Sign Rules for Multiplication and Division
Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
What a learner can do afterwards
- Apply the sign rules when multiplying two integers (positive × negative, negative × negative)
- Apply the sign rules when dividing two integers
- Solve multi-step real-world problems involving all four operations with positive and negative rational numbers
1 · Read
When you multiply two numbers, the signs tell you the sign of the answer. If both numbers have the same sign, positive times positive or negative times negative, the answer is positive. If the numbers have different signs, one positive and one negative, the answer is negative.
Look at −3 × −4. Both numbers are negative, so they have the same sign. The answer is positive: −3 × −4 = 12.
Now look at division: −20 ÷ 5. The numbers have different signs, one negative and one positive, so the answer is negative: −20 ÷ 5 = −4. Multiplication and division follow the exact same sign rule.
A fast way to check bigger problems: count how many negative numbers you are multiplying or dividing. An even count of negatives gives a positive answer, and an odd count gives a negative answer. This works with fractions and decimals too, not just whole numbers.
Same signs make a positive answer, different signs make a negative answer, whether you multiply or divide.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.