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Very dumb question:

What is the order of operations in the following:

PEMDAS a/b+c = a : b + c (where ":" is the division symbol)

7/1+6 or 7:1+6

in the example below is it 1 or 13?

Arturo Magidin
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John
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    Standard order convention would have it be $13$. You would need $7/(1+6)$ or $7\colon(1+6)$ for it to be interpreted as $1$. – Arturo Magidin Jun 29 '12 at 15:42
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    If you are entering things into a computer program, you need to know the order of precedence that it uses. If you are communicating with a human, if in doubt use parentheses. – André Nicolas Jun 29 '12 at 15:47

3 Answers3

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It is better written as $\dfrac{a}{b}+c$ or $(a/b)+c$ to avoid such possible ambiguity, assuming that is what it means (else, $a/(b+c)$ or $\dfrac{a}{b+c}$). I think we can all agree that, for example, $ab+c$ is shorthand for $(ab)+c$ rather than $a(b+c)$, but division with / (or ÷) can add human parsing problems if parentheses are not used. See also Gerry Myerson's answer to a related question.

Community
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Jonas Meyer
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  • Thank you for your reference. As I suspected it is ambiguous. The issue was it's representation: a --- b+c – John Jun 29 '12 at 16:04
  • @John It's not ambiguous. In regards to the linked answer, "There is no Supreme Court for mathematical notation" - there's no need for one, that's what textbooks are for – donaldp Jun 12 '24 at 05:49
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First use PEMDAS and if two operations of same precedence occurs then Standard order convention is to evaluate from left to right.Here, division precedes over addition and hence answer is 13.

Aang
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Ever since the late 19th Century the rule of left associativity has meant that only the first term following a division was in the denominator. Prior to then everything following the division was in the denominator, which meant you could only have 1 division in the whole expression, hence the change

donaldp
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