You may know your numerators from your denominators, your equivalent fractions from your improper ones, but here are some lesser known facts about these lovely mathematical creatures.
The word Fraction comes from the Latin word fractio which means ‘to break’.
The line that separates the numerator and the denominator is called a vinculum, which is also the word used to describe ‘a connecting band of tissue, such as that attaching a flexor tendon to the bone of a finger or toe’. A fact literally at your fingertips.
You can write the fractions in a single list. Here’s how to do it with all the positive fractions:
Some numbers cannot be expressed as a fraction. π, √2 and the golden ratio are examples. They are called ‘irrational’.
The decimal expansion of a fraction either ends or keeps repeating. For example, 1/4 = 0.25 and 1/7 = 0.142857142857142857… and this goes on forever and ever. The decimal expansion of an irrational number goes on forever but never repeats!
The ancient Greek mathematician Pythagoras (you know the one – long beard, loved triangles) didn’t believe irrational numbers could exist. For him and his ‘brotherhood’, the universe was ruled by numbers. Fractions are nice and orderly. The idea that a decimal expansion can go on forever without repeating was blasphemy. Legend has it that when one of Pythagoras’ disciples discovered that √2 can’t be written as a fraction, the brotherhood drowned him to bury the horrific truth. Fractions really can be fatal.
Those ‘irrationals’ may seem a rare breed but here’s a particularly stunning fact: if you dropped a pin randomly onto the number line, it would almost certainly land on an irrational. It’s those lovely fractions that are rare in comparison!
The ancient Egyptians only ever used unit fractions – that is, fractions of the form 1/n. They never conceived of 2/5 as a fraction, for example, and would instead write it as ½ + ⅙. They did all their calculations (which usually involved splitting up sacks of grains and such things) with unit fractions. It was tough going.