1. The Percent Proportion
By Angela Gallacher
7th Grade Mathematics
James Workman Middle School

2. General Objective
NS 1.3 Convert fractions to decimals and percents and use these representation in computations, and applications.
The student will solve problems proportions and percents, then explain to a partner how to solve a percent problem using proportions

3. Vocabulary In a percent proportion:
Percentage: The number that is compared to another number called the base. The ‘part’.
Base: The number to which the percentage is compared. The ‘total’ or ‘whole’.
Rate: The ratio of a number to 100.
Percent Proportion: P = R B

4. Method One: Finding the Percent One Number Is of Another
What percent of 92 is 66?
Set up a proportion to find the percent.
Think: What number is to 100 as 66 is to 92? =
number
100
part
whole
Set up a proportion. n
100 66 92 =
Substitute.
n  92 = 100  66
Find the cross products.
92n = 6600
Simplify.

5. How to use a percent proportion:
40 is 20% of what number?
Remember: P = R or is = %
B of
40 = 20 B
20b = 4000
b = 200

6. Solve using a proportion
What percent of 140 is 21?
Method 1: Set up a proportion.
Think: What number is to 100 as 21 is to 140? =
number
100
part
whole
Set up a proportion. n
100 21
140 =
Let n represent the percent.
n  140 = 100  21
Find the cross products.
140n = 2100
Simplify.

7. What percent of 140 is 21?
Method 2: Set up an equation.
percent  whole = part Set up an equation.
p  140 = Let p represent the percent.
140p
140 = 21
Divide both sides by 140.
p = Simplify.
21 is 15% of 140.

8. What percent of 33 is 22? percent  whole = part Set up an equation.
p  33 = Let p represent the percent.
33p 33 = 22
Divide both sides by 140.
p = Simplify.
22 is 66 2/3% of 33.

9. Practice Write and solve a proportion for each.
What percent of 91 is 45?
What percent of 1270 is 375?
What percent of 240 is 180?
What percent of 186 is 75?

10. Think and Write
Show why 5% of a number is less than 1/10 of the number.
Demonstrate two ways to find 70% of a number.
Name fractions in simplest form that are the same as 40% and as 250%