Transcript Percent Proportion

Percent Proportion &
Equation
Percent Proportion & Equation
Objective:
7.1.01 Develop and use ratios, proportions, and
percents to solve problems
Essential Question:
How can I use proportions and
equations to solve problems
involving percents?
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 (=).
Percent Proportion & Equation
NEW Vocabulary:
Percent Proportion: a proportion that can be used to
determine percents of numbers.
IS
OF
%
100
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.
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.
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.
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
Percent Proportion & Equation
Method One: The Percent Proportion
IS
OF
%
100
Percent Proportion & Equation
Method One: The Percent Proportion
Part
Base
Percent
100
Percent Proportion & Equation
Method Two: The Percent Equation
IS
OF
%
100
Part
IS % OF
% Base
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%
Percents Proportion & Equation
Example 1: How to find a Percent
A) What percent of 150 is 45
The Percent Proportion
IS
OF
%
100
45
150
30%
x
100
Percents Proportion & Equation
Example 1: How to find a Percent
B) What percent of 25 is 20
The Percent Proportion
IS
OF
%
100
20
25
80%
x
100
Percents Proportion & Equation
Example 1: How to find a Percent
C) What percent of 400 is 8
The Percent Proportion
IS
OF
%
100
8
400
2%
x
100
Percents Proportion & Equation
Example 2: How to find a Part (IS)
A) 30% of 150 is what number? 45
The Percent Proportion
IS
OF
%
100
x
150
30
100
Percents Proportion & Equation
Example 2: How to find a Part (IS)
B) 20% of 25 is what number?
The Percent Proportion
IS
OF
%
100
x
25
5
20
100
Percents Proportion & Equation
Example 2: How to find a Part (IS)
C) 2% of 400 is what number?
The Percent Proportion
IS
OF
%
100
x
400
8
2
100
Percents Proportion & Equation
Example 3: How to find a Whole (OF)
A) 30% of what number is 45?
The Percent Proportion
IS
OF
%
100
45
x
150
30
100
Percents Proportion & Equation
Example 3: How to find a Whole (OF)
B) 20% of what number is 5?
The Percent Proportion
IS
OF
%
100
5
x
25
20
100
Percents Proportion & Equation
Example 3: How to find a Whole (OF)
C) 2% of what number is 8?
The Percent Proportion
IS
OF
%
100
8
x
400
2
100
Percent Proportion & Equation
Method One: The Percent Proportion
We can use the percent
proportion to find:
IS
OF
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30
%
100
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
OF
%
100
$160
Percent Proportion & Equation
Independent Practice:
Solve the examples with a proportion or equation:
1. What is 80% of 12
= 9.6
2. 48 is 60% of what number = 80
3. What percent of 90 is 50
4. What is 175% of 85
= 55.6%
= 148.75
5. 96 is 160% of what number = 60
6. What percent of 24 is 72
= 300%
Percent Proportion & Equation
Summary:
We can use the percent
proportion to find:
IS
OF
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30
%
100
Percent Proportion & Equation
Using the Percent Equation
Not Discussed in class
Percent Proportion & Equation
HOMEWORK
•Solving Percent Problems Using Proportions
COURSE 2 LESSON 6-5
117 is 45% of what number?
The model shows the relationship.
117
45
=
n
100
Write the proportion.
45n = 117(100)
Write the cross products.
45n
117(100)
=
45
45
Divide each side by 45.
n = 260
Simplify.
117 is 45% of 260.
6-5
•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
15
=
n
100
Write the proportion.
15n = 96(100)
Write the cross products.
15n
96(100)
=
15
15
Divide each side by 15.
n = 640
Simplify.
Check 15% of 640 = 0.15 • 640 = 96
6-5
COURSE 2 LESSON 6-5
•Solving Percent Problems Using Proportions
Use a proportion to solve.
1. What percent of 240 is 60?
2. 90 is what percent of 120?
25%
75%
3. 75% of what number is 66?
88
4. 24 is 96% of what number?
25
6-5