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# Intro to order of operations

CCSS.Math:

## Video transcript

in this video we're going to talk a little bit about order of operations and I want you to pay close attention because really everything else that you're going to do in mathematics is going to be based on you having a solid grounding in order of operations so what are we even taught mean when we say order of operations so let me give you an example the whole point is so that we have one way to interpret a mathematical statement so let's say I have the mathematical statement seven seven plus three times five now if we didn't all agree on an order of operations there would be two ways of interpreting this statement you could just read it left to right so you could say well let me just take seven plus three you could say seven plus three and then multiply that times five and 7 plus 3 is 10 and then you multiply that by five ten times five it would get you 50 so that's one way you would interpret it if we didn't agree on an order of operations maybe it's a natural way you just go left to right another way you could interpret it you say I like to do multiplication before I do addition so you might interpret it as I'll try to color code it seven plus and you do the three times five first seven plus three times five which would be 7 plus 3 times 5 is 15 and 7 plus 15 is 22 is 22 so notice we interpreted this statement in two different ways this was just straight left-to-right doing the addition then the multiplication this way we did the multiplication first then the addition we get two different answers and that's just not cool in mathematics if so this was part of some effort to send something to the moon because two people interpreted a different way or not one computer interpreted one way and another computer interpret another way that the satellite might go to Mars so this is just completely unacceptable and that's why we have to have an agreed-upon order of operations and agreed-upon way to interpret this statement so the agreed-upon order of operations is to do parentheses first let me write it over here for the C's paren the C's first then do exponents if you don't know what exponents are don't worry about it right now exponents and in this video we're not going to have any exponents in our examples so you don't really have to worry about them for this video then you do multiplication I'll just write multiplication then you do multiplication and division next they kind of have the same level of priority and then finally you do addition and subtraction finally you do addition and subtraction so what is this order of operations let me label it this right here that is the agreed-upon order of operations and if we follow these order of operations we should always get to the same answer for a given statement so what does this tell us what is the best way to interpret this up here well we have no parentheses parentheses look like that those little curly things around numbers we don't have any parentheses here I'll do some examples that do have parentheses we don't have any exponents here but we do have some multiplication and division or we actually just have some multiplication so the order of operations say do the multiplication and division first so it says do the multiplication first that's a multiplication so it says do this operation first it gets priority over addition or subtraction so if we do this first we get the 3 times 5 which is 15 and then we add the 7 the addition or subtraction I'll do it here addition we just have addition just like that so we do the multiplication first get 15 then add the 7 22 so based upon the agreed order of operations this right here is the correct answer the correct way to interpret this statement let's do another example I think it'll make things a little bit more clear and I'll do the example in pink so let's say I have 7 plus 3 7 plus 3 put some parentheses there times 4 divided by 2 - five times six so there's all sorts of crazy things here but if you just follow the order of operations you'll simplify it in a very I guess clean way and hopefully we'll all get the same answer so let's just follow the order of operations the first things we have to do is look for parentheses are there parentheses here yes there are there's parentheses around the seven plus three so it says let's do that first so 7 plus 3 is 10 so this we can simplify just looking at this order of operations 210 times all of that let me copy and paste that so I don't have to keep rewriting it so let me copy and let me paste it so that simplifies to 10 times all of that we did our parentheses first then what do we do when there are no more parentheses in this expression then we should do exponents I don't see any exponents here and just so if you're curious what exponents look like an exponent would look like you know 7 squared you'd see these little small numbers up in the top right we don't have any exponents here so we don't have to worry about it then it says to do multiplication and division next so where do we see multiplication to me we have a multiplication a division a multiplication again now when you have multiple operations at the same level within our order of operations multiplication and division are at the same level then you do left to right so in this situation you're going to multiply by 4 but and then divide by - you won't multiply by 4 divided by 2 and but then we'll do the 5 times 6 before we do this subtraction right here so let's figure out what this is so we'll do this multiplication first we'll do that multiplication first we could simultaneously do this multiplication because it's not going to change things but I'll do what things one step at a time so the next step we're going to do is this 10 times 4 10 times 4 is 40 10 times 4 is 40 then you have 40 divided by 2 let me copy and paste all of that again then it simplifies to that right there remember multiplication division they're the exact same level so we're going to do it left - right you could also Express this as multiplying by 1/2 and then it wouldn't matter the order but for simplicity multiplication division go left to right so then you have 40 divided by 2 - 5 times 6 so division you just have one division here you want to do that this is going to take you have this division then you have this multiplication they're not together so you can actually kind of do them simultaneously and to make it clear that you do this before you do the subtraction because multiplication division take priority over addition subtraction we could put parentheses around them just say look we're going to do that and that first before I do that subtraction because multiplication division have priority so 40 divided by 2 is 20 we're going to have that minus sign minus 5 times 6 is 30 20 minus 30 is equal to negative 10 and that is the correct interpretation of that so I want to make something very very very clear if you have things at the same level so if you have 1 plus 2 minus 3 plus 4 minus 1 so addition and subtraction are all at the same level in order of operations you should go left to right so this you should interpret this as 1 plus 2 is 3 3 so this is the same thing as 3 minus 3 plus 4 minus 1 then you do 3 minus 3 is 0 plus 4 minus 1 or this is the same thing as 4 minus 1 which is the same thing as 3 you just go left to right same thing if you have multiplication and division all on this they're the same level so if you have 4 times 2/3 times 2 you do 4 times 2 is 8 divided by 3 times 2 and you say 8 divided by 3 is well we're get a fraction there it would be 8/3 so this would be 8/3 times 2 and then 8/3 times 2 is equal to 16 over 3 that's how you interpret it you don't do the multiplication first and the dicta divide the two by that and all of that now the one time where you can be loosey-goosey with order of operations if you have all addition or all multiplication so if you have one plus five plus seven plus three plus two does not matter what order you do it in you can do the two plus three you can go from the right to the left you could go from the left to the right you can start someplace in between if it's only all addition and the same thing is true if you have all multiplication if it's 1 times 5 times 7 times 3 times 2 does not matter what order you're doing there but it's only which it's all multiplication or all addition if there's some division in here if there's some subtraction here you're best off just going left to right