Question

What is the associative property

Answer 1

The associative property is the ability to group certain numbers together in addition/subtraction and multiplication problems because their operations are interchangable. 

Example 1: 

1 + 2 + 3

We can solve this by first doing 1 + 2 = 3, and then adding 3 + 3 = 6. OR we can start with 2 + 3 = 5, and add 5 + 1 = 6. We can even do, 3 + 1 = 4, then add 4 + 2 = 6. Either way, we end up with the same correct answer. 

Example 2:

1 x 2 x 3

Same thing applies to multiplication. We can start by doing 1 x 2 = 2, and then 2 x 3 = 6. OR we can do 2 x 3 = 6, then 6 x 1 = 6. Just like the one above, we can also do, 3 x 1 = 3, then 3 x 2 = 6. Either way you group them, you get the same answer. 

Example 3:

- 1 - 2 - 3

We can do - 1 - 2 = - 3, then - 3 - 3 = - 6. OR - 1 - 3 = - 4, then - 4 - 2 = - 6. OR - 2 - 3 = - 5, then - 5 - 1 = - 6. Again, same answer, three different ways to group it.

THIS DOES NOT WORK WHEN THE ADDITION/SUBTRACTION and MULTIPLICATION OPERATIONS ARE IN THE SAME PROBLEM

If given 1 + 3 - 7 x 4, you cannot rearrange the components like you can with the associative property. You will end up with drastically different answer when there is only one way to do this. 

Here is an incorrect example of it. 

1 + 3 + 7 x 4
1 + 10 x 4
11 x 4 
44.

That is wrong. The correct way is 

1 + 3 + 7 x 4
1 + 3 + 28

Now because all of the operations match you can use associative property to arrive at the same answer the three different ways. 

4 + 28 = 32. OR 1 + 31 = 32. OR 29 + 3 = 32. See the difference in the answers?