Questions: Multiplying Integers

Question 1

What is the sign of the product (-2) × (-3) × (-1)?

• A. Positive, because two negatives make a positive
• B. Negative, because there are three negative factors
• C. Positive, because all numbers are even
• D. Negative, because the product of any negatives is negative

Answer: (B)

Count the negative factors: there are three (-2, -3, and -1). An odd number of negatives gives a negative product. (-2) × (-3) = 6 (positive), then 6 × (-1) = -6 (negative). Three negatives → negative result.

Question 2

Negative times negative equals negative.

• T. True
• F. False

Answer: False

Negative times negative equals positive. For example, (-3) × (-4) = 12. The double-negative 'cancels': multiplying by -1 flips a number to its opposite, so multiplying by -1 twice returns you to the original sign. (-3) × (-4) can be read as 'the opposite of [3 × (-4)]' = 'the opposite of -12' = 12.

Question 3

Using the pattern-based argument, explain why a negative number times a negative number must be positive.

Model answer: Each multiplication by -1 reverses the sign. Starting from a positive product and multiplying by two negatives reverses the sign twice, returning to positive.

Consider the pattern: 3×2=6, 3×1=3, 3×0=0, 3×(-1)=-3, 3×(-2)=-6. Each step decreases by 3. Now extend: (-3)×2=−6, (-3)×1=−3, (-3)×0=0, (-3)×(-1)=3, (-3)×(-2)=6. The pattern forces the result to be positive — it is not a rule imposed from outside but a consequence of how multiplication behaves.