Taking away, another way round

There are adds, and there are take-aways. Can one rule do both?

Yes. Every take-away can be written as an add.

Rule: taking away a number is the same as adding its opposite.

The opposite of 3 is −3. It is the same distance from 0, on the other side.

Taking away 3 walks 3 left. Adding −3 also walks 3 left. So both stop at the same mark.

Here a and b stand for any two numbers. a − b and a + (−b) always stop at the same mark.

The answer to a take-away is the difference. 8 − 3 = 5.

Pick the answer in the lab. Both walks stop on it.