Distributive Property of Rational Numbers

Distributive Property of Multiplication over Addition

Distributive property for multiplication over addition of rational numbers states that any expression of three rational numbers a, b, c in form of a (b + c), then it can be solved as,

a x (b + c) = a x b + a x c

Let us learn with examples.

Example: 1/3 (1/6 + 1/5)

a (b + c) = a x b + a x c

= (1/3 x 1/6) + (1/3 x 1/5)

= (1/18) + (1/15)

= (5 + 6)/90

= 11/90

Distributive Property of Multiplication over Subtraction

If a, b and c are three rational numbers then, this applies to subtraction as,

a (b – c) = a x b – a x c

Let us learn with examples.

Example: 1/3 (1/4 – 1/5)

= (1/3 x 1/4) – (1/3 x 1/5)

= (1/12) – (1/15)

= (5 – 4)/60

= 1/60

a (b – c) = a x b – a x c