Order of Operations

hi i'm tiffany today i'm going to show you how to solve using order of operations order of operations when solving with order of operations there's a few things that you want to keep in mind first you're always going to solve your problem from left to right i'll show some examples to make sure that's understood you want to follow the acronym pemdas to remember what order you're going to go in the p stands for parentheses the e stands for exponents the m is multiplication d division a addition and s subtraction the m and d or multiplication and division are solved at the same time the same is true for the a and the s the addition and subtraction they're also solved at the same time i know that's kind of a lot to remember but we're going to jump into some examples so all of this makes a little more sense let's get into example number one example number one before beginning because i know i'm using our order of operations i always tell my students to start by writing pemdas at the top of your paper so i'm gonna write it right up here p e m d a s my m and d i always say it's a good idea to circle these and my a and i s it is a good idea to circle those okay you want to circle these two because just like in the last slide i explained they work together now if you remember the first bullet point i made in the last slide was you solve your problem from left to right so what i do is look at each letter of my acronym and take my eye from left to right and determine if i have anything in the problem that is that letter so from left to right i'm going to check to see if i have any parentheses no i don't exponents i'm looking from left to right do i have any exponents no i don't multiplication and division this time when i look it doesn't matter if i see multiplication or division it doesn't matter which comes first i'm going to take note of it as i move from left to right so i'm moving from left to right yes i have multiplication okay because i have multiplication that means i need to solve this part right now because that's the step that we're on so to solve this i say rewrite the entire problem except for the portion that you were solving you're going to rewrite it as the solved answer so this is going to look like 32. and you're gonna subtract the 32 was just brought down the subtraction sign was just brought down the five times two is actually solved in this step and what is that going to be it's going to be a 10 so you actually write it as a 10 you don't write the 5 times 2 again so this entire problem was rewritten except for the portion that we solved was written as whatever it ends up being do i have any multiplication or division left in my problem no i don't so it's time to go to my next step and remember i take my eyes from left to right from left to right do i have addition or subtraction yes i do i have one subtraction problem and 32 minus 10 is pretty simple i can do that at the top of my head it's 22. so the answer to example number one is 22 let's move on to example number two example number two again we want to start by writing pemdas at the top of our paper p e m d a s i'm circling my addition and subtraction and my multiplication and division now i'm going to take my eyes from left to right take note of any parentheses i have none exponents i'm going from left to right yes i do have some an exponent right at the end of my problem i have two to the second power okay so i'm going to rewrite my entire problem except for just this portion i'm going to solve okay if you're not so good with exponents check out my video on exponent it will really help you out and give you a good understanding of what's going on i'm not going to go into too much detail here of how to solve this because i'm assuming you already know at this point and if you don't go watch that video okay rewriting i have 12 plus 30. divided by 6 minus so i have rewritten this entire thing except for this portion i will not write 2 to the second power again i will write what the answer to that is and the answer to 2 to the second power is 4. so i'll write a 4 here okay do i have any more exponents in my problem my new problem that i've just created actually no i don't now i check my new problem for multiplication or division does not matter which one comes first okay i'm going from left to right okay i have some division it's the very first thing i've come in contact to that's either multiplication or division so i need to solve it right now let's rewrite the entire problem except for 30 divided by 6 that will be written down as its answer okay so that's 12 it just comes down plus what's 30 divided by 6 5. and then we have a subtraction sign over here you just write that and the four just gets rewritten okay do i have any more multiplication or division no i don't so i'm done with this step now i'm on to the next step addition and subtraction i'm working from left to right i have 12 plus 5 12 plus 5 is 17 so i'm going to rewrite this whole problem except for just the 12 plus 5 part will be rewritten as the new answer so that's 17 now this is subtraction bring it down and the four bring it down okay do i have any more addition or subtraction yes i have subtraction let's solve this seventeen minus four that's pretty easy i can do it off the top of my head it's thirteen write that down good so the answer to example number two is 13. let's move on to example number three example number three let's start off with our pemdas in the top corner p e m d a s you may notice that when i write my pemdas i go ahead and leave a little bit of space because i know i'm in a circle in there okay let's move from left to right do i have any parentheses i do okay when you have parentheses they can be a little trickier i tell my students that parentheses means that you have your own problem inside of these parentheses okay so now you can really think of not having the 45 the division sign in this parentheses or this parentheses let's just think about having a problem 3 to the second power times one that is my new problem so now within that new problem itself i must use the order of operations so within that problem i could end up doing addition and subtraction and multiplication and division and then once all of that is done i have to get whatever my answer is to incorporate it into the full problem okay so these parentheses are really like telling you to solve this one problem first get an answer for it and then solve the whole thing okay so with our parentheses let's rewrite what we have here we have three squared times one let's follow order of operations just on this part of it do i have parentheses here anywhere no do i have exponents i do let's solve that what's three to the second power it's nine so that's nine times one because i'm rewriting the entire problem but just solving that part do i have any multiplication or division i do what is it it's nine times one so that's just nine i'm done if you end up with a single digit you don't really need to go on because there's nothing else that you can do but do not think that this 9 means it's the answer to the entire