Solving Problems Involving Proportions: Definition and Examples

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  • 0:07 Proportions
  • 1:11 Keeping Proportion
  • 1:55 Is This Proportional?
  • 2:45 Find the Missing Side
  • 4:42 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn how you can use proportions to find missing sides and how to increase or decrease the sizes of objects to create models of them in this video lesson.

What Are Proportions?

Things are in proportion if the ratios are equal to each other. For example, if I compared the measurements of a model car to its life-size counterpart, I would find that all those ratios are equal to each other. Measuring the wheel of a model toy car, I find that it measures 1.5 inches. Its life size counterpart has a wheel that measures 18 inches. My wheel ratio is 1.5/18 or 1.5:18.

If the model car is 1/12 life size, is the wheel in proportion? I check by dividing both ratios:

1.5/18 = 0.0833

1/12 = 0.0833

Do I get the same answer for both? I do, so they are proportional.

Keeping Things in Proportion

To keep things in proportion when increasing or decreasing their sizes, all I have to do is to make sure to multiply all the numbers in my original ratio by the same amount.

Here's an example. To make dog cookies, I use a ratio of 1 cup oatmeal to 1 cup peanut butter. That gives me a ratio of 1:1. If I wanted to double the amount of cookies I make without changing the recipe to keep things in proportion, I would simply multiply my ratio by 2 to get 2:2. That means I would need to use 2 cups oatmeal and 2 cups peanut butter to make double the amount of cookies.

Is This Proportional?

You can check to see if you did the math right by dividing your ratios to see if they are proportional. If the ratios divide into the same number, then they are proportional.

For example, the ratios 4:5 and 8:10 are proportional because both divide into the same number:

4/5 = 0.8

8/10 = 0.8

On the other hand, the ratios 8:10 and 7:10 are not proportional because they don't divide into the same number:

8/10 = 0.8

7/10 = 0.7

Find the Missing Side

If you know that two ratios are proportional, you can actually use this information to find the length of a missing side.

For example, say you have a model of the house you are in, and you want to find out how tall your house is. You know how long the room you are in is as well as how long that same room is in the model. You can easily measure how tall the model house is but you can't easily measure how tall your life-size house is. So, how do you use proportions to help you? Let's see how this works.

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