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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.

Learn how to simplify and combine like terms in any algebraic expression that uses addition with this lesson. Also learn how to follow the order of operations when simplifying your expression.

In this video lesson, we look at **addition expressions**, mathematical expressions that have the addition operator. Specifically, we'll look at algebraic expressions where we have to add in order to find our answer. Do you remember what algebraic expressions look like? That's right. They are a combination of letters and numbers.

You can think of the numbers as telling you how many of the letters there are. For example 3*x* tells you that there are 3 *x*'s. Likewise, 4*y* tells you that there are 4 *y*'s. To create an addition expression, we can write 3*x* + 4*y*.

Another way you can think about the numbers and letters is to think of the letters as something like burgers or ice cream bars. So your *x* could stand for burgers. So 3*x* means that you have 3 burgers. If the *y* stands for ice cream bars, then 4*y* means you have 4 ice cream bars. 3*x* + 4*y* then would mean that you have 3 burgers and 4 ice cream bars. Because burgers and ice cream bars are different, we don't combine the two.

But what if you had something like 3*x* + 2*x*? If the *x* stands for burgers, this means that you have 3 burgers and 2 burgers. Well, since it's all a bunch of burgers, you can go ahead and combine them. How many burgers do you have total? You have 5. So 3*x* + 2*x* simplifies to 5*x*.

We call this process 'simplifying' because we are taking an addition expression with more terms and rewriting it with fewer terms. In math, because these terms have the same variable and exponent, we call them 'like' terms. So when we are simplifying, we are, in actuality, combining like terms.

If we had an expression such as 3*x* + 2*x* + 6*y*, we could combine the 3*x* and the 2*x*. We would leave the 6*y* alone because it has a different letter. They are not the same item, so we cannot combine them. Simplifying 3*x* + 2*x* + 6*y*, we get 5*x* + 6*y*.

Let's look at a couple of examples so we can get even more familiar with this process.

*Simplify 4x + 7x + 2y + 7y.*

In this problem, we are asked to simplify or, in other words, combine like terms. We can visualize our like terms by picturing a different item for each letter. For example, our *x* could be puppies and our *y* could be kittens. Of course, we can't combine puppies and kittens together, so we have to leave them in separate groups. In our problem, we see two groups of puppies we can combine, the 4*x* and the 7*x*, and we see two groups of kittens that we can combine, 2*y* and the 7*y*. What do we get when we combine the two groups? We get 11*x* and 9*y*. So our simplified expression becomes 11*x* + 9*y*.

*Simplify 3x + 8y + 4x + 7y.*

In this problem, we see that we, again, are to combine like terms. In this problem, though, our like terms are not grouped as they were before. Let's visualize this one by thinking of *x* as bicycles and *y* as cars on the road. Right now, they're scattered haphazardly all over the place, so that means we have to locate them and group them together.

We see that we have two groups for *x*, and we have two groups for *y*. We can combine our two *x* groups, the 3*x* and the 4*x*, to become 7*x*. We can combine the two groups for *y*, the 8*y* and the 7*y*, to become 15*y*. We get a simplified expression of 7*x* + 15*y*. And we are done!

Let's review what we've learned.

We learned that **addition expressions** are mathematical expressions that have the addition operator. To simplify addition expressions, we combine like terms. Like terms are the ones that share the same letter or variable with the same exponent. Once we have combined all our like terms, we're done simplifying our expression.

The facts and examples in this video lesson could prepare you to:

- Recognize addition expressions and like terms
- Simplify addition expressions by combining like terms

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

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