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Parentheses in Math: Rules & Examples

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  • 0:01 Parentheses
  • 0:29 Multiplication
  • 1:29 Order of Operations
  • 2:33 More Examples
  • 3:31 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.

Watch this video lesson to learn how parentheses are used in math. Learn how to read them as multiplication and how they let you know which numbers to work with first.

Parentheses

We see parentheses all the time when we read. They are the round brackets that separate a group of words from the rest of a sentence in our English language. They usually contain a phrase (like this) that helps us understand the sentence more. In math, parentheses also help us understand our problem better. But we use them in a slightly different manner. We use parentheses in two different ways, which we will talk about in this video lesson.

Multiplication

The first way tells us to multiply. When we see two or more numbers together that are separated by parentheses, then the parentheses are telling us to multiply. For example, when we see 5(2), the parentheses are telling us to multiply the 5 and the 2 together. We can write 5*2 like 5(2) or (5)2 or (5)(2). All of these are multiplication problems, and they all equal 10.

If we see 4(3)(2), it means to multiply the 4 with the 3 and the 2. We get 24. When we are working with parentheses, we can leave the first or the last number without or outside the parentheses. It still means multiplication. Use your imagination and imagine that the parentheses are two arms giving a hug. You can think of the parentheses as telling you to hug or multiply the love between the numbers.

Order of Operations

The second way in which parentheses help us out in math is in telling us which numbers to work with first. In the order of operations, parentheses comes first. If you see parentheses with more than one number inside, you immediately work with those numbers first. It's like a pair of arms holding onto a group of precious items that you don't want to forget. You see them and you put them away first.

For example, if you see the problem (2 + 3)(1 + 2), you would do the 2 plus 3 and the 1 plus 2 first. You end up with (5)(3). Notice how we now have two numbers separated with parentheses. We now go back to our first way of understanding that the parentheses mean multiplication. You get 5*3, which equals 15. The 2 plus 3 and the 1 plus 2 are like special terms that you want to pick up and deal with first. You can tell that you need to apply this second way when you see more than one number inside of a pair of parentheses.

More Examples

Let's look at some more problems. See if you can do these.

5 + 7(3 + 1)

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