There’s an article at the NRICH website https://nrich.maths.org/2515 which gives you some of the history. The Ancient Egyptians (going back about 3800 years) had a complicated system based on reciprocals, so instead of writing, say, 3/5 they would write it as 1/2 + 1/10. The Babylonians (going back a little longer) used a system in which everything was based on 60-ths. In fact, that’s the reason we still divide time up in that way, 1 minute = 1/60 of an hour, 1 second = 1/60 of a minute. Try expressing 3/5, 1/2 and 1/10 all in terms of something/60 to check what I said about 3/5 being equal to 1/2 + 1/10 !

There are two key things to know about fractions. The first is that they are inspired by ratios and ratios lie at the heart of what we mean by an abstract number, whether it be a whole number or a fraction or an irrational number. The second is that multiplying fractions is easier than adding them.

Ratios certainly go back to the Babylonians if not further. You can find then recorded on Cuniform tablets. The word rational comes from ratios and fractions are what are called rational numbers. There are other types of fraction such as the squre root of two which cant be expressed as ratios. My favourite use of fractions was discovered by Pythagoras who found a deep and wonderful link between fractions and music which led on to the invention of the scale.

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Petercommented on :There are two key things to know about fractions. The first is that they are inspired by ratios and ratios lie at the heart of what we mean by an abstract number, whether it be a whole number or a fraction or an irrational number. The second is that multiplying fractions is easier than adding them.

chrisbuddcommented on :Ratios certainly go back to the Babylonians if not further. You can find then recorded on Cuniform tablets. The word rational comes from ratios and fractions are what are called rational numbers. There are other types of fraction such as the squre root of two which cant be expressed as ratios. My favourite use of fractions was discovered by Pythagoras who found a deep and wonderful link between fractions and music which led on to the invention of the scale.