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) × ((2/3) + ¾) = (-½ × (2/3)) + (-½ × ¾)
LHS = (-½) × ((2/3) + ¾)
= (-½) × ((8 + 9)/12)
= -½ × (17/12)
= -17/24
RHS = (-½ × (2/3)) + (-½ × ¾)
= (-1/3) + (-3/8)
= (-8 – 9)/24
= -17/24
By comparing LHS and RHS
LHS = RHS
∴ -17/24 = -17/24
Hence x × (y + z) = x × y + x × z
