Understanding Proportions

Proportions is a way of comparing 2 similar things. You do them every day. Have you ever figured out how many miles your car can get per gallons of gasoline? Or how much something is per ounce? Or How how long it will take you to finish a project? Or how much money you can make per day? If you have you have just used the concept of proportions.

Before we look at problems and solutions using proportions, let’s look at and example together.

Question: Al painted 500 square feet in 6 hours. At that rate how many hours will it take him to paint 1500 square feet?

What is the question? At that rate how many hours will it take him to paint 1500 square feet?

What is the necessary information? 500 square feet, 4 hours, and 1500 square feet. The words at this rate are a clue that we will be using proportions as a setup to solve this problem.

What is the operation? They have given us three pieces of information and we will need to solve for the fourth. To do this we are going to put like things across from each other, cross multiply, and then divide.

So we have our

500 sq ft   =   1500 square feet

6 hours                      x

Remember we are going to place like things across from each other. And we are solving for x, the number of hours. And we need to cross multiply and then divide.

Solve it. So we are going to multiply 1500 x 6 = 9000 and then we need to divide 9000 by 500.

That is going to give us 18.

Does this answer make sense? Do you see that 1500 is 3 times larger than 500? So is 18 three times larger than 6? Yes, so this makes sense and is the correct choice. If you see patterns that double or triple, you can just multiply to get the answer.


500 x 3 = 1500 and

   6 x 3 = 18

So the answer is it will take 18 hours.