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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.

After watching this video lesson, you will understand how the transitive property of equality works when you have two equations that are equal to each other. Learn the formula for this property and how you can use it to help you solve problems.

In this video lesson, we talk about the **transitive property of equality**. This property tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

You can think about it in terms of identical toy trucks. Say you have two identical toy trucks. They are both blue. Now, if the second truck is the same as a third blue toy truck, then we can also say that the first truck is also the same as the third blue toy truck. This is because we know that the first toy truck is equal to the second toy truck, so if either of those toy trucks is equal to a third, then they both are equal to that third truck. It's like a chain. They are all linked to each other.

In math, we have a formula for this property. It says that if *a* = *b* and *b* = *c*, then *a* = *c*. This is telling us that if two things are equal and the second thing is equal to a third, then because the first two things are equal, it also means that the first is equal to the third as well. They are all equal to each other. Let's look at a couple of examples to see how this transitive property of equality works in action.

In this example, we look at how true the transitive property of equality is. We begin with our two equations:

5 = 3 + 2 and 3 + 2 = 5

We can label these two equations with our letters. Or, we can use our toy trucks. The first 5 is our letter *a*, or our first toy truck. The following 3 + 2 is our letter *b*, or our second toy truck. The last 5 is our letter *c*, or our third toy truck. By applying the transitive property of equality, we can say that the first 5 is equal to the last 5, that letter *a* is equal to letter *c*, or that the first toy truck is equal to the third toy truck. Is this true? Let's see.

5 = 5

Yep, that looks pretty true. 5 is equal to 5.

Now, let's look at an example to see how we can use this transitive property of equality to help us solve problems.

Find *x* if *x* = *y* and *y* = 3.

In this problem, we need to find what *x* equals. We see our two equations. We can use our transitive property of equality to help us solve this problem. We can label our *a*, *b*, and *c* parts. Then, we can link the first part with the third part. Our *a* is *x*, and our *c* is 3. Our *b* is *y*. Linking *a* and *c* with each other, we find that *x* = 3. Aha! We have found our answer!

Let's review what we've learned. We learned that the **transitive property of equality** tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing. The formula for this property is if *a* = *b* and *b* = *c*, then *a* = *c*. We use this formula to help us solve problems where we have two equations where the second equation shows us what the second part of the first equation is equal to.

After you've reviewed this video lesson, you will be able to:

- Define transitive property of equality
- Identify the formula for the transitive property of equality
- Explain how to use this property to solve problems

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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
- Transitive Property of Equality: Definition & Example 3:39
- Go to 6th-8th Grade Math: Properties of Numbers

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