The Rule: How to Multiply Negative Numbers

The result of multiplying negative numbers is given as:

• Negative number times negative number = positive number
• Negative number times positive number = negative number
• Positive number times negative number = negative number

This is because multiplying some number by a negative number flips the sign. So, if a positive number gets multiplied by a negative number, the positive number's sign gets flipped to negative.

Likewise, if a negative number gets multiplied by a negative number, the negative number's sign will get flipped to positive.

Multiplying Negative Numbers Example Problems

Let's go through a couple of example problems together to practice multiplying negative numbers.

Example Problem 1

Solve (-4)(3).

Solution:

1. The negative 4 will flip the sign of the positive 3.
2. (-4)(3) = -12

Example Problem 2

Solve (-10)(-2).

Solution:

1. The negative 10 will flip the sign of the negative 2.
2. (-10)(-2) = 20