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Which is greater, (−8) × 3 or (−5) × (−2)?

Class 7Integers (Extended)Integers
  • A(−8) × 3, because 24 is bigger than 10
  • BThey are equal in value.
  • C(−8) × 3, because it carries more minus signs
  • D(−5) × (−2), because 10 is positive while the other product is −24

Step-by-Step Solution

(−8) × 3 = −24, since different signs give a negative product, and (−5) × (−2) = +10, since same signs give a positive one. Every positive integer beats every negative one, so 10 > −24. Comparing the digits 24 and 10 while ignoring the minus sign is the standard trap, and counting minus signs decides nothing on its own.
Answer: D) (−5) × (−2), because 10 is positive while the other product is −24

Key idea: Multiplying integers — same sign vs different sign

**Same sign → positive.**
(both positive)
(both negative — still positive)

**Different signs → negative.**
3 × (−4) = −12
(−3) × 4 = −12

**Why two negatives become positive:** think of −3 as 'the opposite of 3'. So = 'the opposite of ' = the opposite of −12 = +12. The double-negative cancels.

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