1. Percent Proportion & Equation

2. Percent Proportion & Equation
Objective:
Develop and use ratios, proportions, and percents to solve problems
Essential Question:
How can I use proportions and equations to solve problems involving percents?

3. Percent Proportion & Equation
OLD Vocabulary:
Percent: a special ratio comparing a number to 100.
Proportion: a statement where one ratio is equal to another ratio.
Equation: a sentence with an equal sign (=).

4. Percent Proportion & Equation
NEW Vocabulary:
Percent Proportion: a proportion that can be used to determine percents of numbers.
Part: in a percent proportion, the number being compared to the whole quantity.
Base: in a percent proportion, the whole quantity, or the number to which the part if being compared. IS %
100 OF

5. Percent Proportion & Equation
Lets Remember:
This concept is always going to be useful to us whenever we go shopping or are in any situation where tax, tip, or discounts are involved.

6. Percent Proportion & Equation
We have already learned about how to solve proportions and equations.
So the only thing we really have to learn how to do is set up the problem.

7. Percent Proportion & Equation
Possible Algorithms Include:
When you want to solve percent problems you can use either one of two algorithms:
Method One:
The Percent Proportion
Method Two:
The Percent Equation

8. Percent Proportion & Equation
Method One: The Percent Proportion IS % OF
100

9. Percent Proportion & Equation
Method One: The Percent Proportion
Part
Percent
Base
100

10. Percent Proportion & Equation
Method Two: The Percent Equation IS % IS % OF
100 OF
Part %
Base

11. Percent Proportion & Equation
Real World Example:
In a school band of 24 students, 9 students play a brass instrument. What percent of the band members play a brass instrument?
37.5%

12. Percents Proportion & Equation
Example 1: How to find a Percent
A) What percent of 150 is 45
30% 45 x
The Percent Proportion IS %
100
150 OF
100

13. Percents Proportion & Equation
Example 1: How to find a Percent
B) What percent of 25 is 20
80% 20 x
The Percent Proportion IS %
100 25 OF
100

14. Percents Proportion & Equation
Example 1: How to find a Percent
C) What percent of 400 is 8 2% 8 x
The Percent Proportion IS %
100
400 OF
100

15. Percents Proportion & Equation
Example 2: How to find a Part (IS)
A) 30% of 150 is what number? 45 x 30
The Percent Proportion IS %
100
150 OF
100

16. Percents Proportion & Equation
Example 2: How to find a Part (IS)
B) 20% of 25 is what number? 5 x 20
The Percent Proportion IS %
100 25 OF
100

17. Percents Proportion & Equation
Example 2: How to find a Part (IS)
C) 2% of 400 is what number? 8 x 2
The Percent Proportion IS %
100
400 OF
100

18. Percents Proportion & Equation
Example 3: How to find a Whole (OF)
A) 30% of what number is 45?
150 45 30
The Percent Proportion IS % x
100 OF
100

19. Percents Proportion & Equation
Example 3: How to find a Whole (OF)
B) 20% of what number is 5? 25 5 20
The Percent Proportion IS % x
100 OF
100

20. Percents Proportion & Equation
Example 3: How to find a Whole (OF)
C) 2% of what number is 8?
400 8 2
The Percent Proportion IS % x
100 OF
100

21. Percent Proportion & Equation
Method One: The Percent Proportion IS %
We can use the percent proportion to find:
100 OF
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30

22. Percent Proportion & Equation
Real World Example:
The sale price of a new pair of Air Jordan basketball shoes is $120. This is 75% of the original price. What was the original price of the Air Jordan basketball shoes? IS %
100 OF
$160

23. Percent Proportion & Equation
Independent Practice:
Solve the examples with a proportion or equation:
1. What is 80% of 12
2. 48 is 60% of what number
3. What percent of 90 is 50
4. What is 175% of 85
5. 96 is 160% of what number
6. What percent of 24 is 72
= 9.6
= 80
= 55.6% =
= 60
= 300%

24. Percent Proportion & Equation
Summary: IS %
We can use the percent proportion to find:
100 OF
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30

25. Percent Proportion & Equation Using the Percent Equation
Not Discussed in class

26. Percent Proportion & Equation
HOMEWORK

27. Solving Percent Problems Using Proportions
COURSE 2 LESSON 6-5
117 is 45% of what number?
The model shows the relationship. =
117 n 45
100
Write the proportion.
Write the cross products.
45n = 117(100)
Divide each side by 45.
45n 45
117(100) =
n = 260
Simplify.
117 is 45% of 260.
6-5

28. Solving Percent Problems Using Proportions
COURSE 2 LESSON 6-5
Use a proportion to solve: 96 is 15% of what number? Model the relationship.
The model shows the relationship. = 96 n 15
100
Write the proportion.
Write the cross products.
15n = 96(100)
Divide each side by 15.
15n 15
96(100) =
n = 640
Simplify.
Check 15% of 640 = 0.15 • 640 = 96 
6-5

29. Solving Percent Problems Using Proportions
COURSE 2 LESSON 6-5
Use a proportion to solve.
1. What percent of 240 is 60? is what percent of 120?
3. 75% of what number is 66? is 96% of what number?
25%
75% 88 25
6-5