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Multiplication and Division with Negative Numbers
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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

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

### Practice Problems

1. If a positive number is multiplied by a negative number, what can we say about the result? (
Solution
Solution:
2.
)
1. The result will always be positive.
2. The result will always be negative.
3. The result will be negative if the negative value is bigger than the positive value.
4. There is not enough information to draw a conclusion about the result.
2. If a negative number is divided by a negative number, what can we say about the result? (
Solution
Solution:
1.
)
1. The result will always be positive.
2. The result will always be negative.
3. The result will be greater than -1 and less than 1.
4. There is not enough information to draw a conclusion about the result.
Evaluate the following expression:
3. $$8 × (-9) = ?$$ (
Solution
Solution: $$-72$$
Details:
Notice the pattern as we go down the number line, our answers get more negative. A positive number times a negative will always give a negative answer.

$$8 × 1 = 8$$
$$8 × 0 = 0$$
$$8 × -1 = -8 8 × -2 = -16$$
$$8 × -3 = -24$$
$$8 × -4 = -32$$
$$8 × -5 = -40$$
$$8 × -6 = -48$$
$$8 × -7 = -56$$
$$8 × -8 = -64$$
$$\color{red}8 × -9 = -72$$
)
4. $$(-15) × 7 = ?$$ (
Video Solution
Solution: $$-105$$
Details:

(Video Source | Transcript)
)
5. $$(-45) × (-7) = ?$$ (
Solution
Solution:
315
)
6. $$15 ÷ (-3) = ?$$ (
Solution
Solution: $$-5$$
Details:
Notice the pattern, once we divide by a negative, the answer is the opposite. When 15 is divided by 3 the answer is 5, but when 15 is divided by $$-3$$ the answer is the opposite, $$-5$$.

$$15 ÷ 5 = 3$$
$$15 ÷ 3 = 5$$
$$15 ÷ 1 = 15$$
$$\color{red}15 ÷ -1 = -15$$
$$\color{red}15 ÷ -3 = -5$$
$$\color{red}15 ÷ -5 = -3$$
)
7. $$(-63) ÷ (7) = ?$$ (
Solution
Solution:
$$-9$$
)
8. $$(-81) ÷ (-9) = ?$$ (
Video Solution
Solution: 9
Details:

(Video Source | Transcript)
)

## Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.