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# Percents as Fractions

## Write percents as fractions and simplify.

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Percents as Fractions

Remember Randy? Here is the gummy worm dilemma once again.

Randy loves gummy worms. In looking at a package of gummy worms, he has figured out that 45% of the gummy worms in a bag are red ones.

"Look at the red ones," he told his friend Sasha.

"I like red ones too," Sasha commented.

"Yes, but only 45% of this bag are red," Randy explained.

Do you know how many worms that is out of 100?

In the last Concept, we wrote this percent as a fraction with a denominator of 100.

45100\begin{align*}\frac{45}{100}\end{align*}

Now we can simplify this ratio.

This is what you will learn how to do in this Concept.

### Guidance

In the last Concept you saw how you can write a percent as a ratio. Well, remember that one of the ways of writing a ratio is to write it in fraction form. Fractions can be simplified. Therefore, we can write percents as fractions and reduce them to simplest form.

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

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

80100

Now we have eight-tenths to simplify.

810=45\begin{align*}\frac{8}{10}=\frac{4}{5}\end{align*}

Our final answer is that 80% can be written as the fraction 45\begin{align*}\frac{4}{5}\end{align*}.

Yes. Because they are both parts of a whole, we can interchange the way that we write them. A percent can be written as a fraction and a fraction can be written as a percent too.

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, we simplify this fraction. The greatest common factor is 4, so we divide 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*}

12% can be written as the fraction 325\begin{align*}\frac{3}{25}\end{align*}.

Now it's time for you to try a few on your own.

#### Example A

18%

Solution: 18100=950\begin{align*}\frac{18}{100} = \frac{9}{50}\end{align*}

#### Example B

20%

Solution:20100=15\begin{align*}\frac{20}{100} = \frac{1}{5}\end{align*}

#### Example C

4%

Solution:4100=125\begin{align*}\frac{4}{100} = \frac{1}{25}\end{align*}

Now you are ready to simplify. Here is the gummy worm situation once again.

Randy loves gummy worms. In looking at a package of gummy worms, he has figured out that 45% of the gummy worms in a bag are red ones.

"Look at the red ones," he told his friend Sasha.

"I like red ones too," Sasha commented.

"Yes, but only 45% of this bag are red," Randy explained.

Do you know how many worms that is out of 100?

In the last Concept, we wrote this percent as a fraction with a denominator of 100.

45100\begin{align*}\frac{45}{100}\end{align*}

Now we can simplify this ratio.

To do this, we divide the numerator and denominator by the greatest common factor.

The greatest common factor of 45 and 100 is 5.

920\begin{align*}\frac{9}{20}\end{align*}

### Vocabulary

Here are the vocabulary words 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.

### Guided Practice

Here is one for you to try on your own.

Write this percent as a fraction in simplest form.

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

First, we 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.

Our work is complete.

### Video Review

Here is a video for review.

### Practice

Directions: 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. 10%

11. 5%

12. 25%

13. 40%

14. 60%

15. 90%

### Vocabulary Language: English

Proportion

Proportion

A proportion is an equation that shows two equivalent ratios.