Commutative Associative and Distributive Properties Milanese Math

hey how's it going everybody welcome back to melanie's math today we're going to be talking about the commutative associative and distributive properties these are three basic arithmetic properties and if you want to follow along with the worksheet that we have you can find it at the first link in the description below so first up let's take look at the commutative property or the commutative law and that says that we can swap numbers okay or change the numbers out and still get the same answer when we add and so i'll show you an example of that like to think of to remember the commutative property if you think of commuters those are people that travel from place to place for work and so that's sort of what you're going to be seeing here so let me give you an example of when we add we can use the commutative property in other words if have two numbers i'm just going to make up and we get the same thing when we swap those numbers that's an example of the commutative property so for an example we could do 6 plus 3 and that's going to give us the same thing if we do 3 plus six right you're gonna get nine either way okay but that's also true when we multiply so for example if we did how about well let's just look at it in terms of letters so if had any two numbers times would get the same thing if multiplied times so just as quick example if had 2 times 4 that would be eight and would get the same thing if did four times two that's also eight okay now it's worth mentioning that this doesn't work with subtraction okay and it also doesn't work with division so you can do this swapping out for addition or multiplication and that's an example of the commutative property or commutative laws okay that one's one of the easiest ones to remember associative laws are little bit different the associative property or law says that it doesn't matter how we group the numbers okay so it doesn't matter how we group the numbers for example when we add so for example let's take look here if do plus and take that whole group and add it to another number you'd get the same thing even if you regrouped it differently if put my parentheses around the plus i'm still going to get the same final answer so to put some numbers to that as an example let's do 6 plus 3 plus 4. and see that would be 9 plus 4 is 13. so the final answer here is going to be 13. and you'd get the same answer if you regrouped it the differently right so if did the 3 plus 4 and got 7 added it to 6 it's still 13. you get the same answer either way so the associative law says it doesn't matter how we group them when we add or when we multiply so let's do the same kind of thing here but with multiplication so if have group times and multiply that times i'll get the same thing if group it differently in other words if put the parentheses around the and the so to throw some numbers at this as an example if do two times four times three well that's weird looking three okay i'd get the same thing if regrouped it like this and put the parentheses around the 4 and the 3. just to prove that to you 2 times 4 is 8 times 3 is 24 right but you're going to get the same thing if you do 2 times 12 and you're still going to get 24 okay once again doesn't work with subtraction and it also doesn't work with division okay so far so good just quick recap commutative property says you can swap the numbers associative property says you can regroup the numbers but the distributive property is little bit different this distributive law says we get the same answer when we multiply number by group of numbers added together so by group of numbers together or when we do each multiply separately and then add them okay that sounds little bit weird in pers you know just to have it written out in words it's easier if you see it with numbers so essentially what they're saying is if we were to multiply right 3 times the quantity two plus four we would get the same thing if we did all the multiplication separately and then just added together our answers so for example lot of times in math class you'll see this written with little arrows these little distributive property arrows and essentially it's saying that if you have number times quantity you can do the individual multiplications and just add them together so if work down that left hand side 2 plus 4 is 6 right so that would be 3 times 6 which is 18. but that's going to be the same thing if just did these individually 3 times 2 is 6 3 times 4 is oops 12. sorry 3 times 4 is 12 and then if added those together would also get 18. okay so it's just showing you another way to do that and again this doesn't work with division so this is only true kind of for multiplication okay so you can use these laws and all types of context and as you get into some really advanced math you need to know what you can and can't do so that's just quick crash course in commutative associative and distributive properties hope this video was helpful if it was consider subscribing to the channel and as always thanks for watching and we'll catch you next time