Step by Step
1
Positive times positive
Two positive numbers multiplied together give a positive result — the expected, unsurprising case.
2
Positive times negative ("Good × Bad")
A positive multiplied by a negative gives a negative result.
3
Negative times negative ("Bad × Bad")
Two negatives multiplied together give a positive result — this is the one students most often get wrong.
4
Count the negatives as a shortcut
For longer multiplication chains, count the total number of negative signs: an even count gives a positive result, an odd count gives a negative result.
Applied Walkthrough
1
Calculate 3 × −2. One positive, one negative — "Good × Bad = Bad," so the result is negative: −6.
2
Calculate −3 × −2. Both negative — "Bad × Bad = Good," so the result is positive: 6.
3
Calculate −2 × −3 × −1 (three negative numbers). Count the negatives: three is an odd number, so the result is negative: −6.
4
This shortcut (counting negatives) becomes especially useful once problems involve more than two numbers being multiplied together.
Exam Application
Exams test whether you can correctly apply sign rules across multiple multiplied terms, particularly the counterintuitive negative-times-negative-equals-positive rule.
⚠ Common Trap
The most common trap is assuming two negatives multiplied together stay negative — they don't. Negative times negative always produces a positive result.
✓ Quick Self-Check
1. What is positive times negative?
Negative.
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2. What is negative times negative?
Positive.
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3. Calculate −3 × −2.
6.
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4. Calculate −2 × −3 × −1.
−6 (three negatives — an odd count — gives a negative result).
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5. What's the shortcut for figuring out the sign of a long multiplication chain?
Count the total number of negative signs — even count means positive result, odd count means negative result.
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