# 48÷2(9+3) = ?

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2 or 288? Does the division come before the multiplication?

## Answers and Replies

something tells me the answer they want is 2, but the math says its 288.

Museigen

So is the left to right rule for multiplication and definition a rule? or a convention?

What distinguishes a rule from a convention when there can only be one right way?

Museigen

What I mean is, does it arise from axioms or is it just accepted?

uart

Do a search there was an existing thread on this just a few days ago. Eventually it was locked because it ended up in a lot of pointless arguments.

The general consensus was that it's somewhat ambiguous and that we should all try to avoid potentially ambiguous notation.

The main thing to come out of the discussion is to be aware that some people will give implied (or juxtaposition) multiplication a higher precedence than a $\div$ (divide) symbol. So be aware of this potential ambiguity.

Actually that's not the only place it occurs. The same thing happens with notation like $\sin 2x$ which is usually meant to be interpreted as $\sin(2x)$ rather than $x \sin(2)$. But then with numbers and an explicit "times" symbol we would usually interpret $\sin 30 \, \times \, 10$ as $10 \sin 30$ rather than $\sin 300$.

So there's another common example of implied (or juxtaposition) multiplication altering precedence. This is just something that we have to watch out for. Rearrange you equation to make it non ambiguous or use extra parenthesis if there's no other way.

Last edited:
Borek
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