# 6.3: Fractions as Percents

**At Grade**Created by: CK-12

**Practice**Fractions as Percents

Mica measures the screw he is using to build a shelf for his sports trophies. He discovers that it is

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.

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

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

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.

Then, you can cross multiply to find the value of

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

The answer is that the fraction

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.

.

.

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

Write

First, set up the proportion.

Next, cross multiply to solve for the value of

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.

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

Then you can write it as a percent.

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

First, set up the proportion.

Next, cross multiply to solve for the value of

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

#### Example 2

Write

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

Next, you cross multiply to find the value of

**Example 3**

Write

First, set up the proportion.

Next, cross multiply to solve for the value of

#### Example 4

Write

First, set up the proportion.

Next, cross multiply to solve for the value of

The answer is 40%.

#### Example 5

Write

First, set up the proportion.

Next, cross multiply to solve for the value of

The answer is 10%.

### Review

Write each fraction as a percent.

14 12 34 11100 15 48 17100 125100 250100 233100 - \begin{align*}\frac{27}{50}\end{align*}
- \begin{align*}\frac{18}{36}\end{align*}
- \begin{align*}\frac{21}{50}\end{align*}
- \begin{align*}\frac{20}{50}\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.

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