Operation 
Commutative 
True / False 
Addition 
a + (b + c) = (a + b) + c 
True 
Subtraction 
a − (b − c) = (a − b) − c 
False 
Multiplication 
a × (b × c) = (a × b) × c 
True 
Division 
a ÷ (b ÷ c) = (a ÷ b) ÷ c 
False 
Advertisement
For Integers
Let us take three integers 2, 3, 4
Operation 
Number 
Remark 
Addition

a + (b + c) = (a + b) + c Take a = 2, b = 3 & c = 4
L.H.S a + (b + c) = 2 + (3 + 4) = 2 + 7 = 9
∴ a + (b + c) = 9
R.H.S (a + b) + c = (2 + 3) + 4 = 5 + 4 = 9
∴ (a + b) + c = 9 
Since a + (b + c) = (a + b) + c
∴ Addition is associative. 
Subtraction

a − (b − c) = (a − b) − c Take a = 2, b = 3 & c = 4
L.H.S a − (b − c) = 2 − (3 − 4) = 2 − (−1) = 2 + 1 = 3
∴ a − (b − c) = 3
R.H.S (a − b) − c = (2 − 3) − 4 = −1 − 4 = −(1 + 4) = −5
∴ (a − b) − c = −5 
Since a − (b − c) ≠ (a − b) − c
∴ Subtraction is not associative. 
Multiplication

a × (b × c) = (a × b) × c Take a = 2, b = 3 & c = 4
L.H.S a × (b × c) = 2 × (3 × 4) = 2 × 12 = 24
∴ a × (b × c) = 24
R.H.S (a × b) × c = (2 × 3) × 4 = 6 × 4 = 24
∴ (a × b) × c = 24 
Since a × (b × c) = (a × b) × c
∴ Multiplication is associative. 
Division

a ÷ (b ÷ c) = (a ÷ b) ÷ c Take a = 2, b = 3 & c = 4
L.H.S a ÷ (b ÷ c) = 2÷(3÷4) = 2÷(3/4) = 2×4/3 = 8/3
R.H.S (a ÷ b) ÷ c = (2÷3) ÷4 = (2/3)÷4 = 2/3×1/4 = 1/6
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c 
Since a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
∴ Division is not associative. 