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We're asked to simplify 8 plus[br]5 times 4 minus, and then in

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parentheses, 6 plus 10[br]divided by 2 plus 44.

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Whenever you see some type of[br]crazy expression like this

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where you have parentheses and[br]addition and subtraction and

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division, you always want[br]to keep the order of

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operations in mind.

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Let me write them[br]down over here.

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So when you're doing order of[br]operations, or really when

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you're evaluating any[br]expression, you should have

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this in the front of your brain[br]that the top priority

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goes to parentheses.

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And those are these little[br]brackets over here, or however

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you want to call them.

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Those are the parentheses[br]right there.

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That gets top priority.

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Then after that, you want to[br]worry about exponents.

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There are no exponents in this[br]expression, but I'll just

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write it down just for future[br]reference: exponents.

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One way I like to think about it[br]is parentheses always takes

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top priority, but then after[br]that, we go in descending

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order, or I guess we should[br]say in-- well, yeah, in

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descending order of how fast[br]that computation is.

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When I say fast, how[br]fast it grows.

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When I take something to an[br]exponent, when I'm taking

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something to a power, it grows[br]really fast. Then it grows a

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little bit slower or shrinks[br]a little bit slower if I

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multiply or divide,[br]so that comes

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next: multiply or divide.

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Multiplication and division[br]comes next, and then last of

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all comes addition[br]and subtraction.

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So these are kind of the[br]slowest operations.

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This is a little bit faster.

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This is the fastest operation.

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And then the parentheses,[br]just no matter

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what, always take priority.

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So let's apply it over here.

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Let me rewrite this[br]whole expression.

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So it's 8 plus 5 times 4 minus,[br]in parentheses, 6 plus

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10 divided by 2 plus 44.

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So we're going to want to do the[br]parentheses first. We have

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parentheses there and there.

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Now this parentheses is pretty[br]straightforward.

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Well, inside the parentheses[br]is already evaluated, so we

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could really just view[br]this as 5 times 4.

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So let's just evaluate that[br]right from the get go.

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So this is going to result in[br]8 plus-- and really, when

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you're evaluating the[br]parentheses, if your evaluate

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this parentheses, you literally[br]just get 5, and you

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evaluate that parentheses, you[br]literally just get 4, and then

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they're next to each other,[br]so you multiply them.

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So 5 times 4 is 20 minus--[br]let me stay

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consistent with the colors.

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Now let me write the next[br]parenthesis right there, and

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then inside of it, we'd evaluate[br]this first. Let me

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close the parenthesis[br]right there.

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And then we have plus 44.

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So what is this thing right here[br]evaluate to, this thing

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inside the parentheses?

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Well, you might be tempted[br]to say, well, let me

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just go left to right.

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6 plus 10 is 16 and then[br]divide by 2 and

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you would get 8.

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But remember: order[br]of operations.

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Division takes priority over[br]addition, so you actually want

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to do the division first, and[br]we could actually write it

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here like this.

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You could imagine putting[br]some more parentheses.

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Let me do it in that[br]same purple.

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You could imagine putting some[br]more parentheses right here to

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really emphasize the fact that[br]you're going to do the

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division first.

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So 10 divided by 2 is 5, so this[br]will result in 6, plus 10

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divided by 2, is 5.

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6 plus 5.

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Well, we still have to evaluate[br]this parentheses, so

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this results-- what's[br]6 plus 5?

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Well, that's 11.

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So we're left with[br]the 20-- let me

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write it all down again.

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We're left with 8 plus[br]20 minus 6 plus 5,

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which is 11, plus 44.

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And now that we have everything[br]at this level of

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operations, we can just[br]go left to right.

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So 8 plus 20 is 28, so you[br]can view this as 28

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minus 11 plus 44.

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28 minus 11-- 28 minus 10[br]would be 18, so this

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is going to be 17.

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It's going to be 17 plus 44.

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And then 17 plus 44-- I'll[br]scroll down a little bit.

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7 plus 44 would be 51, so[br]this is going to be 61.

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So this is going to[br]be equal to 61.

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And we're done!

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