Some math concepts and terms have multiple definitions or interpretations; learn why you should pay attention to them.
Math is known for precision. Answers to problems are usually black-and-white—right-or-wrong—right? It’s true that math is usually extremely precise, but ambiguity does occasionally creep in. Just like English, the language of math isn’t always exactly…well…exact. In this article, we’ll talk about two specific examples of this ambiguity—the first is interesting but ultimately benign, whereas the second could definitely get you into a bit of trouble.
The Mathematics of Money
We’ve talked a lot about positive and negative integers, and how to add and subtract them by visualizing stepping along the number line. Though this interpretation is helpful, it’s not unique. At the end of the last article I asked you to contemplate how financial transactions like deposits, withdrawals, and debts can be used to help you understand what you’re doing when adding and subtracting positive and negative numbers. How does it work? Here’s the gist.
Imagine you open an account with an initial balance of $0. Depositing money into the account is identical to adding a positive number to the balance, and withdrawing money is identical to adding a negative value (or equivalently, to subtracting that value). For example, when you physically deposit $20 into your new account, you’ve mathematically added positive 20. And if you then physically withdraw $5, you’ve mathematically added -5 (or subtracted 5).
Math and Calculating Debt
Okay, how about debts? Let’s say the entirety of your life’s savings is contained in the $100 you have in your pocket, and you borrow $20 from a friend. Does that mean your net worth is now $120? No, remember you borrowed that $20 and you have to pay it back—so you have a $20 debt. As we talked about in the article on negative integers, this debt can be represented by a negative number—in this case -$20. So your net worth is $100 + $20 + (-$20) = $100 + $20 - $20 = $100. In other words, your net worth hasn’t changed.
Now, what happens if your friend is amazingly generous and tells you not to worry about paying back the loan? Well, since debts are included in our calculation of your net worth by adding negative numbers, it follows that forgiven debts are included by subtracting negative numbers. So, if your friend in our example forgave the $20 debt you owed, your net worth would be expressed as $100 + $20 + (-$20) - (-$20) = $100 + $20 - $20 + $20 = $120. Your net worth increased since your friend gave you $20!