Additive inverses

If two numbers added together equal zero, they are called additive inverses. For example, (9) + (-9):

The additive inverse of 9 is -9
The additive inverse of -9 is 9 (or +9)

Simplifying the adding of mixed integers

The rules are:

Positive & positive = positive
For example, $5++3=5+3=8$
Negative & negative = positive
For example, $5-3=5+3=9$
Negative & positive = negative
For example, $5-+3=5-3=2$
Positive & negative = negative
For example, $5+-3=5-3=2$

Adding integers

Adding integers is where a set of numbers are added together.

For example, $(+7)+(+4)=7+4=11$ (or +11)

Another example, $(-3)+(-8)=-3 -8=-11$

Another example, $(-1)+(+5)=-1+5=5-1=+4$

Another example, $(+6)+(-4)=6-4=2$ (or +2)

Subtracting integers

Subtracting integers is where numbers are taken away from other numbers.

For example, $(-6)-(-5)=-6+5=-1$

Another example, $6-(-5+3)=6+(+5-3)=6+(2)=8$

The key with subtracting something in brackets, is to convert the minus into a plus, and then inverting the content in the brackets. For example, instead of $-(5-3)$ . to have $+(-5+3)$