Fractions

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Fractions make many of us moan and groan, wish for nice simple whole numbers, or reach for our calulators to convert to decimals. In fact, most arithmetical writers of the past in Europe postponed the discussion of fractions until the end of their books. They thought most students couldn't expect to reach fractions. We need fractions to measure things like length, weight, and time.

Fractions were used by the Babylonians as far back as 2000 B.C. These were much like our decimal fractions of today. They were written in place-value form, but the unwritten denominators were successive powers of sixty, and there was nothing to correspond to a decimal point.

The first systematic approach to unit fractions, those whose numerator is one, can be found in the Rhind papyrus (a collection of mathematical examples copied by the scribe Ahmes around 1650 B.C. on an Egyptian papyrus). If a fraction was not a unit fraction, then it was represented by the sum of two or more unit fractions, with a space instead of a plus sign. For example, 5/6 was written 1/3 [+] 1/2. Unit fractions were written using a fraction symbol with the appropriate denominator directly beneath. Some fractions, like 2/3 and 1/2, had special symbols.

The Greeks represented unit fractions by writing the denominator with a single or double accent. Hence 1/5 would be 5" (but with the Greek symbol, epsilon, for 5). The Greeks did not just use unit fractions. Other fractions were often indicated by placing a single accent on the numerator and writing the deminator twice, each time with a double accent. Thus 2/5 would be 2' 5" 5". Sometimes the denominator was written in the position of today's exponent. Other times the denominator was written directly on top of the numerator, the opposite of how they are written today, but no bar was used between them.

Romans had a special name for each fraction, and usually only used a denominator of twelve. Fractions were used quite often in Rome for monetary and meteorological computations. In fact, fractional computations were the main part of arithmetical teaching in Roman schools.

The Hindus seem to have developed our current method of writing fractions. Fractions were written with the numerator above the denominator without the dividing bar in the Bakhshali manuscript (c. sixth century ?). Integers were even written as fractions by placing a one in the denominator. The Arabs introduced the bar in different forms around 1000,
various fraction bar forms
but they did not always use it.

The Arabic word for fraction, alkasr, comes from the verb meaning "to break." The Latin forms fractio and minutm ruptus are given as "broken numbers."