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# Worked example: Order of operations (PEMDAS)

## Thuyết minh video

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 what 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 so let's evaluate this whole thing so how can we simplify it 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 that's easy to evaluate 5 minus 2 is 3 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 then you have and all of those have parentheses around it and of course you have all the stuff on either side the divide for no whoops that's not what I want I wanted to copy and paste I want to copy and paste that right there so copy and then no that's giving me the wrong thing it would have 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 and we always want to do parentheses first we keep wanting to do this is those are 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 seven plus three times three so if you just had seven plus three times three how would you evaluate it well look back to your order of operations we're inside the parentheses here so inside of it they're just they're no longer any parentheses so the next thing we should do is there are no exponents there is multiplication so we do that before we do any addition or subtraction so we want to do the three times three before we add the seven so this is going to be seven plus and the three times three we want to do first we want to do the multiplication first seven plus nine that's going to be in the orange parentheses and then you have the seven times two plus that on the left hand side you have the divided by four times two 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 seven seven plus nine seven plus nine is sixteen and so everything we have simplifies to 7 times two plus 16 divided by 4 times two now we don't have any parentheses left so we won'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 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 you do the multiplication first and remember I told you in the last video when you have to when you have multiple operations of the same level in this case division and multiplication they're at the same level your 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 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 2 because you ought multiplication takes priority over addition this simplifies to 8 and so you get 14 this 14 right here plus plus 8 and what's 14 plus 8 that is 22 that is equal to 22 and we are done