alleryThree rational numbers a, b, c are given. Which of the following is ALWAYS true?
Aa − (b − c) = (a − b) − c
Ba ÷ (b ÷ c) = (a ÷ b) ÷ c
Ca × (b + c) = a × b + a × c
Da ÷ b = b ÷ a, for all non-zero a, b
Answer & Solution
Correct answer: C. a × (b + c) = a × b + a × c
Distributivity (option C) holds for all rationals: a(b + c) = ab + ac.
Option A would require subtraction to be associative — it is not (e.g. 5 − (3 − 1) = 3 but (5 − 3) − 1 = 1).
Option B requires division to be associative — it is not.
**Option D requires division to be commutative — it is not (e.g. 6/2 ≠ 2/6).**
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