# 6.1: Percents

**At Grade**Created by: CK-12

Have you ever thought about percentages? Have you ever thought about them in connection to a candy store?

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?

**Percents are out of 100. Because Randy calculated the number of red gummy worms out of 100, he used a percent. You can also write this value as a ratio. This Concept will teach you how to tackle this dilemma.**

### Guidance

In an earlier Concept, you learned that a *ratio***is a comparison of two numbers and that a ratio can be written in three ways**.

Think about this. If there are 13 red jelly beans and 15 yellow jelly beans in a jar, the ratio of red jelly beans to yellow jelly beans can be written as 13 to 15, 13:15, or \begin{align*}\frac{13}{15}\end{align*}. Each of these ratios is read as “thirteen to fifteen.”

A ** percent** is a type of ratio. You may have worked with percents before, but now we are going to apply them directly to ratios. Hopefully, you will see percents in a new way.

**What is a percent?**

**A** *percent***is a ratio that compares a number to 100. Percent means “per hundred” and the symbol for percent is %**. 100% represents the ratio 100 to 100 or \begin{align*}\frac{100}{100}\end{align*}. Therefore, the value of 100% is 1.

If there are 100 jelly beans in a jar and 19 are black, we can say that \begin{align*}\frac{19}{100}\end{align*} or 19% of the jelly beans in the jar are black. Look at the following examples to better understand percents.

Write a ratio and a percent that describes the shaded part.

The figure shows the ratio of 37 shaded squares to 100 squares.

We can write the ratio as 37 to 100, 37:100, or \begin{align*}\frac{37}{100}\end{align*}.

When the denominator of a ratio in fraction form is 100, you can express the ratio as a percent.

\begin{align*}\frac{37}{100}=37\%\end{align*}

**The ratio that describes the shaded part is 37 to 100, 37:100, or \begin{align*}\frac{37}{100}\end{align*}, and the percent is 37%.**

**This is a visual way of showing a percent as a ratio. We can use the picture to write the ratio and the percent.**

Let’s look at another situation that uses a real-life item.

There were 100 questions on a test and Amanda answered 92 of them correctly. What percent did she answer correctly? What percent did she answer incorrectly?

Amanda answered 92 out of 100 questions correctly. We can write this as the ratio \begin{align*}\frac{92}{100}\end{align*}. Since the denominator is 100, we can write this in percent form as 92%.

Since there were 100 questions on the test and Amanda answered 92 correctly, she answered 100 – 92, or 8 out of 100 incorrectly. We can write this as the ratio \begin{align*}\frac{8}{100}\end{align*} and as the percent 8%.

**Amanda answered 92% of the questions correctly and 8% incorrectly.**

Practice what you have learned by writing a percent for each example.

#### Example A

Karen ate 12 out of 100 blueberries.

**Solution: \begin{align*}12%\end{align*}**

#### Example B

Joey answered 92 questions correctly out of 100 questions on his test.

**Solution: \begin{align*}92%\end{align*}**

#### Example C

Sarah gathered 25 roses out of 100 flowers.

**Solution:\begin{align*}25%\end{align*}**

Remember Randy and the gummy worms? Here is the original problem 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?

To answer this question, let's first write the percent.

\begin{align*}45%\end{align*}

A percent is out of 100, so we can say that this percent means that out of 100 gummy worms that 45 of them are red.

Here is a ratio.

\begin{align*}45\end{align*} out of </math>100</math>

**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 ratio.

\begin{align*}12%\end{align*}

**Answer**

To write this as a ratio, we change the 12% to 12 out of 100.

Now we can write that ratio in fraction form.

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

**This is our answer.**

### Video Review

Here is a video for review.

- This James Sousa video is an introduction to percents.

### Practice

Directions: Write each percent as a ratio with a denominator of 100.

1. 10%

2. 6%

3. 22%

4. 41%

5. 33%

6. 70%

7. 77%

8. 19%

9. 25%

10. 15%

11. 7%

12. 19%

13. 88%

14. 92%

15. 90%

### Image Attributions

Here you'll learn to recognize percent as a ratio whose denominator is 100.