Fractions - A Pinch of History

A fraction represents a part of a whole. In the form $\frac{a}{b}$, '$a$' is the numerator and '$b$' is the denominator.

Ancient Egyptians primarily used 'Unit Fractions', which are fractions with a numerator of $1$, such as $\frac{1}{2}$, $\frac{1}{3}$, or $\frac{1}{10}$.

In ancient India, mathematicians like Brahmagupta wrote fractions as one number above another (e.g., $\begin{smallmatrix} 3 \\ 4 \end{smallmatrix}$) but without the horizontal bar (vinculum). The bar was later introduced by Arabs.

A Proper Fraction is where the numerator is less than the denominator ($a < b$), representing a value less than $1$, like $\frac{3}{5}$.

An Improper Fraction has a numerator greater than or equal to the denominator ($a \ge b$), like $\frac{7}{4}$.

A Mixed Fraction consists of a whole number and a proper fraction, such as $2 \frac{1}{3}$.

Equivalent Fractions are obtained by multiplying or dividing the numerator and the denominator by the same non-zero number. For example, $\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.