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7th Grade Math / Lesson 3: Percents III

What will we be learning in this lesson?

  • In this lesson, you will learn how to evaluate percents.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • Percents are used to help make comparisons. They compare quantities in terms of 100. The word "percent" actually means "per hundred".
  • There is a proportion to use when solving any type of percent problem.

  • Suppose you were going to pay 40% of the original price for a pair of shoes. You paid $60. How much is the original price? To set up this proportion, 40 would be the percent number and 60 would be the "part" because it is NOT the original price. It is the part of the price that you are paying. In this case, it is the "whole" that you are looking for.
  • Let's look at how to solve this.


  • First, put the numbers in where they belong.

  • Then, solve the proportion. Find the numbers on the diagonal that you know. There are two diagonals - the 60 and the 100 is one of them, and the "whole" and the 40 is the other diagonal.

  • We will need to use the diagonal with the 60 and the 100 since we know both of the numbers. MULTIPLY these numbers together. 60 * 100 = 6000

  • Now take that answer and DIVIDE by the other number in the problem that has not been used yet. 6000 40 = 150.
    So the original price for the shoes is $150.


  • Let's find another one. There are 40 students that walk to school. This is 20% of the total number of students. Find out how many students are in the school.
  • You need to figure out what you know and what you are looking for.
  • The problem says to "Find out how many students..." so the percent is NOT the number we are looking for. We need the number of students.
  • Do we need the total number of students?   Yes, we need the total number of students in the school.
  • So we have the percent value and the "part" for the proportion.


  • Now let's solve the proportion.

  • Find the diagonal of numbers that we know.

  • Multiply the numbers on this diagonal. 40 * 100 = 4000

  • Then divide by the other number that you haven't used yet.
    4000 20 = 200

    So the number of students in the school is 200.



  • Once you have your proportion set up, MULTIPLY the diagonal of numbers that you have, then DIVIDE by the number not used yet.

  • Can you set up the proportion to find the total amount in a percent problem?

  • Can you solve the proportion to find the missing number?

  • Be sure to go back to your classroom to get any homework assignments or other activities you need to attend to.