Signed Numbers

Signed Numbers

Positive numbers are the result of any measurement -- in length, weight, volume, loudness, etc. Negative numbers are the result of any measuring process in which a certain zero point is reached. For example, a temperature of -10 is 10 degree units below zero. We can record positive and negative numbers easily by setting up a number line.

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-10 -8 -6 -4 -2 0 +2 +4 +6 +8 +10

Signed numbers are positive (+4 or 4) or negative (-4) and have two parts: magnitude (4) and direction (+ or - ). All numbers to the right of zero on the number line are positive; all numbers to the left are negative. Operations with signed numbers can be represented by movement on the number line.

There are several different approaches to calculations using positive and negative numbers. Two, rather different approaches are presented below. Try them both and use the one that works best for you.

METHOD #1

Addition & Subtraction

STEP 1: Always simplify your work by removing as many "extra" signs as possible. Replace any number in the form - (-n) with +n or simply n. Replace any number in the form of +(-n) or - (+n) with simply -n.

(-8) = +8 or 8 +(-2) or - (+2) = -2

STEP 2: If two numbers that you're combining (adding or subtracting) have the same sign, find the sum and apply that same sign to your answer.

+8 + 2 = +10 = 10
- 8 + (-2) = - 8 - 2 = -10
- 8 - (+2) = - 8 - 2 = -10

STEP 3: If the two numbers you're combining have different signs, find the difference between the two numbers and apply the sign of the larger number to your answer.

+8 - 2 = +6 or 6

- 8 - (-2) = - 8 + 2 = - 6

Multiplication and Division

RULE: For any two numbers being multiplied or divided with the same sign, the result will always be positive. For any two numbers that you're multiplying or dividing with opposite signs, the result will always be negative.

4 × 2 = +8 (+) × (+) = (+)
-4 × 2 = -8 (-) × (-) = (-)
-4 × -2 = 8 (-) × (-) = (+)
(2)(-3)(4)(-1) = (-6) x (-4) = +24 or 24

Any odd number of negative terms, multiplied or divided, will result in a negative answer. Any even number of negative terms, multiplied or divided, will result in a positive answer.

METHOD #2

Addition

Ask yourself if the signs of the numbers you're adding are alike or different. If signs are alike, add the digits, keep the same sign in your answer. If the signs are different, subtract the smaller digit from the larger digit, use the sign of the larger for your answer.

Subtraction

Rewrite all subtraction problems as equivalent addition problems by adding the opposite, e.g., a - b = a + (-b) This phrase says "positive a minus positive b equals positive a plus negative b." Then follow the rules for addition of signed numbers.

-3 - 5 = -3 + (-5) = -8
8 - (-3) = 8 + 3 = 11
-12 - (-5) = -12 + 5 = -7

Multiplication & Division

First, ask yourself if the signs of the numbers are alike? If so, your answer will be positive. In multiplication and division of signed numbers, like signs = a positive result. Are the signs different? If so, your answer will be negative. Different signs = a negative result.

Reference:
http://lac.smccme.edu/signed_numbers.htm