Question

Mention the commutativity, associative and distributive properties of rational numbers. Also, check a × b = b × a and a + b = b + a for a = ½ and b = ¾​

Answer 1

Solution: Commutative identity: a + b = b+ a, a – b ≠ b – a, a × b = b × a and a ÷ b ≠ b ÷ a

Associative property: a + (b + c), a – (b – c) ≠ (a – b) – c, a × (b × c) = (a × b) × c, and a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

When a = ½ and b = ¾

Now, for checking a × b = b × a, consider LHS and RHS.

LHS = a × b = ½ × ¾ = ⅜

RHS = b × a = ¾ × ½ = ⅜

Thus, LHS = RHS (Hence proved).

Answer 2

a + b = b + a

a – b ≠ b – a

a × b = b × a  

a ÷ b ≠ b ÷ a

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

a – (b – c) ≠ (a – b) – c  

a × (b × c) = (a × b) × c

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c