Is this more than the mistake of thinking multiplication is always done before division? I’ve also found students will do the math fact that they know in this situation rather than following the rule.

I would ask them if they are reading right to left or left to right.

This strikes me as a compelling conversation-starter about the commutative property. Why are (8 x 10) and (10 x 8) the same but (10/8) and (8/10) not the same? And so on.

Also the left-right thing.

I would, out of embarrassment, avoid mentioning to the student that I’ve never seen anything like “x÷y·z” outside of a low-level math textbook. Nor would I mention that no one in their right mind would write this when they mean “(x/y)z”. In fact, on a couple of occasions in more advanced math courses I have seen related expressions like “2/xy,” which invariably, and quite sensibly, is taken to mean “2/(xy).”

If I could swallow my pride, I would apologize to the student for subjecting them to the whole thing.

## 4 replies on “Order of Operations”

Is this more than the mistake of thinking multiplication is always done before division? I’ve also found students will do the math fact that they know in this situation rather than following the rule.

I would ask them if they are reading right to left or left to right.

This strikes me as a compelling conversation-starter about the commutative property. Why are (8 x 10) and (10 x 8) the same but (10/8) and (8/10) not the same? And so on.

Also the left-right thing.

I would, out of embarrassment, avoid mentioning to the student that I’ve never seen anything like “x÷y·z” outside of a low-level math textbook. Nor would I mention that no one in their right mind would write this when they mean “(x/y)z”. In fact, on a couple of occasions in more advanced math courses I have seen related expressions like “2/xy,” which invariably, and quite sensibly, is taken to mean “2/(xy).”

If I could swallow my pride, I would apologize to the student for subjecting them to the whole thing.