Learn about Associative Property In this track, let's learn about associative property when it comes to addition, multiplication, subtraction and division. There are three different problems we’re going to solve. Let's do it one by one. The first one says; to fill in the blank where we’re given the left hand side of the equation as (3 + 5) + 6 = 3 + 5 and we have to fill in the blank which equals 14. Now in order to do this, we are going to use the associative property for addition. What associative property says is when we have an equation which is (A + B) + C. If they're all being additive, then we can also write this as A + (B +C). These two should have the same value. Now, if this is true, let's actually substitute the values on both sides because we know the left hand side should be equal to the right hand side. So, the left hand side says A = 3, B = 5 and C = 6. So, if this is to be true, A = 3, B = 5, C = 6. I can substitute these values on the right hand side. So, A = 3 + B= 5 + C = 6. So, 3 + 5 + 6 where 5 + 6 is within the parenthesis, it should be the same as the left hand side. So that is true, we found the answer to fill in the blank which is 5 + 6. Let's double check our answers. On the left hand side, I've got within the parenthesis, I've got 3 + 5 which is 8. Eight when added to six gives me 14. On the right hand side, let's add the numbers within the parenthesis first; 5 + 6 is 11, when added to three, it gives me 14. So, this is correct. So, the final answer here is 5 + 6, that’s what's missing from this blank. Let's do the second question or the second problem which says apply the associative law to this equation which is (3 x 4) x 5 = 3 x we don’t know what the value here is but the final results should be equal to 60. This is the same associative property applied to multiplication which says that (A x B) x C is the same as A x B x C. So, if this is true A = 3, B = 4. C = 5. So, applying the same thing here 3 x B = 4 and C = 5 which means that the missing equation that we’re looking for is 4 x 5. If this is true and the answer indeed is 4 x 5; then, both of these should multiply to give me the result 60. Let's try it, 3 x 4 is 12 x 5 is 60, so that’s correct. Now in the right hand side, 4 x 5 is 20 x 3 is 60. So, this is correct as well. Now, the third question asks us if the associative law works for subtraction and division. Let's try this. The easiest way to figure this out is to write it down. So, we need to know if associative law or the associative property works for subtraction and for division. Let's write down what would happen if the associative law was to work for subtraction. If it was to work for subtraction, then A – (B – C) should be the same as (A – B) – C. So, let's actually replace some numbers that we think about. So, let's say A = 2. B = 5, and C = 3. Let's substitute the values. So, on the left hand side, what do we see? A is 2 – B – C is 5 – 3. Let's solve this. 5 – 3 is 2, 2 – 2 = 0. So, the left hand side, this value is zero. Let's look at the right hand side. I'm just using the acronyms RHS for right hand side. A – B – C, A is 2 – B is 5, within the parenthesis minus C is three. So, 2 – 5 is (-3) – 3 = (-6). So the right hand side value is (-6). The left hand side value is zero, this is (-6). This is not equal which means the associative law does not work for subtraction. Let's try it for division. Let's use the same exact thing which is if we look at division, A ÷ (B ÷ C) should be equal to (A ÷ B) ÷ C. Let's substitute random values in there. Let's say the values are 12, six and two. So, 12 ÷ (6 ÷2) should be equal to (12 ÷ 6) ÷ 2. So, 6 ÷ 2 is 3 and 12 ÷ 3 is 4. So, the left hand side is four. The right hand side is 12 ÷ 6 is 2 ÷ 2 which is equal to 1. Left hand side is not equal to right hand side, so the associative property does not work for division either. So going back to recap what we've learned, the associative property does not work for subtraction or division. Both of t