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College Algebra: Help and Review27 chapters | 228 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.

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.

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.

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.

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.

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

5 + 7(3 + 1)

We see one pair of parentheses with two numbers inside, so that means we work on these numbers first. We have 3 + 1 that equals 4. Now we can multiply this 4 with the 7 to get 28. Next, we finish the problem by adding 5 to get 33.

Let's try one more.

2(4 + 1) + 7(2)

Here we see two sets of parentheses. The first has two numbers inside. That means we work with these two numbers first. We get 4 + 1 equals 5. The next set of parentheses only has one number inside, so it means multiplication. We multiply the 7 by the 2 to get 14. Now we can multiply the 2 with the 5 to get 10. We finish the problem by adding the 10 to the 14 to get 24.

Let's review what we've learned. We learned that **parentheses**, round brackets, are used two different ways in math. The first is to tell us to multiply. The second is to tell us to work with a group of numbers first. If we see a set of parentheses with more than one number inside, then it is the second way. If our parentheses only has one number inside, then we know it means multiplication.

Following a thorough review of this lesson, you could:

- Illustrate parentheses
- Interpret the order of operations that dictate the two ways in which parentheses are used in math
- Display your ability to solve example problems containing parentheses

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College Algebra: Help and Review27 chapters | 228 lessons

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