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*}

\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*}\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

is equal to .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.

.\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*}\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*}\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*}\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*}\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

.

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

.

The answer is 10%.

### Review

Write each fraction as a percent.

- \begin{align*}\frac{1}{2}\end{align*}
- \begin{align*}\frac{3}{4}\end{align*}
- \begin{align*}\frac{11}{100}\end{align*}
- \begin{align*}\frac{4}{8}\end{align*}
- \begin{align*}\frac{17}{100}\end{align*}
- \begin{align*}\frac{125}{100}\end{align*}
- \begin{align*}\frac{250}{100}\end{align*}
- \begin{align*}\frac{233}{100}\end{align*}
- \begin{align*}\frac{27}{50}\end{align*}
- \begin{align*}\frac{18}{36}\end{align*}
- \begin{align*}\frac{30}{60}\end{align*}

### Review (Answers)

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