You may recall that multiplying numbers is repetitive addition. It means you are adding a number to itself a number of times. Here is the strategy for performing multiplication for positive and negative numbers.
Multiply the two numbers as you would if they were both positive numbers, except the result is negative.
If you examine the left table below, you will see that the number five is being multiplied by various numbers. The number six is first, then five and finally two in a decreasing order. You will notice the result is decreasing, too. In fact, the result is decreasing by five.
5 x 6 = 30
5 x 5 = 25
5 x 4 = 20
5 x 3 = 15
5 x 2 = 10
5 x 1 = 5
5 x 0 = 0
5 x -1 = -5
5 x -2 = -10
5 x -3 = -15
If we continue this multiplication pattern, you will see a justification for the strategy in the green box above. The result keeps lowering by five until negative numbers are achieved. This justifies the fact that a positive number times a negative number is the same as dealing with two positive numbers, except the result is negative.
Let us examine two quick examples that use this fact.
Example #1: 4 x -3
4 x -3 = -12. This is true because 4 x 3 = 12, but a positive times a negative is a negative. Therefore, 4 x -3 = -12.
Example #2: 6 x -7
Since 6 x 7 = 42, 6 x -7 = -42 because a positive times a negative is a negative.
To help you learn other skills with Integers, use the links below.