# Subtraction Property of Equality: Definition & Example

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• 0:01 Definition
• 0:56 Formula
• 1:24 Example 1
• 2:18 Example 2
• 3:19 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 video lesson, we look at the subtraction property of equality. Learn how it helps you to solve problems and how it keeps equations the same. Learn what you must do to both sides of an equation.

## Definition

In math, we deal a lot with equations. Equations are those math expressions with an equals sign. The two sides must equal each other. You can liken it to two bowls that both have the same number of chocolate candies in them. The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same.

So, if you are thinking of our two bowls of chocolate candies, you can think of eating a couple of candies from one bowl. Now, to keep the two bowls the same, you would also have to eat a couple of candies from the other bowl. It is the same with equations. To keep them the same, you have to do the same to both sides of the equation. If you subtract four from one side, you have to subtract four from the other as well.

## Formula

The formula we use to tell us this is if a = b, then a - c = b - c. This is telling us that if we have two bowls that each have the same number of chocolate candies, then if we take away from one bowl, we have to take away the same amount from the other bowl to keep the two bowls the same. Let's look at a couple of examples that show this subtraction property of equality in action.

## Example 1

In this first example, we will see how the subtraction property of equality really does keep the equation the same. We'll look at how it really does keep the number of candies in your two bowls of chocolate candies the same.

We begin with our two bowls. Each bowl has ten candies in it: 10 = 10.

Now, what happens if we take two candies from the bowl on the left? How many candies will we have in that bowl? We will have eight: 10 - 2 = 10; 8 = 10.

Our bowls aren't equal anymore. What do we need to do to make them equal again? We need to also take two candies from the bowl on the right: 10 - 2 = 10 - 2; 8 = 8.

Now our bowls are equal again!

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