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:
Associative Property of Addition
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.
Does the given equation hold the associative property of addition? (12 + 1) + 5 = 12 + (1 + 5)
Solution:
As we know, according to the associative property of addition: (a + b) + c = a + (b + c) Here, a = 12, b = 1, c = 5 L.H.S (a + b) + c => (12 + 1) + 5 => 13 + 5 => 18 R.H.S a + (b + c) = 12 + (1 + 5) => 12 + 6 => 18 L.H.S = R.H.S Thus, the associative law of addition holds for the given equation
Find x in given equations using the associative property of addition a) (22 + 11) + 7 = 22 + (11 + x) b) 9 + (3 + x) = (9 + 3) + 2
Solution:
Here, a = 22, b = 11, c = 7 If the associative property of addition holds, then a + (b + c) = (a + b) + c a) Since (22 + 11) + 7 = 40 and addition satisfies the associative property of addition, thus 2 + (11 + x) = 40 => 11 + x = 38 => x = 7 b) Since (9 + 3) + 2 = 14 and addition satisfies the associative property of addition, thus 9 + (3 + x) = 14 => 3 + x = 5 => x = 2
