When we multiply numbers, we have three possibilities-

- If both numbers are positive then product is also positive.

Examples –

- 6 × 3 = 18
- 2 × 6 = 12

- If both numbers are negative then also the product is positive.

Examples –

- – 6 × – 3 = +18 and – 3 × – 6 = +18
- – 18 × – 2 = +36 and – 2 × – 18 = +36

- If we have any one positive and one negative number to multiply, then we get negative product.

Examples –

- (-3) × (4) = -12 and 3 × (-4) = -12

- (-18) × (2) = -36 and 18 × (-2) = -36

## Properties of Multiplication of Integers

### Closure property for multiplication of integers** :**

We have two integers, then the product is also an integer; that is if a and b are integers then a × b is also an integer.

Examples –

- 3 × 6 = 18
- 210 × 2 = 420
- -8 × 6 = -48

### Commutative law for multiplication of integers :

If we change the order of numbers to multiply then also we get same product, that is, a × b = b × a.

Examples –

- 3 × 6 = 18 and 6 × 3 = 18
- 160 × -3 = -480 and -3 × 160 = -480

### Associative law for multiplication of integers :

If we have three integers to multiply, we get the same multiplication if we carry out the second multiplication first or first multiplication first, that is, we have a, b and c integers then-

(a × b) × c = a × (b × c)

Examples –

- (5× 3) × 2 = 15 × 2 = 30 and 5× (3 × 2) = 5 × 6 = 30
- (-6 × 4) × 3 = -24 × 3 = -72 and

-6 × (4 × 3) = -6 × 12 = -72

### Distributive law of multiplication over addition :

If we have any three integers a, b and c, we have

a × (b + c) = a × b = a× c

Example –

- We have , and and

### Multiplication property of 0 :

If we

**multiply**any**integer**by 0 or 0 by any integer we get 0, that is,

If we have ‘’ as any**integer**, then

and

Examples –

- and
- and

### Existence of multiplication of identity

**:**

If we**multiply**any**integer****by 1**or 1 by any integer, we get the same integer. That is,

If we have ‘’ as any integer, then

and

Examples –

- and
- and

The integer 1 is the multiplicative identity.