LEARN · THEORY
Working with negative numbers
When you multiply or divide negative numbers, first calculate using the numbers without their signs. Then decide whether your answer is positive or negative.
Remember the sign rule:
Same signs → positive (+)
Different signs → negative (−)
Theory A · Multiplying negative numbers
Multiply the numbers as usual. Count the negative signs to decide the sign of the answer.
Example 1 · Different signs
−4 × 6 = −24
4 × 6 = 24. One negative factor means the answer is negative.Example 2 · Same signs
−5 × (−3) = 15
5 × 3 = 15. Two negative factors mean the answer is positive.Theory B · Dividing negative numbers
The same sign rules apply when you divide.
Example 3 · Different signs
−42 ÷ 7 = −6
42 ÷ 7 = 6. The signs are different, so the answer is negative.Example 4 · Same signs
−36 ÷ (−6) = 6
36 ÷ 6 = 6. The signs are the same, so the answer is positive.Sign rules at a glance
| Signs | Result | Example |
|---|---|---|
| + and + | Positive | 3 × 4 = 12 |
| − and − | Positive | −3 × (−4) = 12 |
| + and − | Negative | 3 × (−4) = −12 |
| − and + | Negative | −12 ÷ 3 = −4 |
Theory C · More than two factors
When multiplying several non-zero numbers, count how many negative factors there are.
−2 × (−3) × (−4) = −24
Three negative factors: an odd number. The answer is negative.−2 × (−3) × (−4) × (−1) = 24
Four negative factors: an even number. The answer is positive.Useful checks: Multiplying by zero always gives zero. You cannot divide by zero. Calculate inside brackets first and remember the order of operations.