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
\(-3 × 2 = -6\)
\(-10 ÷ 5 = -2\)

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

1. If a positive number is multiplied by a negative number, what can we say about the result? (
   Solution

   x

   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

   x

   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.

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