History of Fractions: The Timeline

What does the word fraction mean to you? A fraction represents a part of a whole or, more generally, any number of equal parts. In real life, when we cut a piece of apple from the whole of it, then the portion is a fraction of the apple.

Fractions in Math represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing. For example, 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator. On the basis of the numerator and the denominator, they are categorized as proper fractions, improper fractions, and mixed fractions.

On the basis of groups, they are categorized as like fractions, unlike fractions, and equivalent fractions. Fractions play an important part in our daily lives. There are many examples of fractions you will come across in real life.. For example, break a bar of chocolate into two parts, then each part of the broken chocolate will represent a fraction.

A basic concept in modern math, fractions, might seem intimidating to the child during the initial stages of learning. Games or other activities seem to help enrich the learning experience. 

The invention of fractions: who invented and when?

Decimal fractions had already been introduced by the Flemish mathematician Simon Stevin in 1586. Simon Stevin (1548–1620), sometimes called Stevens, was a Flemish mathematician, scientist, and music theorist.

Although he did not invent decimal fractions and his notation was rather unwieldy, he established their use in day-to-day mathematics. He declared that the universal introduction of decimal coinage, measures, and weights would be only a question of time.

History of fractions infographic

Fractions: A brief history

  • The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. The Egyptians used Egyptian fractions until c1000 BC. About 4000 years ago, Egyptians divided with fractions using slightly different methods. The word fraction actually comes from the Latin word “fractio” which means to break. The Arabs were the ones to add the “fraction line” between the numerator and denominator. The huge disadvantage of the Egyptian system for representing fractions is that it is very difficult to do any calculations. To try to overcome this, the Egyptians made lots of tables so they could look up answers to problems.
  • c530 BC- The Greeks used unit fractions and continued fractions. Followers of the Greek philosopher Pythagoras (c. 530 BC) discovered that the square root of two could not be expressed as a fraction of integers.
  • c AD 500 -A modern expression of fractions known as bhinnarasi seems to have originated in India and is seen in the work of Aryabhatta (c. AD 500), Brahmagupta (c. 628), and Bhaskara (c. 1150). The fractions are denoted by placing the numerators amsa over the denominators cheda, but without a bar between them.
  • 1548- 1620-The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation,  by the Flemish mathematician Simon Stevin.

Fractions And Various Cultures

The Babylonians had one of the oldest written records of fractions and decimals, dating from around 2000 BC. Our current number system uses base10 the Babylonian number system was in base 60.

The Egyptians also developed fractions, and while they worked in base10, they only had unit fractions, in which the numerator is always one.

Around 300 BCE the Greeks were writing fractions using the alphabet to represent numbers. The number 2 was written as β, and the number 5 was denoted with ε. In the Greek system the denominator was written with two ticks (“) written after it. For non-unit fractions, the numerator was written with one tick (‘) after it. So the unit fraction 1/ 5 was written as 5″ or ε “

Ancient Romans used only written words to represent fractions. Most of them were based on a Roman weight system. Around 30 BC the Chinese were adding, multiplying, and subtracting fractions. Around 500 BC Hindu culture was using fractions very much like the present day; the number system they used developed into the one we use today, including a  zero. Like the Chinese, the numerator was placed over the denominator and there was no line to separate them.

The Arabs adopted this number system. Around 1200 CE they added the line that separates the numerator from the denominator. In 1202CE Fibonacci introduced Italy to fractions and the Hindu Arabic number system in his book The Book of Calculation, based in part on his studies with Arabs in Northern Africa. The Hindu-Arabic number system then spread to other European countries. Simon Stevin is also credited with bringing fractions and decimals to Europe in his 1585 booklet called The Art of Tenths. 

Fractions and the modern world

The definition of fractions has almost remained the same through the ages. It still denotes a part of a whole. 

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection. 

A fraction is a quotient of numbers, the quantity obtained when the numerator is divided by the denominator. For example, 34 represents three divided by four.

In the modern world of math fractions are denoted also by the:

  1. Decimal Representation

In this format, the fraction is represented as a decimal number. For Example, The fraction 3/4 can be shown as a decimal by dividing the numerator (3) by the denominator (4). 3/4/ = 0.75.Thus, in decimal representation, 3/4 is written as 0.75.

2) Percentage Representation
The present-day math has fractions being depicted in percentage form too. For example: In this representation, a fraction is multiplied by 100 to convert it into a percentage. If we want to represent as a percentage, we should multiply 3/4 by 100. 3/4 x 100 = 0.75 x 100 = 75. Thus, we can represent 3/4 as 75%.

3) On number lines
Fractions are sometimes depicted on a number line too. Between two whole numbers, values lie in the form of fractions. For example, ½ between whole numbers 1 and 2.

Summing up,

We saw how fractions have evolved throughout the ages, and in their present form, it is widely used in our everyday life. We use fractions to split objects, bills, medical prescriptions, and even to read the time. 

The applications of fractions in everyday life are endless; they are of great importance and profoundly impact everything around us. Fractions might not be a very easy concept for the child to understand and the educator may use additional resources like games and activities to familiarise the child with it. 

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