How to solve a Proportion
It is important that your child knows how to work with ratios and proportions. We can use a ratio to compare two things. Suppose for every 3 girls in a class< there are 2 boys. Then the ratio of girls to boys can be written in one of # ways: 3/2, 3 to 2, 3:2. This does NOT mean that there are ONLY 3 girls and 2 boys in the class. There could be< but here we”d need more information to determine the TOTAL number of kids in the class.
What is a Proportion?
If you have 2 ratios that are equal, we can write them with an equal sign between them. This is a proportion. So for example 3/2 and 6/4 are two ratios that are equal, so we can write them as 3/2 =6/4.
So you have a proportion when you set equivalent fractions equal. Here the proportion is 3/2 = 6/4.
In a proportion the cross products are equal. To find the cross products, you multiply the numbers on the diagonal. So here, to find one cross product we do 6 times 2. To find the other cross product, we do 3 times 4. As you can see, here both cross products are 12. This is not a coincidence. If you have a proportion, the cross products will be equal.
Finding a missing part of a proportion
Because the cross products are equal, if there is one missing component of the proportion, we can find it.
- For example, suppose we have 2/7 = x/3, where x is an unknown number.
- To find x, we set the cross products equal: 7x = 2(3) which becomes 7x = 6.
- Now, we want to isolate (solve) for x, so we need to get rid of the 7. We can get rid of the 7, by dividing the left side of the equation by 7.
- To keep our equation balanced, whatever is done on one side of the equation MUST be done on the other side of the equation. So we must divide the right side of the equation by 7 as well.
- So on the left side the 7s cancel out, and we’re left with x.
- On the right side of the equation, we have 6/7.
- So we end up with x = 6/7.
Do you always set the cross products equal to solve a proportion?
You can set the cross products equal to solve a proportion, but you don’t always have to. If you had
3/2 = x/4, instead of taking extra steps and setting the cross products equal and then solving for x, here we should easily recognize that to go from 2 in the first fraction to 4 in the 2nd fraction, we multiplied by 2. Because we have equivalent fractions, whatever we did to the bottom has to be done to the top, so we must multiply 3 by 2 as well to get that x must be 6.
It’s very important to be able to work with proportions. For example, the student may deal with many proportions when working with percents.
What other math concept is your child struggling with? Let me know what other math how tos you’d like me to do in the comments below.