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Associative property under addition:
Addition is associative for integers. For any three integers a, b and c, a + (b + c) = (a + b) + c
Ex: 5 + (– 6 + 4) = 5 + (– 2) = 3;
(5 – 6) + 4 = (– 1) + 4 = 3
∴ 5 + (– 6 + 4) = (5 – 6) + 4.

Associative property under subtraction:
Subtraction is associative for integers. For any three integers a, b and c, a – (b – c) ≠ (a – b) –
c
Ex: 5 – (6 – 4) = 5 – 2 = 3;

(5 – 6) – 4 = – 1 – 4 = – 5
∴ 5 – (6 – 4) ≠ (5 – 6) – 4.

Associative property under multiplication:
Multiplication is associative for integers. For any three integers a, b and c, (a × b) × c = a × (b
× c)
Ex: [(– 3) × (– 2)] × 4 = (6 × 4) = 24
(– 3) × [(– 2) × 4] = (– 3) × (– 8) = 24

∴ [(– 3) × (– 2)] × 4 = [(– 3) × (– 2) × 4].

Associative property under division:
Division is not associative for integers.

Distributive property
Distributive property of multiplication over addition:
For any three integers a, b and c, a × (b + c) = (a × b) + (a × c).
Ex: – 2 (4 + 3) = –2 (7) = –14
= (– 2 × 4) + (– 2 × 3)
= (– 8) + (– 6)

= – 14.

Distributive property of multiplication over subtraction:
For any three integers, a, b and c, a × (b - c) = (a × b) – (a × c).
Ex: – 2 (4 – 3) = – 2 (1) = – 2
= (–2 × 4) – (– 2 × 3)
= (– 8) – (– 6)
= – 2.

The distributive property of multiplication over the operations of addition and subtraction is
true in the case of integers.

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