# Properties of Multiplying Integers

The properties of multiplying integers are explained using examples.

For any integers ‘a’, ‘b’ and ‘c’, etc.

1. Closure property:

a × b is an integer i.e., product (multiplication) of two integers is always an integer

For example: 2 and 3 are two integers, now 2 × 3 = 6, which is an integer.

2. Commutative property:

a × b = b × a.

For example: 2 × 5 = 5 × 2      and so on.

3. Associative property:

a × (b × c) = (a × b) × c.

For example: 2 × (3 × 4) = (2 × 3) × 4      and so on.

4. Multiplicative Property of Zero:

a × 0 = 0 × a = 0

For example: 5 × 0 = 0 × 5 = 0      and so on.

The result of multiplication of any number with zero (0) is always zero.

i.e., any number × 0 = 0 and 0 × any number = 0

Thus, 7 × 0 = 0, 0 × 7 = 0, (-10) × 0 = 0, 0 × (-10) = 0

5. Multiplicative identity property:

a × 1 = 1 × a = a

For example: 3 × 1 = 1 × 3 = 3      and so on.

6. Distributive of property multiplication over addition:

(i) a × (b + c) = a × b + a × c,

For example: 2 × (4 + 5) = 2 × 4 + 2 × 5      and so on.

(ii) (b + c) × a = b × a + c × a

For example: (4 + 9) × 3 = 4 × 3 + 9 × 3    and so on.

7. Distributive of property multiplication over subtraction:

(i) a × (b - c) = a × b - a × c

For example: 4 × (7 - 9) = 4 × 7 - 4 × 9      and so on.

(ii) (b - c) × a = b × a - c × a

For example: (2 - 8) × 6 = 2 × 6 - 8 × 6      and so on.