Associative Property of Addition

The associative property of addition states that the sum of 3 or more numbers provides the same result regardless of how they are grouped. It can be best understood using colored blocks.

For any three numbers a, b, and c, the formula is:

Let us group 12, 8, and 6 to prove the associative property of addition using an example.

Step 1: Group the 3 numbers in two ways: 12 + (8 + 6) and (12 + 8) + 6

Step 2: Add the numbers within the parenthesis of L.H.S of the equation of L.H.S of the equation: (8 + 6) = 14

Step 3: Add the result to the other number 14 + 12 = 26 to get the result

Step 4: Follow steps 1 to 3 for the R.H.S of the equation

As we know, according to the associative property of addition:

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

Here, a = 12, b = 8, and c = 6

Solving L.H.S

a + (b + c)

= 12 + (8 + 6)

= 12 + 14

 = 26

Solving R.H.S

(a + b) + c

= (12 + 8) + 6

= 20 + 6

 = 26

L.H.S = R.H.S

Thus, the associative law of addition holds.