hope you're well this lesson we're going to talk about the commutative property of addition and multiplication now I know that this part of the work is really boring I I mean I used to find this part really boring um when I teach it I think it's really boring but I'm going to try and make it as exciting as possible um and we'll try to do it as quickly as possible as well so that we can just move on to the more exciting and proper kind of maths okay so commute I want you to look at the word commute and I want you to maybe some of you know what the word commute means but commute means to move to move okay so then so that's going to be quite an important thing whenever I hear whenever you hear the word commute I want you to think of move okay so in this lesson we'll look at the commutative property for addition and we'll also look at it for multiplication okay so for addition let's quickly do this so if we go a plus I'm first going to use letters and then I'm going to use numbers A + B plus C and then we going to go uh for example b + a + C so what I want you to notice is that the a was position number one the B was position number two and the C was position number three now if we look on this side over here we can see that the a is now in position two and the B is in position one it doesn't really matter that this one hasn't changed but can you see that these two have moved can you see um they've moved from where they were and that is what the commutative property does it's all about one of the numbers or both of the numbers or all of the numbers have moved for example it could also go a plus b plus c equal to C + a + b as long as one of them has moved from the original then it's called the commu ative property so what does it really mean if we say 5 + 2 + 1 well you could quickly calculate that for me what does that give you well that gives you eight right so could we add it up in a different way or could we say 2 + 5 + 1 have a look at that we've moved the two and the five around can you see we've moved them but if you do that do you still get the same answer yes and so what we are now saying is that when you are busy with addition you know when you're adding numbers together if you use if you move one of them or two of them or all three of them the answer will remain the same because of this amazing thing called the commutative property of addition here's another example if you say 3 + 2 + 6 will that be the same as 6 + 2 + 3 well yes according to the the commutative property but let's just see if it actually does work so what is 3 + 2 that's 5 what is 5 + 6 11 what is 6 + 2 that's 8 what is 8 + 3 11 so when you are adding numbers together and you move them around it doesn't matter the answer will still be the same because of the commutative property of addition okay so that's what I want you to know for addition now we're going to quickly look at M multiplication so with multiplication it works exactly the same way if you say 3 * 2 * 4 um let's quickly work that out what is 3 * 2 well that is 6 what is 6 multi 4 24 now do we get the same answer if we switch things around a little bit can you see how I've moved things around here we had a two in position two a three in position one and the four was in position three now you can see it's totally different over here but let's see if it works does it give us the same answer well what is 2 * 4 8 what is 8 * 3 24 so what we can say then is that when you are multiplying numbers together and by the way on the next slide I'm going to show you that it it does not work with subtraction and Division and so I should have actually started with the overall rule which is a a multi B multi C is going to be the same as B multi a multi C or you could even use um c multip b multip by a it doesn't matter as long as you move one of them maybe you want to do like that it doesn't really matter as long as you are moving them it'll still give you the same answer and we and because we are moving them we call it the commutative property cuz commute means to move now this is is called the commutative property of multiplication whereas on the previous slide we looked at the commutative property of addition so it's a mathematical thing and it means that whether you're doing multiplication or addition if you move the numbers around the answer will still be the same okay now does it work with subtraction well let's have a look let's say we had 7 - 3 now is that the same as 3 3 - 7 well 7 - 3 is 4 3 - 7 is - 4 can you see that the numbers are not the same so we can therefore say does not work with subtraction what about division well let's say 10 / 2 what is 10 ID 2 that's 5 what is 2 / 10 now some students say five but it's actually not correct if you do it on your calculator you would actually end up getting like a fraction maybe 1 over 5 or your calculator might say 0a 2 which is definitely not the same as this so therefore does not work with division and so that's it for this lesson guys we've learned about the commutative property of multiplication and addition and in a test they're going to ask you is this commutative or is this associative or distributive which we're going to look at in future lessons and you need to be able to know which one is commutative and what did I tell you in the very beginning of this lesson commutative is all about when it moves because that's what the word commute means when your parents go to work they commute to work