welcome to math with Mr J [Music] in this video I'm going to cover what the commutative property is now the commutative property is used all throughout math everything from basic math facts to working through problems with multiple steps to simplifying algebraic expressions to whatever else the case may be the commutative property is important to be familiar with now simply put the commutative property States changing the order doesn't change the answer and we can think of commute or move when it comes to the commutative property now both addition and multiplication are commutative but subtraction and division are not we will take a look at all of this as we go through our examples let's jump into our examples starting with numbers 1 and 2 where we will take a look at the commutative property of addition which states a plus b equals B plus a that just means the order of the add-ins doesn't change the sum add-ins are the numbers that are being added together and then the sum is the answer to an addition problem now don't let the letters confuse you those are just there in place of numbers to show that this will work for any numbers a plus b will equal the same exact thing as B plus a let's take a look at number one and see exactly what this means we have 15 plus four that equals nineteen fifteen and four are the add-ins the numbers being added together 19 is the sum the answer the commutative property states that we can change the order and that will not change the answer so 4 plus 15 equals 19 as well and that's the commutative property fifteen plus four equals 19 4 plus 15 equals 19. let's move on to number two and take a look at another example of addition so we have 200 plus 75 that equals 275 change the order 75 plus 200 and that does not change the answer so 75 plus 200 equals 275 as well so to recap addition is commutative we can change the order of the add-ins and that doesn't change the sum we get the same answer either way now let's try this with the inverse of addition so the opposite of addition which is subtraction and see if subtraction is commutative I'm going to come to the side here let's do 5 minus 3 which we know is 2. let's change the order three minus five well that equals negative 2. so subtraction is not commutative we can't change the order and get the same answer so again subtraction not commutative let's move on to numbers three and four where we are going to take a look at the commutative property of multiplication so a times b equals B times a that just means that the order of the factors doesn't change the product factors are the numbers being multiplied and then the product is the answer to a multiplication problem so a times B is going to equal the same exact thing as B times a let's take a look at number three and see exactly what this means so 9 times 8 that equals 72. change the order eight times nine that equals 72 as well 9 times 8 equals 72 and 8 times 9 equals 72. changing the order didn't change the answer order didn't matter let's move on to number four where we have eleven times six that equals 66 change the order 6 times 11 that equals 66 as well so that's what the commutative property looks like when it comes to multiplication we can change the order of the factors and that doesn't change the product now let's take a look at the inverse of multiplication so the opposite of multiplication which is division let's see if division is commutative I'll come to the side here let's do eight divided by 4 which equals 2. let's change the order four divided by 8 that equals one-half so division is not commutative we can't change the order and get the same answer so again to recap addition and multiplication are commutative subtraction and division are not so there you have it there's what the commutative property is I hope that helped thanks so much for watching until next time peace foreign