How can one make sense out of a negative number?

Question

We know that if you have 3 apples and somebody gives you 4 apples, you then have 7 apples but then if we deal with negative numbers and we have -3 apples and somebody gives us -4 apples, things can get confusing and nonsensical. How can we make sense out of integers like these?

Answer 1

For the example you gave, having -3 apples could be seen as owing someone 3 apples. Any apples that you get when you have a negative "apple balance" or an "apple debt" must go to the person to whom the apples are owed (until you owe no more apples, ie. you have $\geq$ 0 apples).

Gaining an apple when you have a negative apple balance reduces the amount of apples you owe by one (decreases your apple debt). If someone "gives you" a negative amount of apples when you already have a negative apple balance, your apple debt increases by the absolute value of the number of apples you were given. eg. -3 apples + -4 apples = -7 apples

You start with -3 apples, which means you have an apple debt of 3. If you gain 4 apples, you must give 3 of them away because you owe 3 apples. 4 + -3 = 1, so your apple balance is no longer negative.