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6.4: Percent of a Number

Difficulty Level: At Grade Created by: CK-12
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Taylor’s family owns a candy store. During her winter vacation, Taylor has the opportunity to work in the candy store and earn some extra money. Since candy is one of her favorite things, she never turns down an opportunity to help out in the store.

The first day that Taylor worked in the store, a family with three small children came into the store. The little children each wanted gummy bears to eat. Since there weren’t enough gummy bears in the jar, Taylor had to open a new bag of them. The bag said 400 on it.

Taylor took out the bag and began to open it.

“Please give us 25% of the bag,” the Mom said smiling.

Taylor looked at the bag and then back up at the Mom. She took out a piece of paper and a pencil.

“You can estimate,” she said smiling.

Taylor estimated 25% or 14\begin{align*}\frac{1}{4}\end{align*} of the bag. The family paid and then left smiling.

After they had left, Taylor began thinking about how many gummy bears would be 25%. She picked up the pencil and began to do some figuring.

This Concept is all about percents. To work with a percent you have to understand how they relate to parts and fractions. Pay attention and by the end of the lesson, you will be able to do some gummy bear arithmetic.

Guidance

The table below shows the fraction equivalents for common percents.

5%12010%11020%1525%1430%31040%2550%1260%3570%71075%3480%4590%910\begin{align*}& 5\% && 10\% && 20\% && 25\% && 30\% && 40\% && 50\% && 60\% && 70\% && 75\% && 80\% && 90\%\\ & \frac{1}{20} && \frac{1}{10} && \frac{1}{5} && \frac{1}{4} && \frac{3}{10} && \frac{2}{5} && \frac{1}{2} && \frac{3}{5} && \frac{7}{10} && \frac{3}{4} && \frac{4}{5} && \frac{9}{10}\end{align*}

The word “of” in a percent problem means to multiply. If you know the fraction equivalents for common percents, you can use this information to find the percent of a number by multiplying the fraction by the number. If you want to find a part of a whole using a percent, you use multiplication to solve this.

Find 40% of 45.

40% of 45 means 40%×45\begin{align*}40\% \times 45\end{align*}.

Look at the chart. The fraction 25\begin{align*}\frac{2}{5}\end{align*} is equivalent to 40%.

40%×45=25×45=251×4591=181=18\begin{align*}40\% \times 45 = \frac{2}{5} \times 45 = \frac{2}{\underset{1}{\cancel{5}}} \times \frac{\overset{9}{\cancel{45}}}{1}=\frac{18}{1}=18\end{align*}

Our answer is that 40% of 45 = 18

What about if the percent is not on the chart?

For a percent that is not on the chart, change the percent to a fraction in simplest form.

Find 85% of 20.

85% of 20 means 85%×20\begin{align*}85\% \times 20\end{align*}.

85%85%×20=85100=85÷5100÷5=1710=1720×20=17201×2011=171=17\begin{align*}85\% & = \frac{85}{100} = \frac{85 \div 5}{100 \div 5} = \frac{17}{10}\\ 85\% \times 20 & = \frac{17}{20}\times 20 = \frac{17}{\underset{1}{\cancel{20}}}\times \frac{\overset{1}{\cancel{20}}}{1}=\frac{17}{1}=17\end{align*}

The answer is that 85% of 20 is 17.

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

Example A

What is 10% of 50?

Solution: 5

Example B

What is 25% of 80?

Solution: 20

Example C

What is 22% of 100?

Solution: 22

Here is the original problem once again.

Taylor’s family owns a candy store. During her winter vacation, Taylor has the opportunity to work in the candy store and earn some extra money. Since candy is one of her favorite things, she never turns down an opportunity to help out in the store.

The first day that Taylor worked in the store, a family with three small children came into the store. The little children each wanted gummy bears to eat. Since there weren’t enough gummy bears in the jar, Taylor had to open a new bag of them. The bag said 400 on it.

Taylor took out the bag and began to open it.

“Please give us 25% of the bag,” the Mom said smiling.

Taylor looked at the bag and then back up at the Mom. She took out a piece of paper and a pencil.

“You can estimate,” she said smiling.

Taylor estimated 25% or 14\begin{align*}\frac{1}{4}\end{align*} of the bag. The family paid and then left smiling.

After they had left, Taylor began thinking about how many gummy bears would be 25%. She picked up the pencil and began to do some figuring.

Taylor wants to figure out how many gummy bears 25% is out of 400.

To do this, she needs to multiply. 25% of 400 means 25% times 400.

We can change 25% to the fraction 14\begin{align*}\frac{1}{4}\end{align*}.

Here is our new problem.

14×4001=11×1001=100\begin{align*}\frac{1}{\cancel{4}}\times \frac{\cancel{400}}{1}=\frac{1}{1}\times \frac{100}{1}=100\end{align*}

Our answer is that 25% of 400 is 100. The exact number would have been 100 gummy bears.

“Wow!” thought Taylor, “That is a lot of candy. I hope they remember to brush their teeth.”

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.
Improper Fraction
a fraction greater than one where the numerator is larger than the denominator.

Guided Practice

Here is one for you to try on your own.

What is 18% of 50?

To figure this out, we change the percent to a fraction and create a proportion.

18100=x50\begin{align*}\frac{18}{100}=\frac{x}{50}\end{align*}

Now we use cross products and solve.

100x=900\begin{align*}100x = 900\end{align*}

x=9\begin{align*}x = 9\end{align*}

18% of 50 is 9.

Video Review

Here is a video for review.

Practice

Directions: Use fraction multiplication to find each percent of a number.

1. 10% of 25

2. 20% of 30

3. 25% of 80

4. 30% of 90

5. 75% of 200

6. 8% of 10

7. 10% of 100

8. 19% of 20

9. 15% of 30

10. 12% of 30

11. 15% of 45

12. 25% of 85

13. 45% of 60

14. 50% of 200

15. 55% of 300

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