Joe Doe (joe_doe_zero) wrote in 0_arithmetic,
Joe Doe
joe_doe_zero
0_arithmetic

Connections Between Addition and Subtraction

Addition and subtraction are almost totally linked. Let's take three numbers in which one is the sum of the other two: 3, 5, and 8

3 + 5 = 8

5 + 3 = 8
8 = 5 + 3
8 = 3 + 5

Now let's do it with subtraction.

8 - 5 = 3
8 - 3 = 5
5 = 8 - 3
5 = 8 - 5

Ignoring the fact that 5 + 3 = 8 and 8 = 5 + 3 are the same thing, let's only focus on the addition and subtraction. Let's take three more numbers: 4, 2, and 6. We can construct four equations.

4 + 2 = 6
2 + 4 = 6
6 - 2 = 4
6 - 4 = 2

Let sum be represented by an "S".

General pattern:
A + B = S
B + A = S
S - B = A
S - A = B

Using the Adding Chart and what we just learned we can construct an entire system of adding and subtracting numbers. (Doing so would be an exercise in tedium so please don't do so unless you need a hand workout.)

You also should have noticed that

A + 0 = A
0 + A = A
A - 0 = A
A - A = 0

Addition is commutative while subtraction is not commutative. That is

A + B is equal to B + A
A - B is NOT equal to B - A

If A and B are equal then A - B = B - A but the statement is true only for that particular case. In order for an equation or a statement to be held as being true in mathematics, it must hold true for every case and not just specific cases.
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