# Does an inline algebra expression with multiplication in the dividend imply a quantity?

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 ?

• My instinct: The first. Not making this an "answer" since I don't have a source. – dbx Jan 31 '19 at 17:01
• 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 $\frac{2a+b}{3c}$ – kingW3 Jan 31 '19 at 17:09
• – kingW3 Jan 31 '19 at 17:17

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).