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Multiplication Property of Equality: Definition & Example

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  • 0:04 Definition
  • 1:12 Formula
  • 1:44 Example 1
  • 2:24 Example 2
  • 3:30 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.

After watching this video lesson, you will learn to use the multiplication property of equality to help you solve problems in math. You will also learn the formula for this property.

Definition

Meet Jim and John. They are twins. As you can see, they are dressed to match each other.

image of twins

If Jim changes something, like he puts on a blue sweater, then John will also do the same. If John decides to wear a gray scarf, then Jim will also do the same. See, they have this agreement between them that they will always match each other. So, when they go out, they will always call or talk to each other to make sure they are wearing the same outfits. If Jim and John represent different sides of an equation, then what they are wearing represents the operations that are performed on the equation.

This is where our multiplication property of equality comes in. This property states that if we multiply one side of an equation, we also multiply the other side of the equation by the same number to keep the equation the same. This is just like the twins matching each other. What one does the other does as well. In our mathematical case, we are talking about multiplication. If we multiply one side of an equation by 3, then we also must multiply the other side by 3 as well.

Formula

In math language, the formula is if a = b, then a * c = b * c. This is saying that if both sides of the equation are equal to begin with, like if they are twins, then if we multiply one side of the equation, the other side must also be multiplied by the same number so that the equation remains the same, so that they are still matching twins. Do you want to see some examples of this property in action? Let's take a look.

Example 1

In this example, we see if this property really does what it says it does. We begin with an equation that we know is true.

2 = 2

Now, what if we multiply the left side by a 3? What do we get on that side? We get a 6.

2 * 3 = 2

6 = 2

Hey, now the sides are not equal. What do we need to do? According to the multiplication property of equality, we must also multiply the right side by the same number, by 3. So:

2 * 3 = 2 * 3

6 = 6

Hey, look at that. They are the same! The property works! The twins are matching now.

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