Associative law:

The associative law for addition states in which addends might be related or combined in any order and will result in the similar sum. In equation form we have:

(a + b) + c = a + (b + c)

For example, the numbers 3, 5, and 7 could be grouped within any order and added to achieve the similar sum:

(3 + 5) + 7 = 15 OR 3 + (5 + 7) = 15

The sum of both operations is 15, but it is not reached the similar way.  The first equation, (3 + 5) + 7 = 15, is actually completed in the order (3 + 5) = 8.  The 8 is replaced in the formula that is now 8 + 7 = 15.

The second equation is completed in the order (5 + 7) = 12, then 3 + 12 = 15. Addition could be done in any sequence, and the sum will be the similar.

While several numbers are added together, it is simpler to arrange the numbers in columns along with the place positions lined up above each other.  First, the unit's column is added.  After when the unit column is added then the number of tens is carried over and added to the numbers within the tens column. Some hundreds number is then added to the hundreds column and so on.

Example:

Add 345, 25, 1458, and 6.

Solution:

 345

   25

1458

  + 6

---------------

1834

While adding the units column, 5 + 5 + 8 + 6 = 24.   A 4 is placed under the units column, and a 2 is added to the tens column.

Then, 2 + 4 + 2 + 5 = 13.  A 3 is placed under the tens column and a 1 is carried over to the hundreds column.  The hundreds column is added as give below:  1 + 3 + 4 = 8.

An 8 is placed under the hundreds column along with nothing to carry over to the thousands column, so the thousands column is 1.  The 1 is placed under the thousands column, and the sum is 1834.  For verify the sum, the numbers should be added within reverse order.  In the above instance, the numbers should be added from the bottom to the top.