6th Grade Math Textbook, Fundamentals

 &KDSWHU

7-6

Update your skills. See page 413 XIV.

Find the Original Number or the Base

Objective To find a number when a percent of it is known, using the percent formula or a

percent proportion • To determine whether the percentage, base, or percent is missing in a percent

problem and solve the problem

Six of Greene County’s middle schools sent bands to the

Earth Day Festival. If 30% of the county’s middle schools sent

bands to the event, how many middle schools are in the county?

To find the total number, or base, solve: 30% of what numberis 6?

Use the percent formula or a proportion to find the base.

0% 30%

0 6?

100%

Remember:

Percent Formula

r• b p

rate (r) • base (b) percentage (p)

Method 1 Use the Percent Formula: r • bp

Let bthe total number of middle schools in the county.

30% • b 6 Substitute 30% for rand 6 for p.

0.3b 6 Write the percent as a decimal.

 Divide both sides by 0.3 to isolate b.

b  20

6

0.3

0.3b

0.3

Method 2 Use a Percent Proportion

Let bthe total number of middle schools in the county.

Solve: 

6 • 100  30 b Cross multiply.

600  30 b Simplify.



20 b

So both methods show that there are 20 middle schools in the county.

Divide both sides by 30

to isolate b.

Substitute 6 for pand

30 for the percent.

30 b

30

600

30

30

100

6

b

60% of what number is 12?

Use the percent formula: r• b p.

60% • b 12 Substitute 60% for rand 12 for p.

0.6• b 12 Rename 60% as a decimal.



b  20

So 60% of 20 is 12.

Divide both sides

by 0.6 to isolate b.

12

0.6

0.6b

0.6

(^1) 120% of what number is 24?
Use a percent proportion.

24 • 100  120 b Cross multiply.

20 b
So 120% of 20 is 24.
Divide both sides
by 120 to isolate b.
120 b
120
2400
120
120
100
24
b
2
Check:
600  600 Tr u e
Substitute 20 for b
and cross multiply.
30
100
(^6) ?
20
Remember:
Percent Proportion

percent (%)
100
percentage (p)
base (b)
part
whole
percentage base
percent