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Division of integers is not commutative. For which of these pairs does a ÷ b nevertheless give the same result as b ÷ a?

Class 7Integers (Extended)Integers
  • A
  • B
  • C
  • DNo pair of non-zero integers ever works.

Step-by-Step Solution

Test it: (−7) ÷ 7 = −1 and 7 ÷ (−7) = −1, so the two quotients agree. This matching happens only when a and b are equal or opposite. With 12 and 3 you get 4 one way and a fraction the other; the pair 0 and 5 fails twice over, because 5 ÷ 0 is undefined rather than 0. 'Never works' overstates the rule — division is not commutative in general, but special pairs can still agree.
Answer: B)

Key idea: Properties — same as for whole numbers, mostly

Integers obey:
- **Commutative** for addition and multiplication: a + b = b + a; a × b = b × a.
- **Associative** for addition and multiplication: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c).
- **Distributive**: a × (b + c) = a × b + a × c — and this is true even when a, b, c are negative.

Subtraction and division are NOT commutative or associative for integers (they aren't for whole numbers either). Order and grouping matter.

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