# order of operations division

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?

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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
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

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.