Properties of Multiplication

Property 01

Closure Property

a × b ∈ ℤ

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Property 02

Commutative Property

a × b = b × a

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Property 03

Associative Property

(a × b) × c = a × (b × c)

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Property 04

Distributive Property

a × (b + c) = ab + ac

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Property 05

Multiplicative Identity

a × 1 = a

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Property 06

Property of Zero

a × 0 = 0

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Closure Property

The product of any two integers is always an integer.

If a and b are integers, then their product is also always an integer.

a × b ∈ ℤ

(–5) × (+4) = –20
(–4) × (–2) = +8
1 × 0 = 0
7 × (–3) = –21

Commutative Property

Changing the order of multiplication does not change the product.

If a and b are integers, the result is the same regardless of order.

a × b = b × a

3 × 2 = 2 × 3 = 6
(–8) × (+3) = (+3) × (–8) = –24
1 × 0 = 0 × 1 = 0
(–7) × 4 = 4 × (–7) = –28

Associative Property

The grouping of integers does not affect the product.

If a, b, c are integers, you can regroup them freely.

(a × b) × c = a × (b × c)

(2 × 3) × (–4) = 2 × (3 × –4) = –24
(–5 × 2) × 3 = –5 × (2 × 3) = –30

Distributive Property

Multiplication distributes over addition.

If a, b, c are integers, you can distribute the multiplication across the sum.

a × (b + c) = (a × b) + (a × c)

(+6) × [(+3) + (–2)] = (+6)×(+3) + (+6)×(–2) = 18 – 12 = 6

Multiplicative Identity (Property of 1)

Multiplying any integer by 1 returns the same integer.

1 is called the multiplicative identity because it leaves any number unchanged.

a × 1 = 1 × a = a

(–5) × 1 = –5
1 × (+6) = +6
0 × 1 = 0
1 × (–17) = –17

Multiplicative Property of Zero

Any integer multiplied by zero gives zero.

Zero is the absorbing element — no matter what you multiply, the result is always 0.

a × 0 = 0 × a = 0

2 × 0 = 0
0 × (–15) = 0
0 × 0 = 0
(–9) × 0 = 0

🎯 Multiplication Properties Quiz

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