<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

Fractions as Percents

Convert fractions to percents.

Atoms Practice
Estimated5 minsto complete
%
Progress
Practice Fractions as Percents
Practice
Progress
Estimated5 minsto complete
%
Practice Now
Fractions as Percents

Let’s Think About It

License: CC BY-NC 3.0

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

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*}47100 as a percent.

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

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

47%

\begin{align*}\frac{47}{100}\end{align*}47100 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*}25 as a percent.

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

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

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.”

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

2×2025==4040100

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*}

40%

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

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

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

13=100

Converting \begin{align*}\frac{1}{3}\end{align*}13 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*}

100÷3=0.3333333

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

Guided Practice

Write the fraction as a percent.

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

2350

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

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

2350=100

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*}

2350=46100

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*}

46%

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

Examples

Write the following fractions as a percent.

Example 1

\begin{align*}\frac{48}{100}\end{align*}

48100

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

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

Example 2

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

82100

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

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

Example 3

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

91100

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

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

Follow Up

License: CC BY-NC 3.0

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 \begin{align*}\frac{325}{500}\end{align*}325500 with the denominator of 100.

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

325500=100

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*}

500÷5325÷5325500===1006565100

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*}

65%

Sam has traveled 65% of the total trip.

Video Review

http://www.youtube.com/watch?v=-gB1y-PMWfs

http://www.youtube.com/watch?v=aUJ-4oD9Oe8

Explore More

Write each fraction as a percent.

  1. \begin{align*}\frac{4}{100}\end{align*}4100
  2. \begin{align*}\frac{24}{100}\end{align*}24100
  3. \begin{align*}\frac{20}{100}\end{align*}20100
  4. \begin{align*}\frac{76}{100}\end{align*}76100
  5. \begin{align*}\frac{61}{100}\end{align*}61100
  6. \begin{align*}\frac{1}{4}\end{align*}14
  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

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.

Image Attributions

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

Explore More

Sign in to explore more, including practice questions and solutions for Fractions as Percents.

Reviews

Please wait...
Please wait...

Original text