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# Percents as Fractions

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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.

$\frac{45}{100}$

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.

$\frac{80}{100}$

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

$\frac{8\bcancel{0}}{10\bcancel{0}}$

Now we have eight-tenths to simplify.

$\frac{8}{10}=\frac{4}{5}$

Our final answer is that 80% can be written as the fraction $\frac{4}{5}$ .

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.

$\frac{12}{100}$

Next, we simplify this fraction. The greatest common factor is 4, so we divide the numerator and the denominator by 4.

$\frac{12\div 4}{100 \div 4}=\frac{3}{25}$

12% can be written as the fraction $\frac{3}{25}$ .

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

#### Example A

18%

Solution: $\frac{18}{100} = \frac{9}{50}$

#### Example B

20%

Solution: $\frac{20}{100} = \frac{1}{5}$

#### Example C

4%

Solution: $\frac{4}{100} = \frac{1}{25}$

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.

$\frac{45}{100}$

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.

$\frac{9}{20}$

This is our answer.

### 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.

$33\%$

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

$\frac{33}{100}$

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%