Question 69927
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: {{{(+8)/(+2) = +4}}} but {{{(+8)/(-2) = -4}}} and {{{(-8)/(+2) = -4}}} but 
{{{(-8)/(-2) = +4}}}

Hope this helps you to get a grasp of the basic rules.  The rest involves lots of practice
until they become automatic to you.