Have you ever met anyone who liked to clean up?

Sam’s least favorite part of her after school job at the supermarket is closing. When closing the store, the break room has to be swept and mopped. Each of the students who work at the store part-time take turns closing, and every Friday night is Sam’s turn. On Friday, Sam got her mop and broom and headed up to the break room. It seemed to be even messier than usual. “Oh no, I will never get done,” Sam sighed, but she picked up the broom and began to sweep.

In just fifteen minutes, Sam had swept four-fifths of the room. She was amazed at how quickly the task was getting done with a little focus and effort.

What fraction of the room does Sam still have to sweep? What percent of the room is this?

**
In this Concept, you will learn how to identify fractions and convert them to percents. This is exactly what Sam will need to accomplish the task.
**

### Guidance

In our last Concept, you learned how to understand percents.
**
Remember that a percent means a part of a whole, and the whole is 100.
**
You also learned how to take a percent and write it as a decimal and as a fraction. In this Concept, you will learn to work the other way around. Let’s begin by learning how to write fractions as a percent.

**
When writing a percent as a fraction, we can drop the % sign and make that the denominator of 100. Then we take the quantity and write it in the numerator above the 100. This is our fraction.
**

Write \begin{align*}14\%\end{align*} as a fraction.

**
First, we drop the % sign. % means out of 100, so 100 becomes our new denominator.
**

**
@$\begin{align*}14\%\end{align*}@$
becomes
@$\begin{align*}\frac{14}{100}\end{align*}@$
.
**

**
Yes! We can change the denominator of 100 to a % sign and add that to the quantity in the numerator. Here is what that looks like.
**

Write @$\begin{align*}\frac{47}{100}\end{align*}@$ as a percent.

**
First, drop the 100. Then write 47 with a % sign.
**

@$\begin{align*}\frac{47}{100}\end{align*}@$ becomes @$\begin{align*}47\%\end{align*}@$

**
Our answer is
@$\begin{align*}47\%\end{align*}@$
.
**

**
Not all fractions have a denominator of 100. How do we write a fraction as a percent when the denominator is not 100?
**

**
This is the next thing that we need to learn. If a fraction does not have a denominator of 100, to write it as a percent we need to rewrite it as an equal fraction with a denominator of 100.
**

Write @$\begin{align*}\frac{2}{5}\end{align*}@$ as a percent.

To write @$\begin{align*}\frac{2}{5}\end{align*}@$ as a percent, we must first rewrite it as a fraction with a denominator of 100. Write a proportion to show this comparison.

@$$\begin{align*}\frac{2}{5}=\frac{}{100}\end{align*}@$$

**
What number was multiplied by 5 to get 100 as a product?
**
**
20! So we multiply the numerator by 20 and we will have an equivalent fraction with a denominator of 100.
**

@$$\begin{align*}2 \times 20 &= 40\\ \frac{2}{5}=\frac{40}{100}&=40\%\end{align*}@$$

**
Our answer is
@$\begin{align*}40\%\end{align*}@$
.
**

**
One special fraction to work with is one-third. To convert one-third to a percent is a little tricky because 3 does not divide evenly into 100. Take a look.
**

@$$\begin{align*}\frac{1}{3}=\frac{}{100}\end{align*}@$$

When completing this problem, we end up with a repeating decimal; the 3’s just continue on and on and on.

@$\begin{align*}0.33333333\end{align*}@$ etc.

**
To work with this fraction, we call it 33
@$\begin{align*}\frac{1}{3}\end{align*}@$
%.
**

Write each fraction as a percent.

#### Example A

@$\begin{align*}\frac{48}{100}\end{align*}@$

**
Solution:
@$\begin{align*}48\%\end{align*}@$
**

#### Example B

@$\begin{align*}\frac{82}{100}\end{align*}@$

**
Solution:
@$\begin{align*}82\%\end{align*}@$
**

#### Example C

@$\begin{align*}\frac{91}{100}\end{align*}@$

**
Solution:
@$\begin{align*}91\%\end{align*}@$
**

Remember Sam? Let's use what we have learned to help Sam with her sweeping dilemma.

In just fifteen minutes, Sam had swept four-fifths of the room. She was amazed at how quickly the task was getting done with a little focus and effort.

What fraction of the room does Sam still have to sweep?

What percent of the room has she finished? What percent of the room is still left?

Let’s work through this solution. If Sam has completed four-fifths of the room, then she has one-fifth left to complete.

What percent of the room has she completed?

To figure this out, we have to figure out what four–fifths is as a percent. To do this, we can figure it out by using an equal ratio out of 100.

@$$\begin{align*}\frac{4}{5}=\frac{80}{100}=80\%\end{align*}@$$

Sam has completed 80% of the room.

**
What percent of the room does she have left?
**

You can figure this out two different ways. The first way is to simply subtract 80% from 100%. 100% - 80% (what Sam has completed) @$\begin{align*}= 20\%\end{align*}@$

The other way is to convert one-fifth (the amount left) to a percent. We can do this by creating an equal ratio out of 100.

@$$\begin{align*}\frac{1}{5}=\frac{20}{100}=20\%\end{align*}@$$

**
Since it only took Sam 15 minutes to complete 80% of the room, if she continues with her great effort she will be finished in no time at all.
**

### Guided Practice

Here is one for you to try on your own.

Write @$\begin{align*} \frac{23}{50}\end{align*}@$ as a percent.

**
Answer
**

To write this fraction as a percent, we have to rewrite the fraction with a denominator of 100. We can set up a proportion to do this.

@$\begin{align*}\frac{23}{50} = \frac{x}{100}\end{align*}@$

Now we can solve the proportion.

**
The answer is
@$\begin{align*}46\%\end{align*}@$
.
**

### Video Review

Here are videos for review.

Khan Academy, Percents, Decimals, and Fractions

James Sousa, An Example Relating Fractions, Decimals, and Percents

### Explore More

Directions: Write each fraction as a percent.

1. @$\begin{align*}\frac{4}{100}\end{align*}@$

2. @$\begin{align*}\frac{24}{100}\end{align*}@$

3. @$\begin{align*}\frac{20}{100}\end{align*}@$

4. @$\begin{align*}\frac{76}{100}\end{align*}@$

5. @$\begin{align*}\frac{61}{100}\end{align*}@$

6. @$\begin{align*}\frac{1}{4}\end{align*}@$

7. @$\begin{align*}\frac{3}{4}\end{align*}@$

8. @$\begin{align*}\frac{3}{6}\end{align*}@$

9. @$\begin{align*}\frac{2}{5}\end{align*}@$

10. @$\begin{align*}\frac{4}{5}\end{align*}@$

11. @$\begin{align*}\frac{8}{10}\end{align*}@$

12. @$\begin{align*}\frac{6}{10}\end{align*}@$

13. @$\begin{align*}\frac{6}{50}\end{align*}@$

14. @$\begin{align*}\frac{3}{25}\end{align*}@$

15. @$\begin{align*}\frac{20}{50}\end{align*}@$