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# Percent of a Number

## Use multiplication and proportions to find the percent of a number.

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Percent of a Number

Lee loves basketball. He hopes to be just as good as his favorite player, Kobe Bryant. On average, Kobe makes 83% of all his free throws. Lee practices shooting 50 free throws every day. If Lee wants to shoot free throws as well as Kobe, how many does he need to make?

In this concept, you will learn how to find the percent of a number.

### Finding the Percent of a Number

A percent is a ratio that describes a quantity out of 100. A percent is also a part of a whole. Let’s take a look at finding the percent of a number is the part of a number that is equivalent to the percent. You can find the percent of a number two ways. One method is to use a proportion, an equation that shows equivalent ratios.

Let’s, find 10% of 25 using a proportion.

First, write the percent as a fraction. 10% is also 10 out of 100.

\begin{align*}10\%=\frac{10}{100}\end{align*}

Next, write a proportion to find the equivalent fraction of 10% of 25. The second fraction is the unknown quantity, represented by \begin{align*}x\end{align*}, over the whole, 25.

\begin{align*}\frac{10}{100} = \frac{x}{25}\end{align*}

Then, cross multiply to find the cross products. To cross multiply, multiply the numerator of one fraction with the denominator of the other fraction. The products should be equal.

\begin{align*}10(25)=100x\end{align*}

Finally, simplify the equation to solve for \begin{align*}x\end{align*}. Multiply 10 by 25 and divide both sides by 100.

\begin{align*}\begin{array}{rcl} 10(25) & = & 100x\\ \frac{250}{100} & = & \frac{100x}{100}\\ 2.5 & = & x \end{array}\end{align*}

10% of 25 is 2.5.

Let’s review the steps of using a proportion.

Another method is to use key words and multiplication. Let’s look again at the problem.

What 10% of 25?

First, look for key words that suggest an operation. The word “of” tells you to multiply 25 by 10%.

Next, convert 10% to a decimal.

\begin{align*}10\% = 0.1\end{align*}

Then, write an equation to find the unknown number, \begin{align*}x\end{align*}.

\begin{align*}x = 25 \times 0.1\end{align*}

Finally, solve for \begin{align*}x\end{align*} by multiplying 25 by 0.1.

\begin{align*}25 \times 0.1 = 2.5\end{align*}

The answer is the same. 10% of 25 is 2.5.

### Examples

#### Example 1

Earlier, you were given a problem about Lee practicing his free throw.

Lee wants to make just as many free throws as Kobe. To find out how many he needs to make, Lee must multiply 50 by 83%.

First, convert 83% to a decimal.

\begin{align*}83\% = 0.83\end{align*}

Next, write an equation to find the unknown number, \begin{align*}x\end{align*}.

\begin{align*}x = 50 \times 0.83\end{align*}

Then, solve for \begin{align*}x\end{align*} by multiplying 50 by 0.83.

\begin{align*}\begin{array}{rcl} 50 \times 0.83 & = & 41.50\\ x & = & 41.5 \end{array}\end{align*}

83% of 50 is 41.5. Lee needs to make at least 41 out of 50 free throws to be just as good as Kobe.

#### Example 2

What is 15% of 200?

The keyword “of” tells you to multiply 200 by 15%. First, convert 15% to a decimal.

\begin{align*}15\% = 0.15\end{align*}

Next, write an equation to find the unknown number, \begin{align*}x\end{align*}.

\begin{align*}x = 200 \times 0.15\end{align*}

Finally, solve for \begin{align*}x\end{align*} by multiplying 200 by 0.15.

\begin{align*}\begin{array}{rcl} 200 \times 0.15 & = & 30.00\\ x & = & 30 \end{array}\end{align*}

15% of 200 is 30.

#### Example 3

What is 10% of 54?

First, convert 10% to a decimal.

\begin{align*}10\% = 0.1\end{align*}

Next, write an equation to find the unknown number, \begin{align*}x\end{align*}.

\begin{align*}x = 54 \times 0.1\end{align*}

Then, solve for \begin{align*}x\end{align*} by multiplying 54 by 0.1

10% of 54 is 5.4.

\begin{align*}\begin{array}{rcl} 54 \times 0.1 & = & 5.4\\ x & = & 5.4 \end{array}\end{align*}

#### Example 4

What is 25% of 80?

First, convert 25% to a decimal.

\begin{align*}25\% = 0.25\end{align*}

Next, write an equation to find the unknown number, \begin{align*}x\end{align*}.

\begin{align*}x = 80 \times 0.25\end{align*}

Then, solve for \begin{align*}x\end{align*} by multiplying 80 by 0.25.

\begin{align*}\begin{array}{rcl} 80 \times 0.25 & = & 20.00\\ x & = & 20 \end{array}\end{align*}

25% of 80 is 20.

#### Example 5

What is 5% of 78?

First, convert 5% to a decimal.

\begin{align*}5\% = 0.05\end{align*}

Next, multiply 78 by 0.05.

\begin{align*}\begin{array}{rcl} 78 \times 0.05 & = & 3.90\\ x & = & 3.9 \end{array}\end{align*}

5% of 78 is 3.9.

### Review

Find the percent of each number.

1. What is 2% of 10?
2. What is 5% of 50?
3. What is 10% of 30?
4. What is 25% of 18?
5. What is 20% of 36?
6. What is 11% of 40?
7. What is 8% of 80?
8. What is 15% of 45?
9. What is 20% of 100?
10. What is 25% of 250?
11. What is 4% of 60?
12. What is 5% of 85?
13. What is 2% of 18?
14. What is 15.5% of 90?
15. What is 20.5% of 70?

To see the Review answers, open this PDF file and look for section 8.17.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

Percent

Percent means out of 100. It is a quantity written with a % sign.

Proportion

A proportion is an equation that shows two equivalent ratios.