Division is a fascinating lie: Why I can’t divide

The Basics: Left-to-Right thinking

First, let’s start with the easy. Addition is easy. 1 + 1 = 2. Our brains are making the calculation in a left-to-right!left-to-right thinking is not a real thing that I’m aware of. I am just using this terminology to represent a mode of thinking movement, as in our thought process is “one plus one is two” – it matches the direction of the equation.

Subtraction is also easy. 2 - 1 = 1. Our brains are still thinking in a left-to-right “two minus one is one” direction.

Multiplication is easy. 3 X 4 = 12. Once again, left-to-right thought process “three fours is twelve”.

Now I understand that not everyone will solve these problems in the same way. Perhaps your personal thought process for the above multiplication example is “four threes is twelve” instead of “three fours is twelve” because you think that multiplying with the larger number first is easier for you. And that’s fine because ultimately, you are using the same formula. X multiplied by Y is the exact same answer as Y multiplied by X after all.

The Problem With Dividing

Division is hard. 4 ÷ 2 = 2. Looks simple enough, but how do you phrase that as a left-to-right process like with the others? What is your actual thought process, because here is where I honestly don’t know if there is something broken with me, I actually am stupid, or if this is the way everyone thinks.

I know that “four divided by two is two”, but the reason I know it is because it’s such a simple question that I have the answer memorized. I instantly say “two!” like a parrot. But let’s ignore the “memory” cheat for now and actually think about the way you’d solve this problem if you didn’t already know the answer.

“Four divided by two” isn’t even something that makes sense to me, so I have to change the equation to make more sense. So I change the equation to “what is half of four?”. In this example, the word “half” represents the number two in the equation, and four is the number being divided. I’ve done more than simply reorganize the equation, I’ve changed my mode of thinking to make an impossible question digestible. Even though 4 ÷ 2 = 2 is not an algebraic equation, I’ve rearranged it in a very similar fashion. Now let’s try a more complex equation, one where we can’t simplify it to “what is half of X”.

22 ÷ 4 = 5.5. My question to everyone reading this article, is when you solve that equation in your head, are you actually using division, or are you using algebra to solve it? Are you converting the division into addition and multiplication to solve? Here is my thought process to solve it.

1. twenty-two divided by four? I don’t know how to divide 🙁
2. So… what multiplied by four equals twenty-two? (Y x 4 = 22)
3. Five and a half times four is twenty-two! I smart!