2. Negative numbers

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Negative numbers

Negative of a numbers,

Reciprocal of rational numbers,

The multiplicative inverse of any rational number

Example

The reciprocal of 4/5 is 5/4.

Distributivity of multiplication over addition for rational numbers,

This shows that for all rational numbers p, q and r

1. p(q + r) = pq + pr

2. p(q – r) = pq – pr

Example

Check the distributive property of the three rational numbers 4/7,-( 2)/3 and 1/2.

Solution

Let’s find the value of

This shows that

Distributivity of multiplication over subtraction for rational numbers

The distributive property of rational numbers states that if any expression with three rational numbers A, B, and C is given in form A (B + C), then it can be solved as A × (B + C) = AB + AC. This applies to subtraction also which means A (B - C) = AB - AC. This means operand A is distributed between the other two operands, i.e., B and C. This property is also known as the distributive property of multiplication over addition or subtraction.