We have all read and used the concept of fractions in our daily lives. Fractions are signs that are popularly used to denote parts of quantities. An apple that has been sliced into four, becomes 4 quarter-apples and is denoted by the sign 1/4 apple. A gas tank which is half filled is denoted by the sign ‘½’full, and a glass two-thirds full is written as 2/3 glass.
We express fractions in a particular format – we write the number or algebraic term to be divided (i.e., the dividend) at the top and the divisor at the bottom, thus placing the divisor under the dividend, and separating the two numbers by a line.
For example, we express one third as 1/3; one fifth as 1/5; eight thirds as 8/3 and so on.
It is also common to use a slant line instead of a horizontal one to separate the two numbers i.e., the dividend and the divisor. We place the dividend at the left of the slant- line and the divisor at the right of the slant-line.
The fractions 1/3, 1/5 and 8/3 can be depicted as 1/3, 1/5, 8/3.
In this article we will cover the history of the fraction expression and why we write fractions as we now do.
To understand how fractions have developed into the form we recognise, we’ll have to step back in time to discover what the first number systems were like.
In his book ‘First steps in algebra’, Professor Wentworth writes ‘The dividend is called the numerator and the divisor is called the denominator; and the numerator and denominator are called the terms of the fractions’
The notion of fraction has been present since the beginning of civilization and can be traced back to ancient Egypt –one of the five cradles of civilizations. Ancient Egypt was built along the banks of fertile Nile and flourished for 3000 years before Christ before succumbing to the Persian and Roman invaders.
The Egyptians wrote all their fractions using hieroglyphs. They had a writing system that was based on hieroglyphs and they depicted numbers using the same. Numbers were pictorial symbols and they denoted fractions by means of the same
They wrote all their fractions using what we call unit fractions. We may be familiar with unit fractions- they are the fractions that have 1 as their numerator. The Egyptians put a mouth picture (which meant part) above any number to make it a unit fraction.
For example: if five sticks or tally marks were used to represent the number 5, then one fifth could be represented by drawing a mouth symbol over it.
Here is one fifth. This symbol represents one third.
The Egyptian system of writing fractions was fairly cumbersome while performing calculations. Also, they could only be used to depict unit fractions.
The Ancient Romans also made use of fractions, and they used words rather than picture symbols to describe parts of a whole. The Roman system was based on a unit of weight called the ‘as’, and one ‘as’ was made of 12 uncia.
These fractions were centered around twelfths. 1/12 was called uncia; 6/12 or half was called semis i.e., half an ‘as’; and 8/12 was called a bes.
The Roman system of denoting fractions was also clumsy much like the Egyptian and Babylonian counterparts. Calculations could not be performed efficiently.
We now reach the end of our journey through the history of fractions. The format we know and use today comes from one of the most advanced civilizations of its time; one which has been prolific in its literary and mathematical output – The Indian civilization.
In India fractions were written very much like we do now, with one number (the numerator) above another (the denominator), but without a line. For example
It was the Arabs who added the line (sometimes drawn horizontally, sometimes on a slant) which we now use to separate the numerator and denominator:
Thus, in all fractions the lower number is called the denominator, and the number above the line the numerator
Mr. Gary. S. Goldman illustrates the terminology associated with fractions in simple table format as displayed below
The word ‘numerator’ is derived from Latin word numerātor which means counter or numberer (used for a person who counts or numbers). In arithmetic, the numerator denotes the top number in a fraction. The numerator shows us the number of parts that we have.
The word ‘denominator’ has its roots in Medieval Latin and is used in arithmetic to denote the number of equal parts into which a unit is divided. Numerator shows how many parts we have. The denominator denotes the bottom part of a fraction.
Being able to read fractions is as important as being able to write them. In his books Elements of algebra, the great mathematician Leonhard Euler writes- ‘In a fraction, which we read seven thirds, 7 is the numerator and 3 the denominator.’
We must also read: , two thirds; three fourths; three eighths; twelve hundredths;
and one half, &c.’