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7th Grade Math / Lesson 4: Proportions

What will we be learning in this lesson?

  • In this lesson, you will learn how to use proportions to solve other problems.

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


  • The proportion that you use when solving a percent problem is the basic set up that you use in solving any proportional problem.

  • Proportions are two fractions that are equal to each other.

  • In this section, we will not be using the percent part of the proportion. We will be looking at other units of measurement when it comes to numbers. Things like money and quantity (how many).

  • Solving these proportion problems is just like solving the percent problems.


  • Try solving this proportion.

  • Just as you did with the percent problems, find the numbers on the diagonal that you know. There are two diagonals - the 60 and the 100 is one of them, and the "x" 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.
    The missing number is 150

  • Let's find another one. One store is selling candy bars 4 for $1.20. How much would you spend if you buy 10 candy bars?
  • First figure out where to put the numbers into the proportion. Since it is "4 for $1.20", these two values can make up one of the fractions.

  • On the other side, we need to have the fraction set up the same way as our first one is. The number of candy bars is the numerator (top) and the amount of money is the denominator (bottom).
  • It is VERY important to be consistent when setting up the proportion.

  • Since we are buying 10 candy bars, we put that in and then solve.


  • Multiply on the diagonal that we have.

    1.20*10 = 12.0

  • Then divide by the number that hasn't been used.

    12.0 4 = 3

    You will spend $3.00 to buy 10 candy bars.


  • Here is another example. You bought 8 pots of flowers for $12. Your friend spent $18, how many pots did she buy?

  • Multiply the numbers on this diagonal. 8*18 = 144

  • Then divide by the other number that you haven't used yet.
    144 12 = 12

    So the number of flowers that your friend purchased is 12.

  • Can you set up and solve a proportion to solve for a missing amount?

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