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Assertion (A): The expression (−2) ÷ 0 has no value. Reason (R): Division of integers is not commutative. Which option is correct?

Class 7Integers (Extended)Integers
  • AA is correct but R is incorrect.
  • BBoth A and R are correct, but R is not the reason for A.
  • CA is incorrect but R is correct.
  • DBoth A and R are correct, and R is the correct reason for A.

Step-by-Step Solution

A is correct — dividing by 0 is undefined, so (−2) ÷ 0 has no value at all. R is correct too: 8 ÷ (−2) = −4 whereas (−2) ÷ 8 is not even an integer, so a ÷ b need not equal b ÷ a. But non-commutativity is about swapping the ORDER of two numbers; it says nothing about why zero is barred as a divisor. A statement can be perfectly true and still not be the reason.
Answer: B) Both A and R are correct, but R is not the reason for A.

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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