Multiplying and Dividing Integers
Develop and apply the sign rules for multiplication and division of integers. Understand why a negative times a negative is positive through patterns and properties, and extend to multi-step problems.
A lesson of Pre-Algebra, in Number Sense & Operations, about 10 minutes.
By the end of this lesson, you will be able to multiply and divide integers using sign rules.
The Sign Rules
Same signs → Positive product/quotient
Different signs → Negative product/quotient
| $\times$ or $\div$ | Signs | Result |
|---|---|---|
| $6 \times 7$ | + and + | +42 |
| $(-6)(-7)$ | − and − | +42 |
| $6 \times (-7)$ | + and − | −42 |
| $(-6) \times 7$ | − and + | −42 |
Multiple Factors
Count the number of negative signs:
- Even count → positive
- Odd count → negative
$(-2)(-3)(-4) = -24$ (3 negatives → odd → negative)
$(-2)(-3)(4) = +24$ (2 negatives → even → positive)
Integer Division
Same sign rules apply.
$\frac{-36}{-6} = 6$ (same signs → positive)
$\frac{-36}{6} = -6$ (different signs → negative)
$\frac{36}{-6} = -6$ (different signs → negative)
Order of Operations Review
$(-3)^2 = (-3)(-3) = 9$ (positive — squaring means 2 negatives)
$-3^2 = -(3^2) = -9$ (the negative is applied AFTER squaring)
Summary
Same signs → positive; different signs → negative.
Multiple negatives: even count → positive; odd count → negative.
$(-3)^2 \neq -3^2$: the first squares −3; the second negates $3^2$.