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 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

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.

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

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..

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?

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

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.

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 5 2400 = 2400 Transition: Lets work another problem

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

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 12 432 = 432 An 8 lb turkey breast contains 36 servings of meat. How many pounds of turkey breast would be needed for 54 servings?

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.

????? 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!

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

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

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

Identifying Components 8 is 20% of 40 IS % is % OF 100 of 100

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

Identifying Components is 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.

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

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. 100 x ? = 40 x 20. 100x = 800 so divide 800 by 100 = 8 check work: 100 x 8 = 40 x 20 800 = 800

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

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. 100 x ? = 40 x 20. 100x = 800 so divide 800 by 100 = 8 Check answer 100 x 8 = 40 x 20 800 = 800

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

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 20. 800 = 20x so divide 800 by 20 = 40 Check: 8 x 100 = 40 x 20 800 = 800

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

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 ?. 800 = 40x so divide 800 by 40 = 20 Check: 8 x 100 = 40 x 20 800 = 800 Transition: Preparing for percent word problems using the proportion method requires identifying/understanding some of the key words to watch for.

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

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 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 112.5 lbs; therefore, your answer needs to be less than 112.5 lbs. Set up problem is/of = %/100 x/225 = 40/100 100x = 225 x 40 100x = 9000 x = 90lbs

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 The first problem was done by the teacher, now do a problem with some assistance from the class.

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 100. 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/100 90 x 100 = 450x 9000 = 450x 9000/450 = x x = 20% 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

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.