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Without multiplying anything out, decide the sign of (−3) × (−7) × 2 × (−5) × (−1).

Class 7Integers (Extended)Integers
  • ANegative, because the negative factors outnumber the positive ones.
  • BZero, because the negatives cancel each other.
  • CPositive, because the number of negative factors is even.
  • DIt cannot be decided without multiplying it out.

Step-by-Step Solution

Count the negative factors — −3, −7, −5 and −1 — which is four, an even number, so the product is positive. (It happens to be 210, but you never needed that.) Whether the negatives outnumber the positives is irrelevant; only the odd-or-even count of negatives decides the sign, and cancelling in pairs gives +1 each time, never 0.
Answer: C) Positive, because the number of negative factors is even.

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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