Basically addition and subtraction is just the same. Subtraction is just addition with negative numbers.
There are several ways to remember operations with signed integers:
First way (common way taught in school):
(I used to tutor a 5th grade student who is having a difficult time with math. This is the technique I thought of that time and I think she mastered solving operations with signed integers.)
There are three rules: (I ask her every time we solve a similar problem if what rule can we apply to solve it)
RULE 1. Addition with same signs:
RULE: When adding two integers with the same sign we just add the "absolute value" (or the numbers disregarding their signs) and copy the sign to the sum.
To make it easier for her to understand, it is like adding normal unsigned integers and the "sign" is just an identifier.
a. -2 **+** -4 = -6
b. 2 **+** 4 = 6
Imagine the plus sign being bold so as to remember that it is an operator. The sum depends on the addends on both sides of the operator. The two addends are independent and the plus sign will merge them depending on their signs.
RULE 2. Addition with different signs:
RULE: If both addends have opposing signs, subtract the "absolute value" of the larger number with the smaller number and copy the sign of the larger number.
a. -7 **+** 3 = -4 (7-3=4 and the sign of the bigger number which is 7 is negative)
b. 7 **+** -3 = 4 (7-3=4 and the sign of the bigger number which is 7 is positive)
RULE 3. Subtraction with same or opposite sign:
RULE: Change the sign of the subtrahend (second operand e.g. negative becomes positive) and proceed to addition (make the minus operation a plus operation.
All rules for addition can be applied here.
To sum up:
ADDITION: a. same sign - normal addition but copy the sign common to
the addends b. opposite sign - normal subtraction of the same number
but copy the sign of the bigger number
SUBTRACTION: -change the sign of the second operand and proceed to
As I stated earlier, addition and subtraction is just the same. It is just addition with integers where one or both of the addends can be negative.
Consider all subtraction as addition and refer below:
a. 3 - 7 (this is basically subtraction at first glance)
Consider it this way
3 + (-7)
there is an imaginary plus sign (addition between 3 and -7)
since 3 and -7 have opposite signs we use RULE 2.
3 - 7 = 3 + (-7) = -4
b. -4 - 8
can be written as
(-4) + (-8)
placing a parenthesis or thinking of the negative sign and the number itself as one entity really helps
-4 - 8 = (-4) + (-8) = - 12
from RULE 1
Hope this helps :)
As you noticed above, I focused on the operation addition since subtraction is based on addition. It is the most fundamental operation. We were taught from school that addition and subtraction is just moving to the right and left in a number line. I think that is the most intuitive way to do simple arithmetic on signed numbers for beginners ;)
Furthermore, I believe that doing Math is more of a gut feeling. You don't have to analyze every time you perform an operation the logic behind things. Plus, it's time consuming. Of course at first you have to but once you get a feel with what you are doing, solving problems will just come naturally. That's why I outlined these simple steps.