Question

'Rational numbers are commutative under addition but not commutative under subtraction.' Justify the statement with an ex.

Answer 1

Commutative property of Rational numbers states that , if there are two rational numbers 'a' and 'b' .

Then , a+b = b+a

Let's, verify it -

let a be 5

let b be 6

So, a+b = b+a

5+6 = 6+5

11 = 11

Hence , LHS = RHS

So, Rational numbers are commutative under addition.

But Can we say so for Subtraction?
→ If Rationals are commutative under substraction , then -

a-b = b-a

Let , a be 5

let b be 6

So, 5-6 = 5-6

- 1 ≠ 1

Hence , LHS ≠ RHS

So, Rationals aren't commutative under substraction.