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 two negative numbers.
Multiply the two numbers as you would if they were both positive numbers.
In the previous sections, you learned how to deal with negative numbers by examinging tables of values, see Positive x Negative. Similarly, if you examine the left table below, you will see that the number -3 is being multiplied by various numbers. The number 6 is first, then 5 and finally 2 in a decreasing order. You will notice the result is increasing! In fact, the result is increasing by three.
-3 x 6 = -18
-3 x 5 = -15
-3 x 4 = -12
-3 x 3 = -9
-3 x 2 = -6
-3 x 1 = -3
-3 x 0 = 0
-3 x -1 = 3
-3 x -2 = 6
-3 x -3 = 9
If we continue this multiplication pattern, you will see a justification for the strategy in the green box above. The result keeps increasing by three until positive numbers are achieved. This justifies the fact that a negative number times a negative number is the same as dealing with two positive numbers.
Using opposites, it is exactly the same as taking an opposite of an opposite of a number. For instance, -(-(7)) = 7. The opposite of the opposite of 7 is 7. In fact, -(-(m)) = m, for all Integers m.
Let us examine two quick examples that use this fact.
Example #1: -7 x -1
-7 x -1 = 7 x 1 = 7. This is true because -7 x -1 = -(-(7 x 1)) = -(-(7)) = 7. Therefore it is not necessary to remember this complicated reason. Simply realize that -7 x -1 = 7 because multiplication with double negatives cancels the negatives.
Example #2: -5 x -3
-5 x -3 = 5 x 3 = 15. The negatives cancel each other.
To help you learn other skills with Integers, use the links below.