Rules For Multiplying And Dividing Positive And Negative Numbers
When multiplying or dividing positive and negative numbers, the sign of the result follows two simple rules: same signs give a positive answer, different signs give a negative answer. Positive × Positive = Positive; Negative × Negative = Positive; Positive × Negative = Negative; Negative × Positive = Negative. The same rules apply to division. For example: (−4) × (−3) = +12; (+5) × (−2) = −10. This foundational rule for integer operations is covered in Saxon Math, Course 2, and is essential for 7th grade math and all future algebra.
Key Concepts
Property If the two numbers in a multiplication or division problem have the same sign, the answer is positive. If the two numbers have different signs, the answer is negative.
Examples Same signs are positive: $( 6)( 2) = 12$ and $\frac{ 12}{ 4} = 3$. Different signs are negative: $(+6)( 3) = 18$ and $\frac{25}{ 5} = 5$. Even with fractions the rule applies: $( \frac{1}{2})( \frac{1}{2}) = \frac{1}{4}$.
Explanation Think of signs as friends (+) or enemies ( ). An enemy of an enemy is a friend, so two negatives make a positive! It’s all about vibes: same signs are positive, and different signs are negative. This simple rule keeps your calculations on the right track, whether you're multiplying integers or dividing decimals.
Common Questions
What are the rules for multiplying positive and negative numbers?
Same signs give a positive product; different signs give a negative product. Positive × Positive = Positive, Negative × Negative = Positive, Positive × Negative = Negative.
What is (−4) × (−5)?
(−4) × (−5) = +20. Both numbers are negative, so the result is positive.
What is (+6) × (−3)?
(+6) × (−3) = −18. One positive and one negative gives a negative result.
Do the same sign rules apply to division of integers?
Yes. The same rules apply: same signs give a positive quotient; different signs give a negative quotient. (−15) ÷ (−3) = +5; (+12) ÷ (−4) = −3.
Why does negative times negative equal positive?
One way to see it: multiplying by a negative reverses the sign once. Multiplying by another negative reverses it again, returning to positive. It’s a consistent mathematical rule that preserves the properties of arithmetic.
When do students learn integer multiplication rules?
Multiplication and division of integers with sign rules are introduced in 7th grade math as part of a unit on rational numbers and integer operations.
Which textbook covers rules for multiplying and dividing signed numbers?
Saxon Math, Course 2 covers the rules for multiplying and dividing positive and negative numbers.