Multiplication and Division:
Multiplication and Division with Negative Numbers
Multiplication with negative numbers is the same as normal multiplication with these added rules:
Negative × Negative = Positive
Positive × Negative = Negative
Negative × Positive = Negative
The same is true for division as well.
Examples:
Negative × Negative = Positive
\(-3\cdot (-2)=6\)
\(-10\) ÷ \((-5)=2\)
Positive × Negative = Negative
\(3\cdot (-2)=-6\)
10 ÷ \((-5)=-2\)
Negative × Positive = Negative
\(-3\cdot 2=-6\)
\(-10\) ÷ \(5=-2\)
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
- If a positive number is multiplied by a negative number, what can we say about the result?
- 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?
- 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:
- \(8\cdot (-9)=?\)
- \(-15\cdot 7=?\)
- \(-45\cdot (-7)=?\)
- \(15\) ÷ \((-3)=?\)
- \(-63\) ÷ \(7=?\)
- \(-81\) ÷ \((-9)=?\)