6th Grade Math Textbook, Fundamentals

 &KDSWHU

7-4

Update your skills. See page 412 XIII.

Find a Percentage of a Number

Objective To use the percent formula to find a percentage of a number• To use a percent

proportion to find a percentage of a number

A school poll showed that 15% of the

180 students who responded wanted to

lengthen the school year. How many

students wanted a longer school year?

To find the number of students, find 15% of 180.

Here are two ways to find a percentageof a number:

Method 1 Use the

You can write the percent as a decimal or a fraction.

Percent Formula

• Write the percent as a decimal,
  then multiply.
  r• bp
  15% • 180 p Substitute for rand b.
  0.15 • 180 p Simplify.
  27 p
  
  
  • Write the percent as a fraction, then multiply.
    r• bp
    15% • 180 p
  
  
  
  


• p Simplify. Use the GCF.

27 p

180

1

9

3

20

1

Method 2 Use the

Solve: 

100 p180 • 15 Cross multiply.



p 27

Check:

2700  2700 Tr u e

So 15% of 180 is 27. This means that 27 students are in favor of a longer school year.

2700

100

100 p

100 Simplify. Divide both sidesby 100 to isolate p.

15

100

27

180

15

100

p

180

?



Percent Proportion

Substitute 27 for p. Cross multiply.

Substitute 180 for the base

and 15 for the percent.

Key Concept

Percent Formula

r• bp

rate (r) • base (b) percentage (p)

percent number number

(whole) (part)

Think

15%  10015 203

Find 37 % of 80 using the percent formula.

r• bp

37 % • 80 p Substitute for rand b.

0.375• 80 p Write 37 % as a decimal.

30 p Multiply.

So 37 % of 80^12 30.

1

2

1

2

1

2

1 Find 15.2% of 81 using a percent proportion.

 Write the proportion.

100 p81 • 15.2 Cross multiply.

100 p1231.2

p12.312

So 15.2% of 81 12.312.

Simplify. Divide both sides

by 100 to isolate p.

15.2

100

p

81

2

Key Concept

Percent Proportion

In a percent proportion, one number,

the part (called the ), is

being compared to the whole quantity

(called the ). The other ratio is

the written as a fraction,

where the whole is 100.



percent (%)

100

part

whole

base

percentage (p)

base (b)

percentage

percent

0% 15% (percent)

0? (percentage) 180 (base)

100%