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A driver in Hyderabad begins the year with 12 licence points. Each traffic violation removes 3 points, and 5 violations are recorded against him. What is his points total at the end of the year?

Class 7Integers (Extended)Integers
  • A3
  • B−15
  • C27
  • D−3

Step-by-Step Solution

The violations cost 5 × (−3) = −15 points. Total = 12 + (−15) = −3, so he ends 3 points in the red. Answering 3 computes 15 − 12 and loses track of which number is larger; 27 adds the 15 instead of subtracting it; −15 forgets the 12 points he started with.
Answer: D) −3

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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