac{}{100}\end{align*}

Then, find the unknown numerator.

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

\begin{align*}\frac{23}{50} = \frac{46}{100}\end{align*}

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

\begin{align*}46\%\end{align*}

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

Example 3

Write the fraction as a percent.\begin{align*}\frac{48}{100}\end{align*}

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

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

Example 4

Write the fraction as a percent.

\begin{align*}\frac{82}{100}\end{align*}

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

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

Example 5

Write the fraction as a percent.

\begin{align*}\frac{91}{100}\end{align*}

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

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

Review

Write each fraction as a percent.

1. \begin{align*}\frac{4}{100}\end{align*}
2. \begin{align*}\frac{24}{100}\end{align*}
3. \begin{align*}\frac{20}{100}\end{align*}
4. \begin{align*}\frac{76}{100}\end{align*}
5. \begin{align*}\frac{61}{100}\end{align*}
6. \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*}

To see the Review answers, open this PDF file and look for section 8.14.

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Vocabulary Language: English

TermDefinition
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 means equal in value or meaning.
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.