Multiplication of Signed Numbers in Mathematics
INTRODUCTION 7.0
To multiply signed numbers, we follow the basic rules of multiplication for positive real numbers. However, negative
numbers introduce another dimension to be considered.
Lecture 7.1: Signed Multiplication
There are four multiplication combinations of positive and negative numbers:
1. A positive number times a positive number
2. A negative number times a positive number
3. A positive number times a negative number
4. A negative number times a negative number
A positive number times a positive number:
This is probably the most used combination of multiplication. Here, we are multiplying two positive numbers by one
another. For example:
2x4=8
2 and 4 are both positive numbers with a result of a positive 8. It may not be explicitly defined as a positive 8,
but it is implied.
A negative number times a positive number:
Whenever we multiply a negative number by a positive number, the result will always be a negative number.
For example:
-2 x 4 = -8
A positive number times a negative number
Whenever we multiply a positive number by a negative number, the result will always be a negative number.
For example:
2 x - 4 = -8
A negative number times a negative number
Whenever we multiply a negative number by a negative number, the result will always be a positive number.
For example:
-2x-4=8
To sum up the rules above, we have the following table:
Now that we have established the four base cases, let's explore a little more. What sign would result in the
following multiplication problem?
(-2)(4)(-10)(-1) = ?
Using the commutative properties of multiplication, we can rearrange the problem to:
(-2)(-1)(-10)(4) = ?
Now we clearly have a Case 4 and a Case 2. Case 4 tells us that a negative times a negative equals a positive,
so 2 x 1 = 2:
2 x (-10)(4) = ?
Case 2 tells us that a negative times a positive is equal to a negative. So, -10 x 4 = - 40:
(2)(- 40) = ?
Finally, we have a case 3: A positive times a negative is equal to a negative.
(2)(- 40) = 80
Therefore, (-2)(4)(-10)(-1) = 80.
Conclusion: none
References: none