The Rules
A number with no sign is considered to be POSITIVE. For example:
3 = +3
8 + 2 = ( + 8) + ( + 2)
8  3 = ( + 8)  ( + 3)
Sometimes you find the '+' sign in front of a positive number, other times it is omitted, especially in higher level classes. In the first time I recommend you to use it (rewrite the problem with '+' signs), but as you proceed you should try to solve the problems without it. I show you examples here for both ways.
NOTE: Signed numbers should always be in parantheses. As a general rule, we can never write two signes next to each other:
Instead of 5 + 3 you should write: 5 + ( 3 ). Or instead of
4 + +2 you should write: 4 + (+ 2 ).
First ask yourself: Do the numbers have the same sign?
Based on your answer choose rule #1 or rule #2.
Rule 1. If the nubers have same signs
Examples:
(+5)+(+4)  (3)+(7) 
2 + 4 = (+2)+(+4) 
Add the UNSIGNED numbers 
5 + 4 = 9  3 + 7 = 10 
2 + 4 = 6 
Include the original sign
to your answer 
+ 9   10 
+ 6 
Rule 2. If the nubers have different signs
Examples:
(5)+(+4)  (+3)+(7) 
2 + 4 = (2)+(+4) 
Subtract the UNSIGNED numbers: 
5  4 = 1  7  3 = 4 
4  2 = 2 
Include the original sign of the LARGER number to your answer: 
 1   4 
+ 2 
Turn your subtraction into addition as follows:
Examples:
(6)(+4)  (+4)(7) 
3  4 = (3)(+4) 
Change to addition: 
(6) + (4)  (+4)+(+7) 
(3)+(4) 
Follow the rules of addition: 
 10  + 11 
 7 
Believe or not, the hard part is over. Multiplication and division are far easier than addition and subtraction.
They even have the same rules:
Examples:
(6)
(+4)  (+4)
(7) 
(12)
(4) 
Ignore the sign and do the operation: 
6
4 = 24  4
7 = 28 
12 4 = 3 
Follow the rule of signes: 
 24   28 
+ 3 
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