Order of operations
More Complicated Order of Operations Example More Complicated Order of Operations Example
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- Now that we've got the basics of order of operations out of
- the way, let's try to tackle a really hairy and
- beastly problem.
- So here, we have all sorts of parentheses and
- numbers flying around.
- But in any of these order of operations problems, you really
- just have to take a deep breath and remember, we're going
- to do parentheses first.
- Parentheses.
- P for parentheses.
- Then exponents.
- Don't worry if you don't know what exponents are, because
- this has no exponents in them.
- Then you're going to do multiplication and division.
- They're at the same level.
- Then you do addition and subtraction.
- So some people remember PEMDAS.
- But if you remember PEMDAS, remember multiplication,
- division, same level.
- Addition and subtraction, also at the same level.
- So let's figure what the order of operations say that
- this should evaluate to.
- So the first thing we're going to do is our parentheses.
- And we have a lot of parentheses here.
- We have this expression in parentheses right there, and
- then even within that we have these parentheses.
- So our order of operations say, look, do your parentheses
- first, but in order to evaluate this outer parentheses-- this
- orange thing-- we're going to have to evaluate this thing
- in yellow right there.
- Well, if we look at just inside of it, the first thing we want
- to do is simplify the parentheses inside
- the parentheses.
- So you see this 5 minus 2 right there?
- We're going to do that first no matter what.
- And so this simplifies to-- I'll do it step by step.
- Once you get the hang of it, you can do multiple
- steps at once.
- So this is going to be 7 plus 3 times the 5
- minus 2, which is 3.
- And all of those have parentheses around it.
- And of course, you have all the stuff on either
- side-- the divide 4-- no.
- Oops.
- That's not what I want.
- I wanted to copy and paste.
- I want to copy and paste that right there.
- So copy, then-- no, that's giving me the wrong thing.
- It would've been easier-- let me just rewrite it.
- That's the easiest thing.
- I'm having technical difficulties.
- So divided by 4 times 2.
- And on this side, you had that 7 times 2 plus this thing in
- orange parentheses there.
- Now, at any step you just look again.
- We always want to do parentheses first.
- Well, you keep wanting to do and is there really
- no parentheses left?
- So we have to evaluate this parentheses in orange here.
- So we have to evaluate this thing first.
- But in order to evaluate this thing, we have
- to look inside of it.
- And when you look inside of it, you have 7 plus 3 times 3.
- So if you just had 7 plus 3 times 3, how would
- you evaluate it?
- Well, look back to your order of operations.
- We're inside the parentheses here, so inside of it there are
- no longer any parentheses.
- So the next thing we should do... There are no exponents. The next thing is multiplication.
- So we do that before we do any addition or subtraction.
- So we want to do the 3 times 3 before we add the 7.
- So this is going to be 7 plus-- and the 3 times
- 3 we want to do first.
- We want to do the multiplication first.
- 7 plus 9.
- That's going to be in the orange parentheses.
- And then you have the 7 times 2 plus that, on
- the left hand side.
- You have the divided by 4 times 2 on the right hand side.
- And now this-- the thing in parentheses-- because we
- still want to do the parentheses first.
- Pretty easy to evaluate.
- What's 7 plus 9?
- 7 plus 9 is 16.
- And so everything we have simplifies to 7 times 2 plus
- 16 divided by 4 times 2.
- Now we don't have any parentheses left, so we
- don't have to worry about the P in PEMDAS.
- We have no E, no exponents in this.
- So then we go straight to multiplication and division.
- We have a multiplication-- we have some multiplication
- going on there.
- We have some division going on here, and a
- multiplication there.
- So we should do these next, before we do this
- addition right there.
- So we could do this multiplication.
- We could do that multiplication.
- 7 times 2 is 14.
- We're going to wait to do that addition.
- And then here we have a 16 divided by 4 times 2.
- That gets priority of the addition, so we're going to do
- that before we do the addition.
- But how do we evaluate that?
- Do we do the division first, or the multiplication first?
- And remember, I told you in the last video, when you have 2--
- when you have multiple operations of the same level--
- in this case, division and multiplication-- they're
- at the same level.
- You're safest going left to right.
- Or you should go left to right.
- So you do 16 divided by 4 is 4.
- So this thing right here-- simplify 16 divided
- by 4 times 2.
- It simplifies to 4 times 2.
- That's this thing in green right there.
- And then we're going to want to do the multiplication next.
- So this is going to simplify to-- because multiplication
- takes priority over addition-- this simplifies to 8.
- And so you get 14-- this 14 right here-- plus 8.
- And what's 14 plus 8?
- That is 22.
- That is equal to 22.
- And we are done.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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