The main rule to remember with forward slashes is that you rarely need to use them at all. Their main use these days is in URLs: https://www.apostrophes.com.au.
If you need to write a fraction in text, you may need to use a forward slash as the line that divides the numerator and denominator (or the top and bottom numbers of the fraction): 3/4. Their other main use is also mathematical: to represent the division symbol: 3/4 x 100 = 75. (When you think about it, the use of a forward slash in a fraction is the same as its use to mean divided by.)
Forward slashes are also used in accounting (and less often in business) to mean a financial year, rather than a calendar year. For example, here in Australia 2016/17 means from 1 July 2016 to 30 June 2017, while 2016-17 means from 1 January 2016 to 31 December 2017. If you are not working with specialised accounting material, using the forward slash in this shorthand way is probably better avoided, as some people may misunderstand it. There is the further complication that different countries (and even some large corporations) work to different financial years: in the UK, the financial year is from 1 April to 31 March, while in the USA, the federal government’s financial year runs from 1 October to 30 September, but state governments and businesses can pick their own dates.
Some people also use slashes to suggest alternatives: The question he posed was to be/not to be. Unless you are writing a text message or some type of test where you want people to circle the correct answer, avoid this use of slashes. While it makes writing a fraction quicker and simpler for the writer, it means that reading becomes just slightly harder and longer for the reader. And the aim of good writing is to make simple and clear for the reader. The use of and/or is a classic example of something that does not achieve this aim, as it requires the reader to stop and think out the different alternatives. If you really mean and/or, it is much better to write it the alternatives in full for clarity. Compare For breakfast, I could have muesli and/or tea and toast with For breakfast, I could have muesli or tea and toast, or muesli and tea and toast (or For breakfast, I could have muesli or tea and toast or both). Which is easier to understand?
Finally, some people have tried to use s/he as a new pronoun in English to mean she or he. After some thirty years, it still hasn’t caught on, and is probably now unlikely to. We seem to have settled on they as a non–sex specific singular pronoun – but that’s a topic for another week.
And Slash, of course, was a member of Guns N’ Roses
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