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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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, you will learn about the division property of equality, its formula, and how you can use it to help you solve problems where you are looking for an unknown number.

In this video lesson, we talk about the **division property of equality**. It is a pretty simple property. It states that if you divide one side of an equation by a number, you also must divide the other side by the same number so that your equation stays the same.

So, if you divide the left side of an equation by 2, for example, then you must also divide the right side of the equation by 2 as well. It's like serving two apple pies so that everyone gets the same amount from each pie. If you serve a slice from one apple pie, you also serve the same size slice from the other apple pie. This way, both pies will always be the same size.

In math, we have a formula that tells us this: if *a* = *b*, then *a* / *c* = *b* / *c*. This is saying that if we begin with two same size pies, then if we divide one pie a certain way, then the only way to keep the two pies identical is to divide the other pie in the same way. Let's look at a couple of examples.

In this first example, we will look at how this property works. I will show you that you do get the same answer on both sides of the equation. We begin with a simple statement that we all know is true.

10 = 10

Now, if we divide the left side by 2, for example, what do we get?

10 / 2 = 10

5 = 10

Hmmmâ€¦ now our equation is not true; the two sides are not equal. So, what can we do to make our equation true again? We divide our right side by 2 as well.

10 / 2 = 10 / 2

5 = 5

Hey, look at that! The two sides are equal, and our equation is true again. If these were pies, our pies are looking the same again!

In the second example, we will see how we can use this division property of equality to help us solve math problems.

3*x* = 6

In this problem, we need to find out what *x* equals. Right now, it is being multiplied by a number 3. In order to solve for this *x*, we need to somehow get rid of this number 3. In math, the way we go about getting rid of the 3 is by performing the opposite operation. Right now, the 3 is being multiplied.

What is the opposite operation of multiplication? Division. So, we divide by 3 on the left side to get the *x* by itself. Applying our division property of equality, we know that since we divided the left side by 3, we must also divide the right side by 3. Let's see what we get.

3*x* / 3 = 6 / 3

*x* = 2

Ah, our *x* equals 2. We have solved our problem. Our pies are still equal.

Let's review what we've learned. We learned that the **division property of equality** is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same. The formula for this property is if *a* = *b*, then *a* / *c* = *b* / *c*. We use this property to help us solve various math problems where we need to divide to find a missing number.

After you've completed this lesson, you should be able to:

- Define division property of equality
- Identify the formula for the division property of equality
- Explain how to use this property to solve equations

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Commutative Property of Addition: Definition & Examples 5:02
- Commutative Property of Multiplication: Definition & Examples 4:40
- The Multiplication Property of Zero: Definition & Examples 2:40
- Distributive Property: Definition, Use & Examples 6:20
- Reflexive Property of Equality: Definition & Examples 3:43
- Addition Property of Equality: Definition & Example 3:51
- Subtraction Property of Equality: Definition & Example 3:54
- Multiplication Property of Equality: Definition & Example 4:05
- Division Property of Equality: Definition & Example 3:51
- Symmetric Property of Equality: Definition & Examples 3:26
- Go to 6th-8th Grade Math: Properties of Numbers

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