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# Order of operations example

CCSS.Math:

## Video transcript

simplify negative 1 times this expression in brackets negative 7 plus 2 times 3 plus 2 minus 5 in parenthesis squared so this is an order of operations problem and remember order of operations you always want to do parentheses first parenthesis parenthesis first then you do exponents exponents and there are there is an exponent in this problem right over here then you want to do multiplication multiplication and division and then finally you do addition and subtraction so let's just try to tackle this as best we can so first let's do the parentheses let's do the parentheses we have a 3 plus 2 here in parentheses so we can evaluate that to be equal to 5 and let's see we could do other things in other parts of this expression that won't affect what's going on right here in the parenthesis we have this negative 5 squared or actually I should say we have we're subtracting a 5 squared we want to do the exponent before we worry about it being subtracted so this 5 squared over here we can rewrite as 25 and so let's not do too many steps at once so this whole thing will simplify to negative 1 and then in brackets we have negative 7 plus 2 times 5 plus 2 times 5 and then 2 times 5 and then closed brackets minus 25 minus 25 now this thing we want to do multiplication you could say hey wait I still have a parenthesis here why don't I do that first but when you just evaluate what's inside of those parentheses you just get a negative 7 it doesn't really change anything so we could just leave this here as a negative 7 and this expression we do want to evaluate this whole expression before we do anything else I mean we could distribute this negative 1 and all of that let's just do straight-up order the order of operations here so let's evaluate this expression we want to do multiplication before we add anything so we get a 2 times 5 right over there 2 times 5 is 10 that is 10 so our whole expression becomes a normal you would have to rewrite the expression this many times but we're going to do it this time just to make sure no one gets confused so it becomes negative one times negative seven plus ten plus ten and we close our brackets minus 25 minus 25 now we can evaluate this pretty easily negative seven plus ten you can view it we're starting at negative seven so I was going to draw a number line there so we're starting let me draw a number line so we're starting at negative seven and then so this the length of this line is negative seven and then we're adding 10 to it we're adding 10 to it so we're going to move 10 to the right if we move 7 to the right we get back to zero and then we're going to go we're going to go another 3 after that so we're going to go 7 8 9 10 so that gets us to positive 3 another way to think about it is we are adding integers of different signs we can view the this this sum is going to be the difference of the integers and since our the larger integer is positive our answer will be positive so you could literally just view this as 10 minus 7 10 minus 7 is 3 so this becomes a 3 and so our entire expression becomes negative 1 negative 1 times and just to be clear brackets and parentheses are really the same thing sometimes people will write brackets around a lot of parenthesis just to make it a little bit easier to read but they're really just the same thing as parentheses so these brackets out here I could just literally write them like that and then I have a minus 25 out over here now once again you want to do multiplication or division before we do addition and subtraction so let's multiply the negative 1 times 3 is negative 3 and now we need to subtract our 25 so negative 3 minus 25 we are adding two integers of the same sign we're already at negative 3 and we're going to become 25 more negative than that so you can view this as the Nate as we're moving 25 more in the negative direction or you could view it as 3 plus 25 is 28 but we're doing it the negative direction so it's negative 28 so this is equal to negative this is equal to negative 28 and we are done