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Here's a trivial one. Given the inline algebra expression (2a + b) / 3c imply that the 3c is a quantity, and that the order of operations should be equivalent to (2a + b) / (3c) ? Or should it be understood as ((2a + b) / 3) c ?

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  • $\begingroup$ My instinct: The first. Not making this an "answer" since I don't have a source. $\endgroup$ – dbx Jan 31 '19 at 17:01
  • $\begingroup$ It's whatever one you like, there is no rule to it. In general avoid such expressions, it doesn't really cost you to use braces or to actually use $\frac{2a+b}{3c}$ $\endgroup$ – kingW3 Jan 31 '19 at 17:09
  • $\begingroup$ Of intrest Do values attached to integers have implicit parentheses? and What is 48÷2(9+3)? $\endgroup$ – kingW3 Jan 31 '19 at 17:17
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While I'm not aware of any source that specifically says this, I would say that pretty much everyone would (just by "eye") read it the first way, with $3c$ treated as a unit. If you intend the second interpretation and you write it this way, then there is a very high probability you will be misunderstood, so it is not recommended.

Some sources consider expressions like $z/xy$ to be ambiguous. That same link says that "some of the Texas Instruments calculators follow two conventions, according to whether multiplication is indicated by juxtaposition or a symbol", which is actually the convention I would prefer (in case of juxtaposition, the multiplication is treated as a unit).

A computer program will be more strict and quite possibly interpret it in the second way, especially if it does not distinguish between implicit multiplication versus multiplication indicated by a symbol, but if you are writing for human readers the first interpretation should prevail.

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