percent proportion & equation
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Percent Proportion & Equation
Percent Proportion & EquationObjective: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?
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.
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
IS
OF%
100
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 ProportionPercent Proportion & Equation
ISOF
%100
Method One: The Percent ProportionPercent Proportion & Equation
PartBase
Percent100
Method Two: The Percent EquationPercent Proportion & Equation
IS OF%IS
OF%
100
Part Base%
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?
Percent Proportion & Equation
37.5%
Percents Proportion & EquationExample 1: How to find a Percent
A) What percent of 150 is 45 30%The Percent Proportion
ISOF
%100
45150
x100
Percents Proportion & EquationExample 1: How to find a Percent
B) What percent of 25 is 20 80%The Percent Proportion
ISOF
%100
2025
x100
Percents Proportion & EquationExample 1: How to find a Percent
C) What percent of 400 is 8 2%The Percent Proportion
ISOF
%100
8400
x100
Percents Proportion & EquationExample 2: How to find a Part (IS)
A) 30% of 150 is what number? 45The Percent Proportion
ISOF
%100
x150
30100
Percents Proportion & EquationExample 2: How to find a Part (IS)
B) 20% of 25 is what number? 5The Percent Proportion
ISOF
%100
x25
20100
Percents Proportion & EquationExample 2: How to find a Part (IS)
C) 2% of 400 is what number? 8The Percent Proportion
ISOF
%100
x400
2100
Percents Proportion & EquationExample 3: How to find a Whole (OF)
A) 30% of what number is 45? 150The Percent Proportion
ISOF
%100
45x
30100
Percents Proportion & EquationExample 3: How to find a Whole (OF)
B) 20% of what number is 5? 25The Percent Proportion
ISOF
%100
5x
20100
Percents Proportion & EquationExample 3: How to find a Whole (OF)
C) 2% of what number is 8? 400The Percent Proportion
ISOF
%100
8x
2100
Method One: The Percent ProportionPercent Proportion & Equation
IS
OF%
100We can use the percent proportion to find:
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30
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?
Percent Proportion & Equation
$160
IS
OF%
100
Independent Practice:Solve the examples with a proportion or equation:
1. What is 80% of 122. 48 is 60% of what number3. What percent of 90 is 504. What is 175% of 855. 96 is 160% of what number6. What percent of 24 is 72
Percent Proportion & Equation
= 9.6= 80= 55.6%= 148.75= 60= 300%
Summary:Percent Proportion & Equation
IS
OF%
100We can use the percent proportion to find:
1) Part (IS) – 60% OF 50 IS _?_
2) Whole (OF) – 60% OF _?_ IS 30
3) Percent (%) – _?_ OF 50 IS 30
Using the Percent Equation
Not Discussed in class
Percent Proportion & Equation
HOMEWORK
Percent Proportion & Equation
117 is 45% of what number?
COURSE 2 LESSON 6-5
117 is 45% of 260.
=117n
45100 Write the proportion.
Write the cross products. 45n = 117(100)
n = 260 Simplify.
The model shows the relationship.
6-5
Divide each side by 45.45n45
117(100)45=
• Solving Percent Problems Using Proportions
Use a proportion to solve: 96 is 15% of what number? Model the relationship.
COURSE 2 LESSON 6-5
=96n
15100 Write the proportion.
Write the cross products. 15n = 96(100)
n = 640 Simplify.
The model shows the relationship.
Check 15% of 640 = 0.15 • 640 = 96
6-5
Divide each side by 15.15n15
96(100)15=
• Solving Percent Problems Using Proportions
Use a proportion to solve.
1. What percent of 240 is 60? 2. 90 is what percent of 120?
3. 75% of what number is 66? 4. 24 is 96% of what number?
COURSE 2 LESSON 6-5
25% 75%
88 25
6-5
• Solving Percent Problems Using Proportions