What are the rules for adding and subtracting negative numbers?

A negative sign and a negative sign next to each other is a positive sign ex..

-14 - -3
= -14 + 3
= -11

a negative sign and a positive sign next to each other is a positive sign ex..

-14 + -3
= -14 - 3
= -17

the bigger a negative number the smaller it is
the bigger a positive number the larger it is
which supports the rule if you are subtracting the
number will become smaller and if you are adding
the number will become larger