Question 69927: I need to know the rules for signed number arithmetic ie: when adding like signs..., unlike..., subtraction, multiplication, division... Thank you!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Addition
(1) When adding two numbers having the same signs, add the numbers and prefix the answer
with the common sign.
Examples:
(+3) + (+6) = +9 and
(-4) + (-2) = -6
(2) When adding two numbers of unlike signs, subtract the smaller number from the larger number,
and give the answer the sign of the larger number. Examples: (+9) + (-6) = +3 and
(-9) + (+6) = -3
Next:
Subtraction: Change the sign of the quantity being subtracted. Then follow the rule for addition.
Examples:
(+5) - (+3) =?? Keep the +5 but change the +3 to -3. Then follow addition rule (2) signs by
subtracting 3 from 5
and prefixing the answer 2 with the same sign as the bigger number, that is the sign of
the 5 which is +. Therefore, the answer is + 2
Another example. (+5) - (-9) =? Change the sign of the number being subtracted and
follow the rules of addition. When you change the sign the -9 becomes + 9 which has the
same sign as the +5. Therefore, follow addition rule (1). Add the two numbers to get 14
and add the common sign which is +. The answer is +14.
Another example. (-9) - (-5). Change the sign of the -5 so it becomes +5 and add it to
-9. Use addition rule 2 because the two numbers (+5 and -9) have different signs.
Subtract the two numbers (9-5) and prefix the sign of the larger number (9 which has a
minus sign). The answer is -4.
Another example: (-8) - (+6) = ? Change the sign of the +6 so that it becomes -6. Then
add the -8 to the -6 by following addition rule 1. Since the numbers have the same sign, add
the numbers (8+6) to get 14 and prefix the common sign of the two which is the negative sign. The answer is -14.
Multiplication.
(1) Multiply the two numbers. If they both have the same sign, the answer will be positive.
Examples: (+4) * (+5) = +20 and (-4)* (5) = +20. [That's correct, both answers are + 20
because in both examples the signs of the numbers being multiplied are the same ... in
the first example they are both + and in the second case they are both -.]
(2) Multiply the two numbers. If they have different signs, the answer will be minus.
Examples: (+4) * (-5) = -20 and (-4) * (+5) = -20
Division.
The same general idea as multiplication, except this time you divide the two numbers and
use the rule that if both the numbers have the same sign the answer is +, but if the two
numbers have opposite signs the answer will be -.
Example:  but  and  but
Hope this helps you to get a grasp of the basic rules. The rest involves lots of practice
until they become automatic to you.
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