Money Owed

A bank balance is a signed number. Money in the account is positive. When you spend more than you have, the account is overdrawn and the balance drops below zero: a balance of -15 means you owe the bank 15 dollars. Deposits add to the balance and purchases subtract from it.

Maya has 30 dollars in her account. She buys a jacket for 45 dollars, then deposits 10. Use a for account: $a = 30-45+10$. Work left to right: 30 - 45 is -15, so the next line is $a = -15+10$, and then $a = -5$. She still owes 5 dollars.

One signed number carries two facts at once: how much, and which side of zero. That is why an overdrawn start is written with its minus sign. An account 20 dollars overdrawn starts at -20, not 20, and the rest of the story is added and subtracted from there.