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Fractions as Percents

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Have you ever thought about a statistic in terms of percent? Take a look at this dilemma.

After conducting a survey of middle school students, Justin learned that 19 out of 50 students will attend summer camp. This is his statistic.

What is this statistic as a percent?

This Concept is about writing fractions as percents. You will be able to complete this problem at the end of the Concept.

Guidance

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 denominator of 100 before you write it as a percent.

\frac{9}{100}

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

\frac{9}{100}=9\%

What do we do if a fraction does not have a denominator of 100?

This is where your work with proportions and equal ratios comes in. Remember that a proportion is two equal ratios. We can write a proportion for a fraction by creating a second fraction equal to the first that has a denominator of 100. Then we solve the proportion. It sounds trickier than it is. Let’s look at an example.

Write \frac{3}{5} as a percent.

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

\frac{3}{5}=\frac{x}{100}

Wow! Here is a proportion. Next, think back to solving proportions. We can cross multiply to find the value of x .

5x& =300\\x& =60\\\frac{3}{5}& =\frac{60}{100}

Now we have a fraction with a denominator of 100. We can write it as a percent.

Our answer is that \frac{3}{5} is equal to 60%.

What about if we had an improper fraction?

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

Write \frac{9}{4} as a percent.

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

\frac{9}{4}=\frac{x}{100}

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

4x& =900\\x& =225\\\frac{225}{100}& =225\%

Our answer is 225%.

Did you know that you already know some common fraction equivalents for percents? Think of 25 cents, 50 cents, and 75 cents.

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

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

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

Sometimes, you can also have fractions that don’t convert easily.

Write \frac{2}{3} as a percent.

First, set up the proportion.

\frac{2}{3}=\frac{x}{100}

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

3x& =200\\x& =66.6

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

Our 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 equivalent of these fractions by heart.

Write each fraction as a percent.

Example A

\frac{1}{4}

Solution: 25\%

Example B

\frac{2}{5}

Solution: 40\%

Example C

\frac{4}{40}

Solution: 10\%

Here is the original problem once again.

After conducting a survey of middle school students, Justin learned that 19 out of 50 students will attend summer camp. This is his statistic.

What is this statistic as a percent?

To figure this out, we first have to write this statistic as a fraction.

19 out of 50 becomes \frac{19}{50} .

Now we can take this fraction and rename it as a proportion out of 100.

\frac{19}{50} = \frac{x}{100}

We can use equal fractions to solve.

50 x 2 = 100

19 x 2 = 38

\frac{38}{100} = 38\%

This is our answer.

Vocabulary

Here are the vocabulary words used in this Concept.

Ratio
the comparison of two quantities. Ratios can be written in fraction form, using a colon or with the word “to”.
Percent
a part of a whole out of 100. It is written using a % sign.
Proportion
two equal ratios form a proportion.
Improper Fraction
a fraction greater than one where the numerator is larger than the denominator.

Guided Practice

Here is one for you to try on your own.

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

Answer

To figure this out, first let's write a fraction to show the part of the pizza that James did eat.

\frac{3}{10}

Next, we convert that to a fraction out of 100.

\frac{3}{10} = {30}{100}

Now we can write it as a percent.

30\%

James ate 30\% of the pizza.

James did not each 70\% of the pizza.

Video Review

Here is a video for review.

This James Sousa video relates fractions, decimals and percents.

Practice

Directions: Write each fraction as a percent.

1. \frac{1}{2}

2. \frac{1}{4}

3. \frac{3}{4}

4. \frac{11}{100}

5. \frac{1}{5}

6. \frac{4}{8}

7. \frac{17}{100}

8. \frac{125}{100}

9. \frac{250}{100}

10. \frac{233}{100}

11. \frac{27}{50}

12. \frac{18}{36}

13. \frac{21}{50}

14. \frac{20}{50}

15. \frac{30}{60}

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