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Multiplication of Signed Numbers

The rules for multiplying signed numbers may be formulated from the fact that multiplication serves as a shorthand notation for addition.  For example, 4 x (3), which means "4 times negative 3" is the same as the following:

(3) + (3) + (3) + (3) 12

As (4)
(3) = 12 and the order of factors in multiplication does not matter, it follows that (3)(4) = 12.  Next, we will examine the product of (4)(3).  It has already been seen that (4)(3) = +12 and (4)(3) = 12, which resulted in opposite answers.  Consequently, since 4 times 3 equals 12, the product resulting from 4 times 3 should be the opposite of 12, which is +12. Therefore:

(4)(3) = +12

From the above example, it becomes apparent that:
  • Mulitplication of two numbers of different signs results in a negative number
  • Multiplication of two numbers of the same sign results in a positive number

For multiplication of several signed numbers, it may be shown that:
  • Product will be positive if there is an even number of negative numbers or zero negative numbers
  • Product will be negative if there is an odd number of negative numbers

Example #1:

Evaluate (2)(3)(1)(2)(2)

Solution #1:

Since there are three negative numbers, the product will be negative.  Therefore, performing the multiplication and inserting a negative sign in front of the answer results in:

(2)(3)(1)(2)(2) = 24

Example #2

Is the following product positive or negative?


Solution #2:

Since there are four negative numbers, the product will be positive.  We do not need to multiply the numbers in order to determine the product will be positive.

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