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What is Ratio in Math? - Definition & Overview

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  • 0:01 Definition
  • 0:44 Writing Ratios
  • 1:26 Using Ratios
  • 2:18 Scaling Ratios
  • 4:21 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.

In this lesson, learn the different ways that mathematicians write ratios. Also learn how ratios are used when cooking. You will also discover how to effectively use ratios to help you get things done.

Definition

A ratio compares two values. It shows you that when you have this much of something, you will need to have that much of something else.

You see ratios used in cooking and when working with model toys. The recipe for hummingbird food, for instance, calls for 4 parts of water for every part of sugar. What this ratio tells you is that however much sugar you put in, you need to put in 4 times as much water. If you use 1 cup of sugar, you need 4 cups of water. If you use 1 tablespoon of sugar, you need 4 tablespoons of water.

Writing Ratios

When you want to write a ratio mathematically, there are three specific formats you can choose from. You can choose to write it in colon form with a colon separating the two numbers. Or you can choose to use the word 'to' in between the numbers. Also, you can write it as a fraction. All are valid and all mean the same thing. When you write it as a fraction though, you will want to keep it in fraction form even if you can simplify it further. As in the hummingbird food recipe, the ratio in fraction form would stay 4/1 even though it can be simplified to just 4.

Using Ratios

Use ratios to describe any two things that have a fixed value when compared to each other. The dimensions of photos, for example, have a fixed value when you compare the length to the width or vice versa. A photo that has a width of 5 and a length of 7 will have a width to length ratio of 5:7. A larger photo, such as one with a width of 8 and a length of 10, has a ratio of 8:10.

Another real world application of ratios is in the building of model toys. Many model toy cars come scaled at 1/12th of life size. What this means is that every measure of the toy car equals 12 measures in real life. What measures 1 cm in the toy car will measure 12 cm in the real world.

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