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# Order of operations example

CCSS.Math:

## Video transcript

we're asked to simplify eight plus five times four - and then in parentheses 6 plus 10 divided by 2 plus 44 whenever you see some type of crazy expression like this where you have parentheses in addition and subtraction and division you always want to keep the order of operations in mind and let me write them down over here so when you're doing order of operations or really when you're evaluating any expression you should have this in the top of your or in kind of the front of your brain is that the top priority goes to parentheses parentheses 4 n parentheses and those are these little brackets over here however you want to call them those are the parentheses right there that gets top priority then after that you want to worry about exponents there are no exponents in this expression but I'll just write it down just for future reference exponents one way I like to think about it is parentheses that always takes top priority but then after that we go in descending order or I guess we should say in well yeah in descending order of how kind of fast that computation is and when I say fast how fast it grows when I take something to an exponent when I'm taking something to a power it grows really fast then it grows a little bit slower or shrinks a little bit slower if I multiply or divide so that comes next multiply or divide multiplication division comes next and then last of all comes addition and subtraction so these are kind of the slowest operations this is a little bit faster this is the fastest operation and then the parentheses just no matter what always take priority so let's apply it over here let me rewrite this whole expression so it's eight plus five times four minus in parentheses six plus 10 divided by two plus forty four so we're going to want to do the parentheses first we have parentheses there and there now this parentheses is pretty straightforward well inside the parentheses that's already evaluated so we could really just view this as five times four so let's just evaluate that right from the get-go so this is going to result in a Plus and really when we're evaluating the parentheses if you evaluate this parentheses you literally just get five and then you evaluate that parentheses you were to just get four and then they're next to each other so you multiply them so five times four is twenty - let me stay consistent with the colors - now let me write the next parenthesis right there and then inside of it we evaluate this first so let me close the parentheses right there and then we have plus forty four plus forty four so what is this thing right here evaluate to this thing inside the parentheses well you might be tempted to say well let me just go left to right six plus ten is is 16 and then divide by two and you would get eight but remember order of operations division takes priority over addition so you actually want to do the division first and we can actually write it here like this you could imagine putting some more parentheses let me do that same purple you could imagine putting some more parentheses right here to really emphasize the fact that you're going to do the division first so 10 divided by 2 is 5 so this will result in 6 plus 10 divided by 2 is 5 6 plus 5 well we still have to evaluate this parentheses so this results with 6 plus 5 well that's 11 so we're left with 20 let me write it all down again we're left with 8 plus 20 minus 6 plus 5 which is 11 plus 44 and now that we have everything at this level of operations we can just go left to right so 8 plus 20 is 28 so you could view this as 28 minus 11 plus 44 28 minus 11 28 minus 10 would be 18 so this is going to be 17 it's going to be 17 plus 44 and then 17 plus 44 I'll scroll down a little bit 17 plus 44 7 plus 44 would be 51 so there's going to be 61 so this is going to be equal to 61 and we're done