Question

Give an example and verify the following statement.

Subtraction is not commutative for rational numbers

Answer 1

let a = `1/2` and b = `-5/6` be two rational numbers.

a − b = `1/2 - (- 5/6)`

= `1/2 + (+ 5/6)`

= `3/6 + 5/6`

= `(3 + 5)/6`

= `8/6`

= `1 2/6`

= `1 1/3`

b − a = `-5/6 - 1/2`

= `-5/6 - 3/6`

= `(-5 - 3)/6`

= `(-8)/6`

= `-1 1/3`

a − b ≠ b − a

∴ Subtraction is not commutative for rational numbers.