Signed Number Arithmetic
Success in performing operations on real numbers, both positive and negative signed numbers,
depends on the ability to use the rules for signed number arithmetic and at the same time visualize the
operations using the real number line. The rules differ for each operation and must be committed to
memory. Adherence to the rules will guarantee correct results.
The Rules
Multiplication
Multiplication of signed numbers can be accomplished for as little as two numbers and up. The
numbers are multiplied together, as if they were all positive in their sign, and then the number of
negative signs will determine the sign of the final result.
Step 1: Disregard the signs for the moment and multiply the real numbers together and obtain a
numeric answer.
Step 2: Count up the number of negative () signs in the original problem; If the number of
negatives is an even number then your answer is positive. If the number of negatives was an odd
number then your answer is negative.
Example
?
2
1
?
3
5
±
=
30. You see that the problem had 2 (even) negative signs; therefore the final
answer is positive (
+
).
Example
?
1
4
?
3
±
?
1
2
=
?
6. You count 3 (odd) negative signs; therefore the final answer is
negative ().
Division
Division is approached the same way as multiplication.
Step 1: Disregard the signs for the moment and do the division of the real numbers and obtain a
numeric answer.
Step 2: Count up the number of negative () signs in the original problem; If the number of
negatives was an even number then your answer is positive. If the number of negatives was an odd
number then your answer is negative.
Example
?
2
3
?
4
±
?
2
?
3
±
=
4. This fraction had 4 (even) negative signs; therefore the final answer is positive
(
+
).
Example
?
4
5
3
8
?
10
3
?
48
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 Spring '08
 ihcsol
 Real Numbers, Addition, Negative Numbers, Ken Broun, Associate Professor Natural Sciences, Mathematics Tidewater Community College, [email protected]

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