Three Types of Percent Problems

Remember, percents are "parts of a whole". The part is the numerator and the whole is the denominator. 17% means 17 parts per 100 or We are going to solve problems involving percents. There are 3 types of problems: 1. Find the part What number is 54% of 34? 2. Find the whole 4 is 60% of what number? 3. Find the percent 18 is what percent of 28?

Two words that will occur in these types of problems are "is" and "of". These words have specific meanings in math. "Is" means equals (=) "Of" means multiply To solve a percent problem, translate the words into an equation. Change the following: 1. Percent into a decimal 2. "is" to "=" 3. "of" to " . " 4. Unknown to "x" Then, solve the equation.

Finding the Part...

Write a mathematical sentence Examples: Find 40% of 60 Write a mathematical sentence Click .40 60 = 24 20% of 90 Write a mathematical sentence Click .20 90 = 18

Write a mathematical sentence X = .10 88 What is 10% of 88? Write a mathematical sentence X = .10 88 X = 8.8 Try these: Find 12% of 70 What is 40% of 28? Answer: .12 x 70 = 8.4 X = .40 x 28 X = 11.20

Another Method: You can also solve percent problems by setting up a proportion. Since percents are parts of a whole, you can create the following proportion:

When figuring out which is the "part" and which is the "whole", remember that you take a percent of the whole and 
the answer is the part. In other words, the whole is with the word "of" and the part is with the word "is".

= Proportion Method Steps 1. Set up the proportion as shown. is % of 2. Substitute given values into the proportion. 3. Solve the proportion. is of % 100 = Note: You can use this box to solve many problems involving percents! Note: Try to find the numbers that are attached to the words/symbols: is, of, or percent.

Click on each box to see if you substituted correctly. Example: What is 25% of 400? Steps 1. Set up the proportion. 2. Substitute. 3. Solve. is of % 100 = ? 25 400 100 Click on each box to see if you substituted correctly. What is 25% of 400? Click 400 x 25 = 100w 10,000 = 100w 10,000/100 = w 100 = w

= Try it: What is 20% of 180? Steps 1. Set up the proportion. % is 2. Substitute. 3. Solve. is of % 100 = Answer: 36

Finding the Whole...

Remember, you can solve this by: 1. Translating into an equation 2. Setting up a proportion 40% of what number is 50? .40 X = 50 X = 50 .40 X = 125

Try This: 100 is 20% of what number? 100 = .20 x 100 = x .20 x = 500

Finding the Percent...

Remember, you can solve this by: 1. Translating into an equation 2. Setting up a proportion What percent of 80 is 24? x 80 = 24 X = 24 80 X = .30 X = 30%

60 is what percent of 15? 60 = X 15 60 = X 15 4 = X 400% = X

You have just studied three different types of percent problems. Try all 3 types: 24 is 40% of what number? 42 is what percent of 840? What is 30% of 45? Answers: 60 5% 13.5