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Now that we've got the basics
of order of operations out of
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the way, let's try to tackle a
really hairy and
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beastly problem.
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So here, we have all
sorts of parentheses and
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numbers flying around.
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But in any of these order of
operations problems, you really
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just have to take a deep breath
and remember, we're going
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to do parentheses first.
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Parentheses.
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P for parentheses.
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Then exponents.
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Don't worry if you don't know
what exponents are, because
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this has no exponents in them.
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Then you're going to do
multiplication and division.
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They're at the same level.
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Then you do addition
and subtraction.
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So some people remember PEMDAS.
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But if you remember PEMDAS,
remember multiplication,
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division, same level.
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Addition and subtraction,
also at the same level.
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So let's figure what the
order of operations say that
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this should evaluate to.
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So the first thing we're going
to do is our parentheses.
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And we have a lot of
parentheses here.
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We have this expression in
parentheses right there, and
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then even within that we
have these parentheses.
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So our order of operations say,
look, do your parentheses
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first, but in order to evaluate
this outer parentheses-- this
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orange thing-- we're going to
have to evaluate this thing
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in yellow right there.
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Well, if we look at just inside
of it, the first thing we want
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to do is simplify the
parentheses inside
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the parentheses.
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So you see this 5
minus 2 right there?
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We're going to do that
first no matter what.
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And so this simplifies to--
I'll do it step by step.
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Once you get the hang of
it, you can do multiple
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steps at once.
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So this is going to be
7 plus 3 times the 5
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minus 2, which is 3.
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And all of those have
parentheses around it.
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And of course, you have
all the stuff on either
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side-- the divide 4-- no.
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Oops.
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That's not what I want.
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I wanted to copy and paste.
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I want to copy and paste
that right there.
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So copy, then-- no, that's
giving me the wrong thing.
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It would've been easier--
let me just rewrite it.
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That's the easiest thing.
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I'm having technical
difficulties.
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So divided by 4 times 2.
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And on this side, you had that
7 times 2 plus this thing in
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orange parentheses there.
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Now, at any step you
just look again.
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We always want to do
parentheses first.
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Well, you keep wanting to
do and is there really
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no parentheses left?
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So we have to evaluate this
parentheses in orange here.
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So we have to evaluate
this thing first.
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But in order to evaluate
this thing, we have
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to look inside of it.
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And when you look inside of it,
you have 7 plus 3 times 3.
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So if you just had 7 plus
3 times 3, how would
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you evaluate it?
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Well, look back to your
order of operations.
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We're inside the parentheses
here, so inside of it there are
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no longer any parentheses.
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So the next thing we should do... There are no exponents. The next thing is multiplication.
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So we do that before we do
any addition or subtraction.
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So we want to do the 3 times
3 before we add the 7.
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So this is going to be 7
plus-- and the 3 times
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3 we want to do first.
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We want to do the
multiplication first.
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7 plus 9.
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That's going to be in
the orange parentheses.
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And then you have the 7
times 2 plus that, on
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the left hand side.
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You have the divided by 4 times
2 on the right hand side.
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And now this-- the thing in
parentheses-- because we
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still want to do the
parentheses first.
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Pretty easy to evaluate.
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What's 7 plus 9?
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7 plus 9 is 16.
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And so everything we have
simplifies to 7 times 2 plus
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16 divided by 4 times 2.
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Now we don't have any
parentheses left, so we
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don't have to worry
about the P in PEMDAS.
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We have no E, no
exponents in this.
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So then we go straight to
multiplication and division.
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We have a multiplication--
we have some multiplication
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going on there.
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We have some division
going on here, and a
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multiplication there.
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So we should do these
next, before we do this
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addition right there.
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So we could do this
multiplication.
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We could do that
multiplication.
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7 times 2 is 14.
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We're going to wait
to do that addition.
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And then here we have a
16 divided by 4 times 2.
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That gets priority of the
addition, so we're going to do
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that before we do the addition.
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But how do we evaluate that?
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Do we do the division first,
or the multiplication first?
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And remember, I told you in the
last video, when you have 2--
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when you have multiple
operations of the same level--
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in this case, division and
multiplication-- they're
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at the same level.
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You're safest going
left to right.
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Or you should go left to right.
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So you do 16 divided by 4 is 4.
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So this thing right here--
simplify 16 divided
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by 4 times 2.
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It simplifies to 4 times 2.
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That's this thing in
green right there.
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And then we're going to want to
do the multiplication next.
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So this is going to simplify
to-- because multiplication
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takes priority over addition--
this simplifies to 8.
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And so you get 14-- this
14 right here-- plus 8.
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And what's 14 plus 8?
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That is 22.
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That is equal to 22.
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And we are done.