What’s the Associative Property? | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover what the associative property is now the associative property can be used all throughout math everything from basic addition or multiplication problems to more complex problems to simplifying algebraic expressions to whatever else the case may be the associative property is important to be familiar with when it comes to the associative property think grouping the associative property states that changing the grouping doesn't change the answer and this property can be used with addition or multiplication not subtraction or division so something to keep in mind let's jump into our examples starting with number one where we will be taking a look at the associative property of addition so a plus b grouped plus C will equal the same exact thing as a plus b plus C grouped so the grouping of add-ins the numbers being added together doesn't change the sum the sum is the answer to an addition problem now don't let those letters confuse you they are there to represent numbers and show that this will work for any numbers let's take a look and use some numbers in order to see exactly what this means for number one we have 27 plus 8 plus 12. now let's start by grouping 27 and 8 and add these numbers so we have 27 plus eight grouped Plus 12. now we can add starting with the parentheses 27 plus 8 that equals 35 bring down the addition sign and the 12 we end with 35 Plus 12. that equals 47. now let's group the eight and the 12 and see if we get the same thing so we have 27 Plus 8 plus 12 grouped let's add starting with the parentheses 8 plus 12 that equals 20. bring down the addition sign and the 27 we end with 27 plus 20 and that equals 47 as well so you can see that the grouping of add-ins didn't matter we got the same sum the same answer either way 27 plus 8 grouped plus 12 equals the same exact thing as 27 plus 8 plus 12 grouped and that's the associative property let's move on to number two and take a look at the associative property of multiplication so a times B grouped times c will equal the same exact thing as a times B times C grouped the grouping of factors doesn't change the product factors are the numbers being multiplied and then the product is the answer to a multiplication problem let's take a look at the example where we have nine times two times five let's start by grouping 9 nine and two so nine times two grouped times five now we can multiply starting with the parentheses nine times two that equals eighteen bring down the multiplication sign and the five we end with eighteen times five which equals ninety now let's group The 2 and the five and see if we get the same thing we have nine times two times five grouped now we can multiply starting with the parentheses we have two times five that equals ten bring down the multiplication sign and the nine we end with nine times ten which equals ninety so we get 90 that way as well nine times two grouped times five equals nine times two times five grouped we got the same thing either way the grouping of factors didn't change the product and that's the associative property so there you have it there's an explanation of the associative property just remember changing the grouping doesn't change the answer and the associative property works with addition or multiplication not subtraction or Division I hope that helped thanks so much for watching until next time peace