In Exercises 111–120, use the order of operations to simplify ...

Question

In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]

Accepted Answer

Welcome back. I'm so glad you're here. We have got an expression and I'll rewrite that a little bit bigger. We've got three cubed three. Race to the third power plus 91 divided by 13. And I'm just writing divided by as that symbol. You also see it up above as a slash 91 divided by 13 minus three times two. And again they've got that asterisk for multiplication and I'm writing that as a dot in the middle. There the same thing times two minus bracket, 81 Divided by parentheses 9 -6 and parentheses and end bracket. And I just want to note that parentheses and brackets pretty much mean the same thing. They just use them usually in alternating. Like so you could have some parentheses inside of a bracket. Inside of the parentheses inside of a bracket. Just so that you don't get lost when there are a lot of them. So those are the same thing to essentially we're supposed to solve for this expression using the order of operations. Well what is the order of operations? Well, the order of operations as you recall from previous lessons, tells us how to go about solving this in what order. And we use the acronym pandas to help remind us of the order of operations. So we start on the left hand side And we look at parentheses first and as you recall, I just mentioned that there are two types of parentheses here, we start with the inner most parentheses. So the inner most parentheses here are this 9 -6. So we're going to do that first. What is 9 -6? Well that is three and now so that we don't start um getting lost in what we're doing or take a step out of turn. We're just going to copy the rest of this down 81 divided by now. It's 81 divided by three. And those parentheses are gone. That were around the nine minus six. Okay do we have any other parentheses? Yes we do those brackets. So we're going to work on the 81 divided by three and that is 27 again we'll copy down the rest of it three cubed plus 91 divided by minus three times two minus 27. Have to get that a little closer. Okay now the next step we've got all of our parentheses done. Next step in pandas is exponents. Do we have any exponents? We're looking at Yes this three cubed and three cubed is 27 And will bring down the rest 27 plus 91 divided by 13 -3 times 2 -27. There you go. 27 And now no more exponents. That one's done. And next we've got multiplication and division going from left to right. So what does that mean? It means that multiplication doesn't come before division and division doesn't come before multiplication. Both of those are equal. Moving from left to right. So we do whichever one is on the left. So the first time we have multiplication or division is this 91 divided by 13. We can go ahead and do that and that is seven so we can bring down the rest 27 plus seven minus three times two minus 27. Now any other multiplication or division happening? We start on the left and work our way over. And the next one we come across is negative three times two negative three times two is negative six. And we'll bring down the rest 27 plus seven minus six minus 27. Great. There is no more multiplication or division that one is done now we can work on addition and subtraction. Much like multiplication and division addition and subtraction just works from left to right. We don't do addition first or subtraction first we do whichever of those two is on the left. So the one that we've got first here is 27 plus seven and that is 34 And we bring down the rest 34 -6 -27. And again starting on the left hand side. The first multiplication addition or subtraction that we run into is 34 -6. And that gives us 28. We bring down the rest 28 - And now there's only one operation left to do and that's 28 -27. And the answer to that is one. We've completed our order of operations and we've come up with an answer that matches with answer choice b. Well done, we'll catch you on the next one.

In Exercises 111–120, use the order of operations to simplify each expression. 8−3[−2(2−5)−4(8−6)]

Key Concepts

Order of Operations

Parentheses

Distributive Property

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