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How to Teach Percentages Using Proportions
Math For Life Situations
By
Reda Berry
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Objectives• Understand ratios
• Offer instructors an effective, easy, and relevant way to teach percents using the proportion method
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What is a Ratio? • A ratio is a comparison of two numbers
4 puzzle parts to 3 gears
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How do you write a ratio?
• 4 puzzle parts to 3 gears– 4 to 3– 4 : 3– 4/3
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More about Ratios• Ratios can be reduced by division
Example: 6/4 = 3/2 (when divided by 2/2)
6 to 4 = 3 to 2
6:4 = 3:2
• Ratios can be increased by multiplication Example: 6/4 = 18/22 (when multiplied by 3/3)
6 to 4 = 18 to 22
6:4 = 18:22
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Find the Ratio mistake• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7
– 20 adults to 100 Children = 100: 20
– 25 female employees to 90 total employees = 5/18
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Find the Ratio mistake• A ratio is a comparison of two numbers
– 34 customers to 7 sales = 34 to 7 correct– 20 adults to 100 Children = 100: 20 should be
20:100– 25 female employees to 90 total employees =
5/18 correct 25/90 divided by 5 = 5/18
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Proportions• When two pairs of numbers have the same ratio, like the
numbers 2, 7 and 10, 35 we say they are proportional.
The equation 2/7 = 10/35 is a proportion• In any proportion, the cross products are equal notice
that 2 x 35 = 7 x 10
70 = 70
Notice: We can use this fact to solve a proportion if one of the 4 numbers is unknown
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Word Problem #1• If it takes 2 gallons of
paint to paint a room which has 480 ft² to be painted, how many gallons will it take to paint a room which has 1200 ft² to be painted?
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Word Problem #1 solved• If it takes 2 gallons of
paint to paint a room which has 480 ft² to be painted, how many gallons will it take to paint a room which has 1200 ft² to be painted?
• 2 gallons paint
• 480 ft² to be painted
• How much paint?
• 1200 ft² to be painted
2/480 = x/1200
2 x 1200 = 480x
2400 = 480x
2400/480 = x
5 gallons of paint = x
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Word Problem #2• An 8 lb turkey breast
contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?
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Word Problem #2 solution• An 8 lb turkey breast
contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?
8 lb/36 = x lb/54
8 x 54 = 36x
432 = 36x
432/36 = 36/36x
12 = x
Check:
8 x 54 = 36 x 12
432 = 432
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How do you introduce percents?
1. What is 20% of 40?
2. 45 is 45% of what number?
3. 35 is what percent of 70?
Students get confused on how to solve these problems.
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?????
1. When do I multiply?
2. When do I divide?
3. How do you multiply or divide with percents?
4. Please, give me an easy way to do it!
The answer is a PROPORTION!
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• All percent problems are composed of three parts– Percent– Part– Whole
• The answer lies in identifying which one is missing.
Basics of Percents
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The percent proportion part percent number whole 100
100
*part is to whole as part is to whole*
isof
%
The percent proportion using key words
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Identifying Components
8 is 20% of 40• Clue Words– IS = Part, portion– % = Percent Symbol– OF = Whole, original
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Identifying Components8
isof
%100
is 20% of 40
100IS
OF%
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Identifying Components
isof
%100
is 20% of 40
1008
OF%
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Identifying Components
isof
%100
is 20% of
1008
40%
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Identifying Components
isof
%100
is % of
1008
4020
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Using proportions to find answers
What is 20% of 40?
isof
%100100
?40
20
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Using proportions to find answers
What is 20% of 40?
isof
%100100
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Using proportions to find answers
What is 20% of 40?
isof
%100100
?40
20
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Using proportions to find answers
8 is 20% of what number?
isof
%100100
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Using proportions to find answers
8 is 20% of what number?
isof
%100100
8?
20
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Using proportions to find answers
8 is what % of 40?
isof
%100100
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Using proportions to find answers
8 is what % of 40?
isof
%100100
840
?
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Start with teaching students how to identify the three components using CLUE WORDS◦ Is – defines the part, or portion
◦ Of – defines the whole or original amount
◦ % symbol – defines percent
Basics of Percents
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Percent Word Problem #1• On average, about 40% of the
body weight of an adult male is muscle. If a certain man weights 225 lbs, how many pounds should be muscle?
A. 325 lbs
B. 25 lbs
C. 90 lbs
D. 112.5 lbs
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Percent Word Problem #1 Solved
• On average, about 40% of the body weight of an adult male is muscle. If a certain man weights 225 lbs, how many pounds should be muscle?
x/225 = 40/100
100x = 225 x 40
100x = 9000
x = 9000/100
x = 90
Check:
100 x 90 = 225 x 40
9000 = 9000
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Percent Word Problem #2• Mrs. Jackson makes
$450 a week. She pays $90 a week for food. Money spent for food is what percent of Mrs. Jackson’s income?
Contemporary GED Math, 2002
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Percent Word Problem #2 solved• Mrs. Jackson makes
$450 a week. She pays $90 a week for food. Money spent for food is what percent of Mrs. Jackson’s income?
90/450 = x/100
90 x 100 = 450x
9000 = 450x
9000/450 = x
20% = x
Check
90 x 100 = 450 x 20
9000 = 9000
Contemporary GED Math, 2002
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Percent Word Problem #3• Eighteen people
attended David’s evening math class. This represents 75% of the number registered for the class. How many people are registered for his class?
Contemporary GED Math, 2002
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Percent Word Problem #3 solution• Eighteen people attended
David’s evening math class. This represents 75% of the number registered for the class. How many people are registered for his class?
18/x = 75/100
18 x 100 = 75x
1800 = 75x
1800/75 = x
24 = x
Check:
18 x 100 = 75 x 24
1800 = 1800
Contemporary GED Math, 2002
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1. Multiplication? Division?2. Eliminates the need to convert
percent into decimals.3. Introduces students to variables.4. Fractions, Unit conversions and
Geometry applications.
Advantages: