How to Teach Percentages Using Proportions

Math For Life Situations

By

Reda Berry

Objectives• Understand ratios

• Offer instructors an effective, easy, and relevant way to teach percents using the proportion method

What is a Ratio? • A ratio is a comparison of two numbers

4 puzzle parts to 3 gears

How do you write a ratio?

• 4 puzzle parts to 3 gears– 4 to 3– 4 : 3– 4/3

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

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

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

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

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?

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

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?

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

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.

?????

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!

• All percent problems are composed of three parts– Percent– Part– Whole

• The answer lies in identifying which one is missing.

Basics of Percents

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

Identifying Components

8 is 20% of 40• Clue Words– IS = Part, portion– % = Percent Symbol– OF = Whole, original

Identifying Components8

isof

%100

is 20% of 40

100IS

OF%

Identifying Components

isof

%100

is 20% of 40

1008

OF%

Identifying Components

isof

%100

is 20% of

1008

40%

Identifying Components

isof

%100

is % of

1008

4020

Using proportions to find answers

What is 20% of 40?

isof

%100100

?40

20

Using proportions to find answers

What is 20% of 40?

isof

%100100

Using proportions to find answers

What is 20% of 40?

isof

%100100

?40

20

Using proportions to find answers

8 is 20% of what number?

isof

%100100

Using proportions to find answers

8 is 20% of what number?

isof

%100100

8?

20

Using proportions to find answers

8 is what % of 40?

isof

%100100

Using proportions to find answers

8 is what % of 40?

isof

%100100

840

?

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

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

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

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

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

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

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

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: