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Fractions as Percents

Convert fractions to percents.

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Fractions as Percents
License: CC BY-NC 3.0

Mica measures the screw he is using to build a shelf for his sports trophies. He discovers that it is \begin{align*}\frac{5}{8}\end{align*} of an inch. Mica wonders what percentage of an inch the screw measures. How can he convert this fraction to a percent?

In this concept, you will learn to write fractions as percents.

Writing Fractions as Percents

A fraction can be written as a percent if it has a denominator of 100. Sometimes, you will be given a fraction with a denominator of 100 and sometimes you will have to rewrite the fraction to have a denominator of 100 before you can write it as a percent.

\begin{align*}\frac{9}{100}\end{align*}

This fraction is already written with a denominator of 100, so you can just change it to a percent.

\begin{align*}\frac{9}{100}=9 \%\end{align*}

A proportion is two equal ratios. If a fraction does not have a denominator of 100, you can write a fraction equal to it that does have a denominator of 100 and then solve the proportion.

Let’s look at an example.

Write \begin{align*}\frac{3}{5}\end{align*} as a percent.

First, notice that the denominator is not 100. Therefore, you need to create a new fraction equivalent to this one with a denominator of 100.

Next, set up a proportion.

\begin{align*}\frac{3}{5}=\frac{x}{100}\end{align*}

Then, you can cross multiply to find the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 5x&=&300 \\ x&=&60 \\ \frac{3}{5}&=&\frac{60}{100} \end{array}\end{align*}

Now you have a fraction with a denominator of 100, and you can write it as a percent.

The answer is that the fraction \begin{align*}\frac{3}{5}\end{align*} is equal to \begin{align*}60 \%\end{align*}.

To work with an improper fraction, you have to think about what improper means. An improper fraction is greater than 1, so the percent would be greater than 100%. Sometimes you can have percents that are greater than 100%. Most often they are not, but it is important to understand how to work with a percent that is greater than 100%.

You already know some common fraction equivalents for percents. Think of 25 cents, 50 cents, and 75 cents.

License: CC BY-NC 3.0
 

.\begin{align*}\frac{1}{4}=25 \%\end{align*}25 cents means 25 cents out of a dollar, or 25% of a dollar. Since a quarter is 25 cents, 

.\begin{align*}\frac{1}{2}=50 \%\end{align*}50 cents means 50 cents out of a dollar, or 50% of a dollar. Since a half dollar is 50 cents, 

\begin{align*}\frac{3}{4}=75 \%\end{align*}75 cents means 75 cents out of a dollar, or 75% of a dollar. Since three quarters of a dollar is 75 cents, .

Let’s look at an example with a fraction that doesn‘t convert easily to a percent.

Write \begin{align*}\frac{2}{3}\end{align*}  as a percent.

First, set up the proportion. 

\begin{align*}\frac{2}{3}=\frac{x}{100}\end{align*}

Next, cross multiply to solve for the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 3x &=& 200 \\ x &=& 66.6 \end{array}\end{align*}

Notice that you end up with a decimal and it is a repeating decimal. If you keep dividing, you will keep ending up with 6s. Therefore, you can leave this percent with one decimal place represented.

The answer is 66.6%.

Sometimes, you will see fractions like this, but you will get used to them and often you can learn the percent equivalents of these fractions by heart.

As a final example, let’s take a look at a real-life word problem.

James ate three out of ten pieces of pizza. What percent of the pizza did he eat? What percent didn’t he eat?

First, let’s write a fraction to show the part of the pizza that James did eat. 

\begin{align*}\frac{3}{10}\end{align*}

Next, you convert that to a fraction out of 100 by setting up a proportion. 

\begin{align*}\frac{3}{10}=\frac{x}{100}\end{align*}

Then you can write it as a percent.

\begin{align*}\begin{array}{rcl} 10x &=& 300 \\ x &=& 30 \end{array}\end{align*}

The answer is James ate 30% of the pizza, and James did not each 70% of the pizza.

Examples

Example 1 

Earlier, you were given a problem about Mica and his shelf screw.

It measured \begin{align*}\frac{5}{8}\end{align*} of an inch. What percent of an inch does this length represent?

First, set up the proportion. 

\begin{align*}\frac{5}{8}=\frac{x}{100}\end{align*}

Next, cross multiply to solve for the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 8x &=& 500 \\ x &=& 62.5 \end{array}\end{align*}

The answer is 62.5% of the students in his school are boys.

Example 2

Write \begin{align*}\frac{9}{4}\end{align*} as a percent.

First, you write a proportion with a denominator of 100.

\begin{align*}\frac{9}{4}=\frac{x}{100}\end{align*}

Next, you cross multiply to find the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 4x &=& 900 \\ x &=& 225 \\ \frac{225}{100}&=& 225 \% \end{array}\end{align*}The answer is \begin{align*}\frac{9}{4}\end{align*} is equal to 225%. 

Example 3

Write \begin{align*}\frac{1}{4}\end{align*} as a percent.

First, set up the proportion. 

\begin{align*}\frac{1}{4}=\frac{x}{100}\end{align*}

Next, cross multiply to solve for the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 4x &=& 100 \\ x &=& 25 \end{array}\end{align*}The answer is 25%.

Example 4

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

First, set up the proportion.

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

Next, cross multiply to solve for the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 5x &=& 200 \\ x &=& 40 \end{array}\end{align*}

The answer is 40%.

Example 5

Write \begin{align*}\frac{4}{40}\end{align*} as a percent.

First, set up the proportion. 

\begin{align*}\frac{4}{40}=\frac{x}{100}\end{align*}

Next, cross multiply to solve for the value of \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 40x &=& 400 \\ x &=& 10 \end{array}\end{align*}

The answer is 10%.

Review

Write each fraction as a percent. 

  1. \begin{align*}\frac{1}{4}\end{align*}
  2. \begin{align*}\frac{1}{2}\end{align*} 
  3. \begin{align*}\frac{3}{4}\end{align*}
  4. \begin{align*}\frac{11}{100}\end{align*} 
  5. \begin{align*}\frac{1}{5}\end{align*}
  6. \begin{align*}\frac{4}{8}\end{align*} 
  7. \begin{align*}\frac{17}{100}\end{align*}
  8. \begin{align*}\frac{125}{100}\end{align*}
  9. \begin{align*}\frac{250}{100}\end{align*} 
  10. \begin{align*}\frac{233}{100}\end{align*} 
  11. \begin{align*}\frac{27}{50}\end{align*}  
  12. \begin{align*}\frac{18}{36}\end{align*} 
  13. \begin{align*}\frac{21}{50}\end{align*}
  14. \begin{align*}\frac{20}{50}\end{align*}
  15. \begin{align*}\frac{30}{60}\end{align*}  

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.3.

Resources

 

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Vocabulary

improper fraction

An improper fraction is a fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.

Proportion

A proportion is an equation that shows two equivalent ratios.

Image Attributions

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

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