problem because remember we only solved this portion so now i must take my 9 and plug it back into the original problem so i have a 45 here divided by the 9 and really this is just the reverse of a multiplication fact and so we know that 45 divided by 9 is five so the answer to example number three is five let's move on to example number four example number four i'm going to start by writing my acronym for pemdas circle my a and my s and my m and my d okay now from left to right i'm going to pick out any parentheses that i have okay i have three squared times two and before i go on i do want to point out that this multiplication symbol is different than some of the others that you may be used to this multiplication symbol is just a dot it is not a decimal it's higher up um then a decimal would be a decimal would be lower but when we're dealing in math we have a lot of variables variables are those letters you see a lot of times like a b well x is a variable that we use a lot but we also use x for multiplication so sometimes when we're getting in more advanced math you're going to see this dot more often because if you had an x for multiplication but you also have x as a variable you're going to be confused if the x represents multiplication or some variable so when you're maturing in your math you're going to see more dots okay so my parentheses is 3 squared times 2. i'm going to solve just that portion three squared is nine i'm going to rewrite my times 2 and i get 18. now i need to plug this 18 into my overall problem so i have 42 minus 18 divided by three remember we've really only solved the parentheses portion in our overall problem we only plug the answer that we got for our parentheses back into the original problem okay so really we're still in the parentheses step we need to check to see if there's any more parentheses there are not now we're only on the exponent set there are no exponents multiplication and division yes we have 18 divided by 3 so 42 and my subtraction sign just get rewritten 18 divided by 3 is 6 and then we just have this one subtraction problem right now and that is 42 minus 6 and that gives us 36. so the answer to example number four is 36. let's move on to example number five example number five let's write our acronym up top p e m d a s okay working from left to right do i have any parentheses um okay i have something a little different these are brackets brackets are a little different brackets are used when you have a set of parentheses inside another set that you want to be parentheses if this problem were written with another parentheses here instead of using brackets it may be a little confusing like where does one parentheses in and where does the other one begin it's confusing you might think that this parentheses mark would go with this last one or vice versa you might think this beginning parenthesis mark went with this first ending this first ending parenthesis you may not know so we clarify this by using something similar to parentheses like brackets and you may find other types of brackets that look slightly different than this that may have like a little squiggle or something and that's fine so we have parentheses and it's everything from this five all the way down to this four and like these closing brackets okay so within that problem i'm going to ask myself do i have any parentheses starting from the 5 yes i do i have this portion the 8 to the second power divided by 4. so i'm going to start off by working just this portion 8 to the second power divided by four okay so within this do i have any parentheses no do i have any exponents i do what's eight times eight sixty-four so you rewrite that divided by four do i have any other exponents no do i have any multiplication or division i do i need to solve what's 64 divided by four 16. the 16 only goes inside these interior parentheses that's the only thing that this 16 substitutes so we're going to rewrite the whole problem with just that and it's going to look like this 5 plus 16 minus two this portion is still in parentheses i've changed to just the regular parentheses because i no longer have two separate sets of parentheses since i simplified that interior one now i need to still follow all my normal order of operations we left off with just parentheses so we do still have parentheses in our problem so we need to add the 5 and the 16 and that gives us 21 and then we subtract 2 and so obviously there's no multiplication or division so we're just going to jump to the last section which is addition and subtraction so we're going to subtract 21 minus 2 gives us 19. so the answer to example number five is nineteen let's move on to our final example example number six example number six let's start by writing our order of operations again p e m d a s do i have any parentheses yes i do actually two okay um i'm looking at the interior parentheses because that's what's going to be done first within my parentheses and it's really simple so instead of rewriting the entire thing i'm just going to solve this portion of my head 15 minus 13 is 2 so now i'm going to rewrite the whole problem except the minus 13 portion will be a two so here i go 36 divided by i'm also writing my parentheses it's a regular parenthesis this time instead of a bracket because i'm only going to have one set i'm not going to have two sets which would need to be used to identify the end of one in the beginning of another so i'm just going to write regular parentheses 2 to the third minus two this two came from subtracting fifteen minus thirteen now i'm going to close my parentheses now i need to solve just this interior portion because really on our overall problem we're still only on the parentheses step when solving justin's interior portion this is going to make it so that we're actually solving a subtraction problem before we solve division if we were to follow the order of operations for our overall problem we would not do that if there were no parentheses here but the parentheses make it so that you solve just this part first so the parentheses control a lot the parentheses may make the problem seem somewhat confusing because you will solve subtraction first but we're only doing that because parentheses are telling us to do this portion first okay now let's solve two to the third power minus two two to the third power is eight i need to rewrite my subtract two eight minus two is six now i need to rewrite my entire problem but instead of writing my parentheses portion i'm gonna write six so i have 36 divided by six 36 divided by six is six so the answer to example number six is six thanks for watching that's the end of this video if you like this video don't forget to click like then head over to super easymath.com for more math tutorials printable 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Channel: Super Easy Math

Views: 1,365,214

Rating: 4.8537936 out of 5

Keywords: math, basic math, mathematics, math help, order of operations, Solving Order of Operations, order of operation

Id: dXvvGc9TldY

Length: 20min 30sec (1230 seconds)

Published: Sat Jun 14 2014