How to Simplify an Addition Expression

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  • 0:01 An Addition Expression
  • 1:12 Simplifying
  • 2:24 Example 1
  • 4:05 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.

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.

An Addition 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 3x tells you that there are 3 x's. Likewise, 4y tells you that there are 4 y's. To create an addition expression, we can write 3x + 4y.

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 3x means that you have 3 burgers. If the y stands for ice cream bars, then 4y means you have 4 ice cream bars. 3x + 4y 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 3x + 2x? 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 3x + 2x simplifies to 5x.

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

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

Example 1

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

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