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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 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

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

9100=9%

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 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

Then, you can cross multiply to find the value of x.

5xx35===3006060100

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 is equal to 60%.

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%25 cents means 25 cents out of a dollar, or 25% of a dollar. Since a quarter is 25 cents, 

.12=50%50 cents means 50 cents out of a dollar, or 50% of a dollar. Since a half dollar is 50 cents, 

34=75%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  as a percent.

First, set up the proportion. 

23=x100

Next, cross multiply to solve for the value of x.

3xx==20066.6

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. 

310

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

310=x100

Then you can write it as a percent.

10xx==30030

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 of an inch. What percent of an inch does this length represent?

First, set up the proportion. 

58=x100

Next, cross multiply to solve for the value of x.

8xx==50062.5

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

Example 2

Write 94 as a percent.

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

94=x100

Next, you cross multiply to find the value of x.

4xx225100===900225225%The answer is 94 is equal to 225%. 

Example 3

Write 14 as a percent.

First, set up the proportion. 

14=x100

Next, cross multiply to solve for the value of x.

4xx==10025The answer is 25%.

Example 4

Write 25 as a percent.

First, set up the proportion.

25=x100

Next, cross multiply to solve for the value of x.

5xx==20040

The answer is 40%.

Example 5

Write 440 as a percent.

First, set up the proportion. 

440=x100

Next, cross multiply to solve for the value of x.

40xx==40010

The answer is 10%.

Review

Write each fraction as a percent. 

  1. 14
  2. 12 
  3. 34
  4. 11100 
  5. 15
  6. 48 
  7. 17100
  8. 125100
  9. 250100 
  10. 233100 
  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.

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Dec 02, 2015
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