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Comment by mrgoldenbrown | Hacker News Reader

1 ambiguous notation, 3 different interpretations. The Casios both have reasonable interpretations, but the iPhone should probably give some kind of warning that it is about to ignore entire numbers.

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I don't think it's ambiguous in the least. Sure, if I were programming I would add another set of parentheses and the implied * symbol so that it's crystal clear and more reader friendly, but I would toss any calculator that gave me anything other than 6÷2(1+2)=9. I've never read or heard anywhere that an implied * symbol has higher priority than an explicit one. But if that is a reasonable interpretation, Casio has a responsibility to give consistent results across it's entire calculator line.

How is that ambiguous? PEMDAS and since multiplication and division have the same rank, you go left to right. Pretty clear if the calculators follow the basic order of operations.

All infix notations (without sufficient parentheses) require an agreement (implicit or explicit) among all concerned parties. This is nothing new. The same ambiguity occurs with the unary negation operator, as in -5^2.

While I wouldn't choose it, I don't think it's entirely unreasonable to give the "multiplication by juxtaposition" operator greater precedence than the normal multiplication and division operators.

If you write the expression as a fraction without anything beside it being multiplied, it is ambiguous as to whether (1+2) ought to go above or below the fraction bar. The fact that parentheses/brackets ought to be resolved before anything else complicates things because 6/2 * 3 could reasonably be interpreted either way. An unambiguous way to write it would be either as (6/2) * 3 or as 6/(2*3).

BEDMAS is easier to remember

There is an ambiguity if Division comes before Multiplication - although in this case you assume left->right

How is that ambiguous?

Although that was probably rhetorical:

It's ambiguous because most people[1] automatically view implicit multiplication as higher rank than both division and explicit multiplication.

[1]this is a wild guess with no data to back it up

edit: baddox's answer is much better

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