A problem that hit the Internet in early 2011 is, "What is the value of 48/2(9+3) ?"
Depending on whether one interprets the expression as (48/2)(9+3) or as 48/(2(9+3)) one gets 288 or 2. There is no standard convention as to which of these two ways the expression should be interpreted, so, in fact, 48/2(9+3) is ambiguous. To render it unambiguous, one should write it either as (48/2)(9+3) or 48/(2(9+3)). This applies, in general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).
In contrast, under a standard convention, expressions such as ab+c are unambiguous: that expression means only (ab)+c; and similarly, a+bc means only a+(bc). The convention is that when parentheses are not used to show the contrary, multiplication precedes addition (and subtraction); i.e., in ab+c, one first multiplies out ab, then adds c to the result, while in a+bc, one first multiplies out bc, then adds the result to a. For expressions such as a−b+c, or a+b−c, or a−b−c, there is also a fixed convention, but rather than saying that one of addition and subtraction is always done before the other, it says that when one has a sequence of these two operations, one works from left to right: One starts with a, then adds or subtracts b, and finally adds or subtracts c.
Why is there no fixed convention for interpreting expressions such as a/bc ? I think that one reason is that historically, fractions were written with a horizontal line between the numerator and denominator. When one writes the above expression that way, one either puts bc under the horizontal line, making that whole product the denominator, or one just makes b the denominator and puts c after the fraction. Either way, the meaning is clear from the way the expression is written. The use of the slant in writing fractions is convenient in not creating
no fixed convention aparently kek but
