In order to help parents reinforce ideas learned in school and in tutoring, Academics Plus, Inc. is offering a Lesson series on our blog that demonstrates basic concepts using items you can find around the house.

**Proportions** –

Proportions can be for solving algebraic equations as well as for finding percentages.

What you will need:

• Toothpicks

• A piece of paper

• A marker/pencil

First, set up the proportion equation, making room to write numbers on the top and bottom of the lines, like so:

Count out 30 toothpicks with your child. Place them in front of you. Then count out 15 additional toothpicks. Place them beside the pile of 30 toothpicks. Then write 15 and 30 on the right side of your equation like so:

This represents 15 out of 30. What we’re going to try and find is what percent of 30 is 15 (15 is what percent of 30?). The right side represents the actual toothpicks, whereas the left side represents percents. We can put 100 on the bottom of the right side of the equation since we know the percent will be out of a total of 100:

“X” represents the value we are trying to discover. So on the left side you have x out of 100 percent and then on the right you have 15 out of 30. To find x, you must cross multiply! This means multiplying 30 by x and 15 by 100. When you multiply a number by x, you end up with that number and x. So 30 multiplied by x is 30x. Cross multiply with your child on the piece of paper like so:

In order to find the solution of x, we have to separate the x from any other numbers. In this case, x is multiplied by 30, so we have to divide both sides by 30 in order to isolate the x. Demonstrate how this is done for your child. This should be the result:

1,500 divided by 30, is 50, which is the value of x. So, 15 is 50% of 30.

You may have to demonstrate this with a different set of numbers to show your child how proportions and cross multiplication work.

**Reader Question**: How did you learn percents?.