History of fractions

Before studying this lesson about history of fractions, I recomment that you become familiar with egyptian numeration system

An extensive treatment of fractions appeared around 1600 B.C. in the Rhind Papyrus, which contained the work of Egyptians mathematicians.

The Egyptians did not expresse fractions as ratios such as 2:5 or 2/5.

They expressed ratios in unit fractions. What are unit fractions?

A unit fraction is a fraction that has a numerator of 1 and the denominator is a positive integer

For example, 1/2, 1/5, and 1/5 are unit fractions. The Egyptians would then write 2/5 as 1/3 + 1/15

Of course, the Egyptians used their symbols to represent this fraction.
1/3 + 1/15 would be represented as shown below:

Egyptian fractions of one-third plus one-fifteenth

Notice that all we care about is the man's feet. Feet pointing toward the direction of writing means add. Otherwise, it means subtract

In this case, it is pointing towards the direction of writing

Notice also that there is a shape that looks like an open mouth (the ellipse). It refers to a fraction

The way we represent fractions today probably came from the Hindus.

Around A.D. 630, Brahmagupta would write the fraction two-fourths without the bar as

Hindus fraction of two-fourths

Then, the Arabs came up with the bar. However, the notation 2/4 was mostly used due to typesetting constraints

The notion of numerator and denominator came from Latin writers. Up to the sixteenth century, the common denominator was found by multiplying the denominators

In the seventh century, the least common multiple was used extensively when adding and subtracting fractions

Multiplication of fractions as we know it today stayed the same for centuries

Division of fractions however, was carried out in a way that is completely different to the way we perform this operation today

The first way was to look for a common denominator

4/2 ÷ 2/3 = 12/6 ÷ 4/6 = 12/4 = 3

The first way was to perform cross-multiplication

4 × 3 = 12 and 2 × 2 = 4, so 12/4 = 3

This concludes our brief history of fractions

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