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, (-1/5) × ((2/15) + (-3/10)) = ((-1/5) × (2/15)) + ((-1/5) × (-3/10))
LHS = (-1/5) × ((2/15) + (-3/10))
= (-1/5) × ((4 – 9)/30)
= (-1/5) × (-5/30)
= (-1/1) × (-1/30)
= 1/30
RHS = ((-1/5) × (2/15)) + ((-1/5) × (-3/10))
= (-2/75) + (3/50)
= (-4 + 9)/150
= 5/150
= 1/30
By comparing LHS and RHS
LHS = RHS
∴ 1/30 = 1/30
Hence x × (y + z) = x × y + x × z
