Vulgar Fractions

Pick up any dictionary and you will find ‘Vulgar’ defined along the lines of:

1. Lacking sophistication or good taste; unrefined
2. indecent; obscene; lewd

… and I’ve often wondered what the poor old fraction has done to deserve such a reputation.

I have visions of unruly fractions, burping and belching and generally terrorising the more gentle and sophisticated numbers.  I have an image of a gang of fractions, probably with a top heavy fraction like ¹⁴⁄₅ as the gang leader, nipping behind the bike shed for an illicit smoke.  I picture some mutton-chopped Victorian mathematician so incensed by the decadent form of these fractions that he describes them as “vulgar little numbers”.

But, alas, the story of the vulgar fraction is much less colourful.  The vulgar in this context is:

• common

and our vulgar fractions are nothing more than common fractions – fractions whose top number* and bottom number* are both integers (whole numbers.)

Although the average schoolboy (or girl) may not agree, fractions are actually pretty useful things and actually make maths a whole lot easier – when we encounter the delights of (harder) algebra, using fractions makes life much, much more simple than dealing with decimals.  So even if they are little vulgar and swear and curse a little, you’ve got to love vulgar fractions.

A Maths Teacher

*I much prefer to use the words “top number” and “bottom number” than numerator and denominator – why confuse things further with fancy words that are easily forgotten.