7th Grade Math: Help Solving Proportions

How to Solve Proportions

A proportion is a statement that two ratios are equal. Proportions are usually written with the ratios in fraction form, like this: 1/2 = 2/4. In 7th grade, you'll learn to solve proportions, which means you'll be given a proportion with an unknown variable that you have to identify.

Using Cross-Multiplication

To solve proportions with variables, we use cross-multiplication. It allows us to convert proportions into traditional equations. To demonstrate cross-multiplication, we'll solve this proportion: 1/2 = 2/x. Let's call the fraction on the left side of the equals sign 'Fraction A' and the fraction to the right 'Fraction B.'

1. Multiply the numerator (top number) of Fraction A by the denominator (bottom number) of Fraction B. In this example, that would give us 1(x), which is equal to x.
2. Multiply the numerator of Fraction B by the denominator of Fraction A. That gives us 2 x 2, which equals four.
3. Put your answers from step one and step two on opposite sides of the equals sign, like this: x = 4. This equation tells you that the value of 'x' in the proportion 1/2 = 2/x is four.
4. Check your work. Plug the value of 'x' back into the original proportion and cross-multiply again. If you've solved the proportion correctly, you should end up with a true equation. In this case, 4 x 1 = 2 x 2 simplifies to 4 = 4, which is true.

Creating Proportions

Many times, you'll use proportions and cross-multiplication to solve word problems, but you won't be given the proportion. Instead, you'll have to set it up yourself. In the following word problem, we demonstrate how to write a proportion and solve it using cross-multiplication.

Samantha weighed her brother in kilograms, and she wants to convert that measurement into pounds. She knows that the ratio of kilograms to pounds is about 1:2.2. That means that for every one kilogram, he weighs about 2.2 pounds. If her brother weighs 50 kg, about how many pounds does he weigh?

First, set up your proportion. Start by writing 1:2.2 as a fraction, like this: 1 kg/2.2 lbs. It's helpful to include the units in your fraction to avoid confusion. Now, create a proportion by setting this fraction equal to one that represents the brother's weight. You know that he weighs 50 kg, but you don't know his weight in pounds yet, so that will be represented by the variable 'w.' The proportion will look like this:

1 kg/2.2 lbs = 50 kg/w

Like units must be lined up horizontally. In this example, the amounts in kilograms are in the numerator, and the amounts in pounds are in the denominator. Now, we're ready to cross-multiply. Since we've successfully set up our proportion, we can drop the units for this part.

1(w) = 50 x 2.2

w = 110

Since w = 110, we know that Samantha's brother weighs 110 pounds.