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# 6.3: Fractions as Percents

Difficulty Level: At Grade Created by: CK-12
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Mica measures the screw he is using to build a shelf for his sports trophies. He discovers that it is 58\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.

9100\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.

9100=9%\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 35\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.

35=x100\begin{align*}\frac{3}{5}=\frac{x}{100}\end{align*}

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

5xx35===3006060100\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 35\begin{align*}\frac{3}{5}\end{align*} is equal to 60%\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.

.14=25%\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,

.12=50%\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,

34=75%\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 23\begin{align*}\frac{2}{3}\end{align*}  as a percent.

First, set up the proportion.

23=x100\begin{align*}\frac{2}{3}=\frac{x}{100}\end{align*}

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

3xx==20066.6\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.

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.

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

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

310=x100\begin{align*}\frac{3}{10}=\frac{x}{100}\end{align*}

Then you can write it as a percent.

10xx==30030\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 58\begin{align*}\frac{5}{8}\end{align*} of an inch. What percent of an inch does this length represent?

First, set up the proportion.

58=x100\begin{align*}\frac{5}{8}=\frac{x}{100}\end{align*}

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

8xx==50062.5\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 94\begin{align*}\frac{9}{4}\end{align*} as a percent.

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

94=x100\begin{align*}\frac{9}{4}=\frac{x}{100}\end{align*}

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

4xx225100===900225225%\begin{align*}\begin{array}{rcl} 4x &=& 900 \\ x &=& 225 \\ \frac{225}{100}&=& 225 \% \end{array}\end{align*}The answer is 94\begin{align*}\frac{9}{4}\end{align*} is equal to 225%.

#### Example 3

Write 14\begin{align*}\frac{1}{4}\end{align*} as a percent.

First, set up the proportion.

14=x100\begin{align*}\frac{1}{4}=\frac{x}{100}\end{align*}

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

4xx==10025\begin{align*}\begin{array}{rcl} 4x &=& 100 \\ x &=& 25 \end{array}\end{align*}The answer is 25%.

#### Example 4

Write 25\begin{align*}\frac{2}{5}\end{align*} as a percent.

First, set up the proportion.

25=x100\begin{align*}\frac{2}{5}=\frac{x}{100}\end{align*}

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

5xx==20040\begin{align*}\begin{array}{rcl} 5x &=& 200 \\ x &=& 40 \end{array}\end{align*}

#### Example 5

Write 440\begin{align*}\frac{4}{40}\end{align*} as a percent.

First, set up the proportion.

440=x100\begin{align*}\frac{4}{40}=\frac{x}{100}\end{align*}

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

40xx==40010\begin{align*}\begin{array}{rcl} 40x &=& 400 \\ x &=& 10 \end{array}\end{align*}

### Review

Write each fraction as a percent.

1. 14\begin{align*}\frac{1}{4}\end{align*}
2. 12\begin{align*}\frac{1}{2}\end{align*}
3. 34\begin{align*}\frac{3}{4}\end{align*}
4. 11100\begin{align*}\frac{11}{100}\end{align*}
5. 15\begin{align*}\frac{1}{5}\end{align*}
6. 48\begin{align*}\frac{4}{8}\end{align*}
7. 17100\begin{align*}\frac{17}{100}\end{align*}
8. 125100\begin{align*}\frac{125}{100}\end{align*}
9. 250100\begin{align*}\frac{250}{100}\end{align*}
10. 233100\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*}

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

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.

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