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# Percent of a Number

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

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Practice Percent of a Number
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Find the Percent of a Number

Do you like to ride roller coasters? Take a look at this dilemma.

At an amusement park there is an average of 30,000 visits daily. Over 75% of those people ride on the biggest roller coasters. About how many people ride the roller coasters?

To figure this out, you will need to find the percent of a number. Pay attention and you will know how to solve this problem by the end of the Concept.

### Guidance

We said that percent are very useful. Part of the usefulness is being able to find percentages of a number. In other words, if you are planning a barbecue and the butcher tells you that 30% of the people want chicken…well, how many people is that? For how many people should you buy chicken?

The key words here are “of a number” this means that you multiply to solve the problem. We can convert the percent to a decimal and multiply or convert it to a fraction and multiply.

Let’s suppose that you invited 58 people to the barbecue. If 30% prefer chicken, then we need to know how many people that is.

First, convert 30% to either a decimal or a fraction

$30\% = .30 \ or \ 30\% = \frac{30}{100} = \frac{3}{10}$

Using the decimal or fraction, you now multiply by the number of people you invited: $.30 \times 58 = 17.4$ or about 17 people

Or

$\frac{3}{10} \times 58 = \frac{174}{10} = 17.4$ or about 17 people.

Solve each problem.

#### Example A

What is 20% of 18?

Solution: 3.6

#### Example B

What is 25% of 40?

Solution: 10

#### Example C

What is 5% of 80?

Solution: 4

Now back to the dilemma from the beginning of the Concept.

First, let's write a statement about the problem.

We need to figure out 75% of 30,000.

To do this, first convert 75% to a decimal.

$75\% = .75$

Next, multiply.

$.75 \times 30,000 = 22,500$

22,500 people ride the roller coasters.

### Vocabulary

Ratio
a comparison between two quantities.
Percent
a ratio that is being compared to the quantity of 100. Percent means out of 100.
Fraction
a part of a whole written using a numerator and a denominator.
Decimal
a part of a whole written in base ten place value.
Proportion
two equal ratios form a proportion.

### Guided Practice

Here is one for you to try on your own.

A survey stated that 15% of the people surveyed like olives. Out of the 500 people surveyed, about how many like olives?

Solution

First, let's write a statement describing the problem.

15% of 500

Now change the percent to a decimal.

$15\% = .15$

Next, multiply.

$.15 \times 500 = 75$

75 of the people like olives.

### Practice

Find the percent of the given number by converting the percent to a decimal. You may round if necessary.

1. 30% of 90
2. 3% of 12
3. 14% of 900
4. 33% of 99
5. 18% of 100
6. 8% of 72
7. 11% of 50
8. 14.5% of 30
9. 12% of 80
10. 2% of 800
11. 150% of 21
12. 45% of 60

1. For every paycheck you receive, your employer pays 6% to social security. Write this percent as a ratio with a denominator of 100.
2. Jimmy’s height is 1.78m. Write his height as a percent of a meter.
3. A store did a survey and found that $\frac{4}{5}$ of its customers have shopped at its competitors’ stores within in the previous month. What percent is that?

### Vocabulary Language: English

Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
fraction

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Percent

Percent

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

Proportion

A proportion is an equation that shows two equivalent ratios.