Randy looked at his smartphone and saw that he had only 15% of his battery power remaining. That got him wondering, ‘What does 15% mean?’ How much of the phone’s total battery power does Randy have left?

In this concept, you will learn to recognize percent as a ratio whose denominator is 100.

### Recognizing Percents

**Percent** means the number of parts per 100. You know that 100% of anything is the entire or whole amount. Therefore, percents can tell you what part of the whole you are dealing with. To understand percents, you will set up ratios.

A **ratio** is a comparison of two numbers and that a ratio can be written in three ways. For example: 1 to 2, 1:2, or \begin{align*}\frac{1}{2}\end{align*}. Percents are ratios in which the second number (or the denominator) is 100.

Let’s look at an example.

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 are now going to apply percents directly to ratios.

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.

Let’s look at another example.

If there are 100 jelly beans in a jar and 19 are black, you can say that \begin{align*}\frac{19}{100}\end{align*}or 19% of the jelly beans in the jar are black.

Let’s look at one more situation that uses a real-life scenario.

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. First, you can write this as the ratio \begin{align*}\frac{92}{100}\end{align*}.

Next, since the denominator is 100, you can write this ratio in percent form as 92%.

Then, since there were 100 questions on the test and Amanda answered 92 correctly, you can determine that she answered

, or 8 out of 100 incorrectly.Next, you can write this as the ratio \begin{align*}\frac{8}{100}\end{align*}and as the percent 8%.

The answer is Amanda answered 92% of the questions correctly and 8% incorrectly.

### Examples

#### Example 1

Earlier, you were given a problem about Randy and his smartphone battery indicator.

It showed that he had 15% of his battery power remaining. How could you write this percent as a fraction?

First, you can write this as the ratio 15:100, which is equivalent to \begin{align*}\frac{15}{100}\end{align*}.

Then, since the denominator is 100, you can write this ratio in percent form as 15%.

The answer is 15% is equivalent to the fraction \begin{align*}\frac{15}{100}\end{align*}.

#### Example 2

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

First, count the number of shaded squares and the number of total squares. The figure shows the ratio of 37 shaded squares to 100 squares.

Next, write this ratio as 37 to 100, 37:100, or \begin{align*}\frac{37}{100}\end{align*}.

Then, 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 answer is: 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. You can use the picture to write the ratio and the percent.

#### Example 3

Solve the following problem. Karen ate 12 out of 100 blueberries. What percent of the blueberries did she eat?

First, you can write this as the ratio \begin{align*}\frac{12}{100}\end{align*}.

Then, since the denominator is 100, you can write this ratio in percent form as 12%.

The answer is she ate 12% of the blueberries.

#### Example 4

Solve the following problem. Joey answered 93 questions correctly out of 100 questions on his test. What percent of the questions did he answer correctly and what percent did he answer incorrectly?

First, you can write this as the ratio \begin{align*}\frac{93}{100}\end{align*}.

Next, since the denominator is 100, you can write this ratio in percent form as 93%.

Then, since there were 100 questions on the test and Joey answered 93 correctly, you can determine that he answered \begin{align*}100 - 93\end{align*}, or 7 out of 100 incorrectly.

Next, you can write this as the ratio

and as the percent 7%.The answer is Joey answered 93% of the questions correctly and 7% incorrectly.

#### Example 5

Solve the following problem. Sarah gathered 25 roses out of 100 flowers. What percent of the flowers were roses?

First, you can write this as the ratio \begin{align*}\frac{25}{100}\end{align*}.

Then, since the denominator is 100, you can write this ratio in percent form as 25%.

The answer is 25% of the flowers were roses.

### Review

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

- 10%
- 6%
- 22%
- 41%
- 33%
- 70%
- 77%
- 19%
- 25%
- 15%
- 7%
- 29%
- 88%
- 92%
- 90%

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.1.