Multiplication with negative numbers is the same as normal multiplication with these added rules:

\(Negative \times Negative = Positive\)

\(Positive \times Negative = Negative\)

\(Negative \times Positive = Negative\)

The same is true for division as well.

### Examples:

Negative × Negative = Positive

\(-3 × -2 = 6\)

\(-10 ÷ -5 = 2\)

Positive × Negative = Negative

\(3 × -2 = -6\)

\(10 ÷ -5 = -2\)

Negative × Positive = Negative

\(-3 × 2 = -6\)

\(-10 ÷ 5 = -2\)

Multiplication and Division with Negative Numbers

Video Source (02:53 mins) | Transcript

If you want more understanding regarding why these rules are true, the first two videos in the additional resources will explain.

## Additional Resources

- Khan Academy: Why a Negative Times a Negative Makes Sense (06:12 mins, Transcript)
- Khan Academy: Why a Negative Times a Negative is a Positive (05:46 mins, Transcript)
- Khan Academy: Multiplying Positive & Negative Numbers (02:53 mins, Transcript)
- Khan Academy: Dividing Positive & Negative Numbers (04:51 mins, Transcript)

### Practice Problems

**If a positive number is multiplied by a negative number, what can we say about the result?**(Solution- The result will always be positive.
- The result will always be negative.
- The result will be negative if the negative value is bigger than the positive value.
- There is not enough information to draw a conclusion about the result.

**If a negative number is divided by a negative number, what can we say about the result?**(Solution- The result will always be positive.
- The result will always be negative.
- The result will be greater than -1 and less than 1.
- There is not enough information to draw a conclusion about the result.

**Evaluate the following expression:**

3. \(8 × (-9) = ?\) (

Solution

4. \((-15) × 7 = ?\) (

Video Solution

5. \((-45) × (-7) = ?\) (

Solution

6. \(15 ÷ (-3) = ?\) (

Solution

7. \((-63) ÷ (7) = ?\) (

Solution

8. \((-81) ÷ (-9) = ?\) (

Video Solution

## Need More Help?

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