Order of operations: Difference between revisions

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===Mixed division and multiplication===

Similarly, there can be ambiguity in the use of the [[slash (punctuation)#Arithmetic|slash symbol]] / in expressions such as 1/2''xn''.<ref name="Ball_1978"/> If one rewrites this expression as {{nowrap|1 ÷ 2''xn''}} and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:

: {{nowrap|1 ÷ 2 × ''xn'' {{=}} 1 × {{sfrac|1|2}} × ''xn'' {{=}} {{sfrac|1|2}} × ''xn''}}.

With this interpretation {{nowrap|1 ÷ 2''xn''}} is equal to {{nowrap|(1 ÷ 2)''xn''}}.<ref name="Bronstein_1987"/><ref name="Rules"/> However, in some of the academic literature, [[multiplication denoted by juxtaposition]] (also known as [[implied multiplication]]) is interpreted as having higher precedence than division, so that {{nowrap|1 ÷ 2''xn''}} equals {{nowrap|1 ÷ (2''xn'')}}, not {{nowrap|(1 ÷ 2)''xn''}}.

For example, the manuscript submission instructions for the ''[[Physical Review]]'' journals state that multiplication is of higher precedence than division with a slash,<ref name="APS_2012"/> and this is also the convention observed in prominent physics textbooks such as the ''[[Course of Theoretical Physics]]'' by [[Lev Landau|Landau]] and [[Evgeny Lifshitz|Lifshitz]] and the ''[[Feynman Lectures on Physics]]''.<ref group="lower-alpha" name="NB1"/>