Question

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking x = -½, y = ¾, z = ¼.

Answer 1

In the question is given to verify the property x × (y + z) = x × y + x × z

The arrangement of the given rational number is as per the rule of distributive property of multiplication over addition.

Then, (-½) × (¾ + ¼) = (-½ × ¾) + (-½ × ¼)

LHS = (-½) × (¾ + ¼)

= (-½) × ((3 + 1)/4)

= -½ × (4/4)

= -½ × 1

= -½

RHS = (-½ × ¾) + (-½ × ¼)

= (-3/8) + (-1/8)

= (-3 – 1)/8

= -4/8

= -½

By comparing LHS and RHS

LHS = RHS

∴ -½ = -½

Hence x × (y + z) = x × y + x × z