7+(-7)=0 demonstrates the "additive inverse property"
Here's what you need to know:
THE ADDITIVE IDENTITY IS 0
There is just one "do-nothing" number for addition.
This is 0 because when you add 0 to a number it "does
nothing" for you get the same number back, so adding
zero does nothing but give you IDENTICALLY the same
number you started with. Every other number besides 0
does something when you add it, but not 0. So 0 is the
additive identity. (There is also a multiplicative
identity, 1, because it does nothing when you multiply
by it. So 0 is the additive identity, and 1 is the
multiplicative identity. But right now for this problem
we only need to talk about the additive identity.)
THE ADDITIVE INVERSE OF A NUMBER
The additive inverse is the "IDENTITY-MAKER", or in the
case of addition, the additive inverse. Every number has
just one "IDENTITY-MAKER" number under addition. The
number 7 has the IDENTITY MAKER -7 because when you add
the number -7 to the number 7 that makes 0, which is the
IDENTITY for addition. (There are also multiplicative
inverses, which are "ONE-MAKERS". (The multiplicative
inverse of 
is 
because when you multiply
by you get the IDENTITY for multiplication.
But right now for this problem we only need to talk about
the additive identity and the additive inverse).
Question: What do you have to add to 7 to make zero,
(which is the "do-nothing" number for addition?)
Answer: You need to add -7 to make zero, the do-nothing number
for addition.
Therefore -7 is the additive inverse of 7. And 0 is the
additive identity.
So when you add the ADDITIVE INVERSE -7 to 7, you get
the identity 0, or 7+(-7)=0
Another word for "ADDITIVE INVERSE" is "OPPOSITE", formed
by changing the sign.
---
Question: What do you have to multiply 7 by to make one,
(which is the "do-nothing" number for
multiplication?)
Answer: You need to multiply by to make
one, the do-nothing number for addition.
Therefore is the muclipicative inverse of 7. And 1 is the
additive identity.
So when you multiply 7 by the MULTIPLICATIVE INVERSE of 7, you get
the identity 1, or x
Another word for "MULTIPLICATIVE INVERSE" IS "RECIPROCAL",
formed by INVERTing it. (That's where they got the name
"INVERSE" in the first place, but they borrowed it for
addition too.
TMI? Depends on how deep your teacher goes!
Edwin
