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Two integers a and b satisfy a × b = 0, and a = −13. What must b be?

Class 7Integers (Extended)Integers
  • A13
  • B−13
  • C1
  • D0

Step-by-Step Solution

A product of integers is 0 only when at least one factor is 0. Since a = −13 is not 0, the other factor must be: b = 0. Answering 13 confuses this with the additive inverse, which makes a SUM of 0 rather than a product; b = 1 would leave the product at −13, and b = −13 would give +169.
Answer: D) 0

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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