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# Percents as Fractions

## Write percents as fractions and simplify.

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Percents as Fractions
License: CC BY-NC 3.0

The gauge on Chantal’s weather monitor reads 34% humidity. She wants to know what this percent is as a fraction in simplest form. How would she write it that way?

In this concept, you will learn to write percents as fractions in simplest form.

### Writing Percents as Fractions

Percents can be written as ratios. One of the ways of writing a ratio is to write it in fraction form with 100 as the denominator. However, some fractions can be simplified. Therefore, you can write percents as fractions and reduce them to simplest form.

As fractions and percents are both parts of a whole, you can interchange the way that you write them. A percent can be written as a fraction and a fraction can be written as a percent too.

To write a percent as a fraction, you write the percent as a ratio with a denominator of 100. You can then write the fraction in simplest form, if possible.

Let’s look at an example.

Write 80 % as a fraction in simplest form.

First, write the percent as a fraction with a denominator of 100.

80100\begin{align*}\frac{80}{100}\end{align*}

Next, simplify this fraction. You can start by canceling a zero in the numerator and one in the denominator.

80100\begin{align*}\frac{8 {\cancel{0}}}{10{\cancel{0}}}\end{align*}

Now you have eight-tenths to simplify. Notice that both 8 and 10 are divisible by 2.

8÷210÷2=45\begin{align*} \frac{8 \div 2 }{10 \div 2}= \frac{4}{5}\end{align*}

Then check to see if your answer can be reduced further. In this case it cannot.

The answer is that 80% can be written as the fraction 45\begin{align*}\frac{4}{5}\end{align*} in simplest form.

Let’s look at another example.

Write 12% as a fraction in simplest form.

First, write the percent as a fraction out of 100.

12100\begin{align*}\frac{12}{100}\end{align*}

Next, you simplify this fraction. The greatest common factor of 12 and 100 is 4, so you divide both the numerator and the denominator by 4.

12÷4100÷4=325\begin{align*} \frac{12 \div 4 }{100 \div 4}= \frac{3}{25}\end{align*}

Then, check to ensure that the fraction cannot not be reduced further. In this instance it cannot.

The answer is 12% can be written as the fraction 325\begin{align*}\frac{3}{25}\end{align*} in simplest form.

### Examples

#### Example 1

Earlier, you were given a problem about Chantal and her weather monitor.

The gauge showed the humidity to be 34%. How could you write this percent as a fraction in simplest form?

First, write the percent as a fraction out of 100.

34100\begin{align*}\frac{34}{100}\end{align*}

Next, you simplify this fraction. The greatest common factor of 34 and 100 is 2, so you divide both the numerator and the denominator by 2.

34÷2100÷2=1750\begin{align*} \frac{34 \div 2 }{100\div 2}= \frac{17}{50}\end{align*}

Then, check to ensure that the fraction cannot not be reduced further. In this instance it cannot.

The answer is that the simplest fraction form of 34% is 1750\begin{align*}\frac{17}{50}\end{align*}.

#### Example 2

Write this percent as a fraction in simplest form.

33%\begin{align*}33 \%\end{align*}

First, you can write it as a fraction with a denominator of 100.

33100\begin{align*}\frac{33}{100}\end{align*}

There isn’t a greatest common factor for 33 and 100, so this is the fraction in simplest form.

The answer is 33% can be written as the fraction 33100\begin{align*}\frac{33}{100}\end{align*} in simplest form.

#### Example 3

Solve the following problem. Write 18% as a fraction in simplest form.

First, write the percent as a fraction out of 100.

18100\begin{align*}\frac{18}{100}\end{align*}

Next, you simplify this fraction. The greatest common factor of 18 and 100 is 2, so you divide both the numerator and the denominator by 2.

18÷2100÷2=950\begin{align*} \frac{18 \div 2 }{100 \div 2}= \frac{9}{50}\end{align*}

Then, check to ensure that the fraction cannot not be reduced further. In this instance it cannot.

The answer is 18% can be written as the fraction 950\begin{align*}\frac{9}{50}\end{align*} in simplest form.

#### Example 4

Solve the following problem. Write 20% as a fraction in simplest form.

First, write the percent as a fraction out of 100.

20100\begin{align*}\frac{20}{100}\end{align*}

Next, you simplify this fraction. The greatest common factor of 20 and 100 is 20, so you divide both the numerator and the denominator by 20.

20÷20100÷20=15\begin{align*} \frac{20 \div 20 }{100 \div 20}= \frac{1}{5}\end{align*}

Then, check to ensure that the fraction cannot not be reduced further. In this instance it cannot.

The answer is 20% can be written as the fraction 15\begin{align*}\frac{1}{5}\end{align*} in simplest form.

#### Example 5

Solve the following problem. Write 4% as a fraction in simplest form.

First, write the percent as a fraction out of 100.

4100\begin{align*}\frac{4}{100}\end{align*}

Next, you simplify this fraction. The greatest common factor of 4 and 100 is 4, so you divide both the numerator and the denominator by 4.

4÷4100÷4=125\begin{align*} \frac{4 \div 4 }{100 \div 4}= \frac{1}{25}\end{align*}

Then, check to ensure that the fraction cannot not be reduced further. In this instance it cannot.

The answer is 4% can be written as the fraction 125\begin{align*}\frac{1}{25}\end{align*}in simplest form.

### Review

Write each percent as a fraction in simplest form.

1. 10%
2. 6%
3. 22%
4. 41%
5. 33%
6. 70%
7. 77%
8. 19%
9. 12%
10. 20%
11. 5%
12. 25%
13. 40%
14. 60%
15. 90%

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.2.

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### Vocabulary Language: English

TermDefinition
Proportion A proportion is an equation that shows two equivalent ratios.

### Image Attributions

1. [1]^ License: CC BY-NC 3.0

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