Identity, Grouping, and Signs
Let’s review the mechanics of addition and subtraction, and make sure you understand how
the signs work. Then we’ll proceed to two important rules, called laws, that govern addition
and subtraction. These laws apply not only to the integers, but to all quantities, expressions,
and numbers you’ll encounter in algebra.
The identity element
There is one special integer that you can add to, or subtract from, any integer, and it will never
change the value. That integer is 0. Because adding 0 to a number gives you the same number
again, 0 is called the additive identity element. You can also call it the “subtractive identity
element,” although that term is informal. The word “identity” means that you always get an
output value identical to the input value. For any integer a, the following two statements are
always true:
a+ 0 = 0
and
a− 0 = 0
0
1
2
3
1
2
Start here
Finish here
Move downward
by-5 units
Figure 4-3 Here, we start with
−3 and then subtract
−5, ending up with 2.
When we go negatively
downward, we go
upward by the
equivalent distance.
Identity, Grouping, and Signs 55
