1. How to Teach Percentages Using Proportions
Math For Life Situations By
Reda Berry

2. Objectives Understand ratios
Offer instructors an effective, easy, and relevant way to teach percents using the proportion method

3. What is a Ratio? A ratio is a comparison of two numbers
4 puzzle parts to 3 gears
A comparison of two numbers normally written as a fraction, but that is not the only way to write it. One of the questions we ask ourselves is when do you teach ratios? Normally fits in nicely after you’ve taught fractions

4. How do you write a ratio? 4 puzzle parts to 3 gears 4 to 3 4 : 3 4/3
When you look at how the ratio is written ; 4 to 3, 4:3, and 4/3, and you compare them to the written words (4 puzzle parts to 3 gears), what do they all have in common? If you allow your students to discover the answer they will remember it! Answer – they are written in the same order as the written words listed above.

5. 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
Another note, ratios remain as an improper fraction in other words it would not become a mixed or whole number

6. 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
1. In doing this game you could do it as groups and let a representative from the group answer. You could also require them to repeat the rules..

7. 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
Transition: What does a ratio have to do with a proportion?

8. 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 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
I will move to the chart paper and show how this multiplication works.

9. 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?
After I read the word problem I will go to the chart paper and solve it. 2 gal/480 ft = ? Gal/1200 ft answer is 5 gallons.

10. 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
After showing on slide how to solve the problem I will check my answer. How do you know the answer is correct? 2 x 1200 = 480 x = 2400 Transition: Lets work another problem

11. 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?
The first problem I worked, the second problem work with the students and have them contribute. Ask questions like, how do I know this would be a proportion problem? Help me to set up the problem correctly. I will then go to the chart paper. 8 lb/36 servings = ?/54 servings. Equals 12 pounds, how do you know your answer is correct? Answer: By cross multiplication

12. Word Problem #2 solution
8 lb/36 = x lb/54 8 x 54 = 36x 432 = 36x 432/36 = 36/36x 12 = x Check: 8 x 54 = 36 x = 432
An 8 lb turkey breast contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?

13. How do you introduce percents?
What is 20% of 40?
45 is 45% of what number?
35 is what percent of 70?
Students get confused on how to solve these problems.

14. ????? When do I multiply? When do I divide?
How do you multiply or divide with percents?
Please, give me an easy way to do it!
The answer is a PROPORTION!

15. Basics of Percents All percent problems are composed of three parts
Whole
The answer lies in identifying which one is missing.

16. The percent proportion
part percent number
whole
*part is to whole as part is to whole*
The percent proportion
using key words is % of
100

17. Identifying Components
8 is 20% of 40
Clue Words
IS = Part, portion
% = Percent Symbol
OF = Whole, original
PART
PERCENT
WHOLE

18. Identifying Components8 is
20% of 40 IS % is % OF
100 of
100

19. Identifying Componentsis
20% of 40 8 % is % OF
100 of
100
Moved 8 into replace the is or also known as the part.

20. Identifying Componentsis
20% of 8 % is % 40
100 of
100
40 is the “of” or the whole amount. To remember which one is on top or bottom, remember “I” comes before “o” so that’s how I remember that “is” is located in the numerator and “of” the denominator.

21. Identifying Componentsis % of 8 20 is % 40
100 of
100
This problem had all the components or parts listed, but what if one is missing?

22. Using proportions to find answers
What is 20% of 40? ? 20 is % 40
100 of
100
I will move to the chart to solve the problem using cross multiplication x ? = 40 x x = 800 so divide 800 by 100 = 8 check work: 100 x 8 = 40 x = 800

23. Using proportions to find answers
What is 20% of 40? is %
100 of
100

24. Using proportions to find answers
What is 20% of 40? ? 20 is % 40
100 of
100
I will move to the chart to solve the problem using cross multiplication x ? = 40 x x = 800 so divide 800 by 100 = 8 Check answer x 8 = 40 x = 800

25. Using proportions to find answers
8 is 20% of what number? is %
100 of
100
We need to place the numbers in the correct place

26. Using proportions to find answers
8 is 20% of what number? 8 20 is % ?
100 of
100
I will move to the chart to solve the problem using cross multiplication. 8 x 100 = ? x = 20x so divide 800 by 20 = 40 Check: 8 x 100 = 40 x = 800

27. Using proportions to find answers
8 is what % of 40? is %
100 of
100
Here we are looking for the percent.

28. Using proportions to find answers
8 is what % of 40? 8 ? is % 40
100 of
100
I will move to the chart to solve the problem using cross multiplication. 8 x 100 = 40 x ? = 40x so divide 800 by 40 = 20 Check: 8 x 100 = 40 x = 800 Transition: Preparing for percent word problems using the proportion method requires identifying/understanding some of the key words to watch for.

29. Basics of Percents
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

30. 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 lbs
B. 25 lbs
C. 90 lbs
D lbs
I will talk about the problem a little bit then move to chart and work problem. This is the first word problem, so I will work out the problem. Begin with 40% in relation to his body. Ask where would 40% be located? A little below half of his waist, so 50% would be exactly half of 225 lbs which would be lbs; therefore, your answer needs to be less than lbs. Set up problem is/of = %/ x/225 = 40/ x = 225 x x = x = 90lbs

31. 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/ x = 225 x x = 9000 x = 9000/100 x = 90 Check: 100 x 90 = 225 x = 9000
The first problem was done by the teacher, now do a problem with some assistance from the class.

32. 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?
I will read the problem then go to the chart to solve this problem. This is problem 2, so work the problem with class participation. What is the question asking for? Answer: the percent. When setting up the problem we already know the x gets placed above the Next question is where do the $450 and $90 go in the proportion? Think of it in terms of the whole amount she makes a week which would be placed on the bottom and 90 as the part on top. It would look like this. 90/450 = x/ x 100 = 450x = 450x /450 = x x = 20%
Contemporary GED Math, 2002

33. 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/ x 100 = 450x 9000 = 450x 9000/450 = x 20% = x Check 90 x 100 = 450 x = 9000
Contemporary GED Math, 2002

34. 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

35. 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/ x 100 = 75x 1800 = 75x 1800/75 = x 24 = x Check: 18 x 100 = 75 x = 1800
Contemporary GED Math, 2002

36. Advantages: Multiplication? Division?
Eliminates the need to convert percent into decimals.
Introduces students to variables.
Fractions, Unit conversions and Geometry applications.
This is the last slide and the end of my presentation. We began our journey with ratios that can be written as a fraction, colon, or the word “to”; then we took the ratio and discussed how a proportion is two ratio’s that are equal to each other. Finally, we used the proportion tool to solve percent problems which included word problems.