Properties of Multiplication

The properties of multiplication are discussed here:

1. The product of two whole numbers is a whole number.

For example:

(i) 7 × 5 = 35 (Closure Property)

(ii) 6 × 6 = 36 (Closure Property)

2. The product of two or three numbers does not change if the order of the numbers multiplied is changed.

For example:

(i) 9 × 5 = 5× 9(Commutative Property)

(ii) 7 ×6 = 6× 7(Commutative Property)

(iii) (15 × 16) × 17 = 15× (16 ×17) (Associative Property)

(iv) (11 × 13) × 7 = 11× (13 × 7) (Associative Property)

3. The product of 1 and any number is the number itself.

For example

(i) 175 × 1= 175

(ii) 854372 ×1= 854372

4. The product of zero and any number is zero.

For example:

(i) 654× 0 = 0

(ii) 1543×0 = 0

5. Distributive property.

For example:

(i) (18+ 15) × 5 = 18 × 5 + 15 × 5

(ii) (18 – 15) × 5= 18 × 5 – 15 × 5

6. When the multiplier is 10, 100, 1000 or 10000 etc, the product has as many zeroson the right side of the number being multiplied as the multiplier.

For example:

(i) 75 × 10 = 750

(ii) 234 × 100 = 23400

(iii) 1692 × 10000 = 16920000

To multiply a number by 2000, 3000 or 4000 and so on, we multiply the number by the digit in the thousands place of the multiplier and write the three zeros on the right of the product.

For example:

(i) 735 × 6000 = (735 × 6) × 1000

= (4410) × 1000

= 4410000

(ii) 2035 × 15000 = (2035 × 15) × 1000

= (30525) × 1000

= 30525000