Percent Proportion & Equation
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Transcript of Percent Proportion & Equation
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Percent Proportion & Equation
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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?
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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
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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
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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
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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
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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
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Method One: The Percent ProportionPercent Proportion & Equation
ISOF
%100
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Method One: The Percent ProportionPercent Proportion & Equation
PartBase
Percent100
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Method Two: The Percent EquationPercent Proportion & Equation
IS OF%IS
OF%
100
Part Base%
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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%
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Percents Proportion & EquationExample 1: How to find a Percent
A) What percent of 150 is 45 30%The Percent Proportion
ISOF
%100
45150
x100
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Percents Proportion & EquationExample 1: How to find a Percent
B) What percent of 25 is 20 80%The Percent Proportion
ISOF
%100
2025
x100
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Percents Proportion & EquationExample 1: How to find a Percent
C) What percent of 400 is 8 2%The Percent Proportion
ISOF
%100
8400
x100
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Percents Proportion & EquationExample 2: How to find a Part (IS)
A) 30% of 150 is what number? 45The Percent Proportion
ISOF
%100
x150
30100
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Percents Proportion & EquationExample 2: How to find a Part (IS)
B) 20% of 25 is what number? 5The Percent Proportion
ISOF
%100
x25
20100
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Percents Proportion & EquationExample 2: How to find a Part (IS)
C) 2% of 400 is what number? 8The Percent Proportion
ISOF
%100
x400
2100
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Percents Proportion & EquationExample 3: How to find a Whole (OF)
A) 30% of what number is 45? 150The Percent Proportion
ISOF
%100
45x
30100
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Percents Proportion & EquationExample 3: How to find a Whole (OF)
B) 20% of what number is 5? 25The Percent Proportion
ISOF
%100
5x
20100
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Percents Proportion & EquationExample 3: How to find a Whole (OF)
C) 2% of what number is 8? 400The Percent Proportion
ISOF
%100
8x
2100
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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
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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
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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%
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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
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Using the Percent Equation
Not Discussed in class
Percent Proportion & Equation
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HOMEWORK
Percent Proportion & Equation
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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
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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
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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