How would you work out -2-3?

Here, we want to subtract a number, 3, from a negative number, -2. Intuitively, this will give us an even smaller negative number than -2, namely a negative number that is smaller than -2 by 3:

-2-3 = -(2+3) = -5

A fun way to think about this is to imagine that an individual, say James, takes a loan of £2 from a bank (a loan he must payback to the bank). This means James owes the bank £2, or has a total bank balance of £-2. Let's now say James decides to take another bank loan out (a loan he must also payback to the bank), this time a loan of £3. What is James' total bank balance now?

Well, after the first loan, James' total bank balance was £-2. Following the second loan, James now owes the bank even more than he did after the first loan, namely £3 more. James now owes the bank 2 + 3 = £5, and thus has a total bank balance of £-5.