What is Fraction

what is fractionSo, what is fraction?

Suppose you divided a cake into 10 pieces and eat 3 pieces. How much of cake do you eat?

We write it as $$$\frac{{3}}{{10}}$$$.

3 is a number of pieces you eat and 10 is total number of pieces.

This is new situation because 3 is not divisible by 10 $$$\left(3<10\right)$$$.

A fraction is a way to represent division of integer into parts: $$$\frac{{n}}{{m}}$$$ is a fraction where both $$${n}$$$ and $$${m}$$$ are integers.

$$${n}$$$ is called numerator, $$${m}$$$ is called denominator: $$$\frac{{\overbrace{{\color{green}{{{n}}}}}^{{{\color{green}{{\text{numerator}}}}}}}}{{\underbrace{\color{purple}{{{m}}}}_{{{\color{purple}{{\text{denominator}}}}}}}}$$$.

So, fractions arise when one number is not divisible by another: since 19 is not divisible by 3, but we want to divide them, we write $$$\frac{{19}}{{3}}$$$.

When integer is divisible by another integer we can write it as fraction, but it is more natural to write it as integer: $$$\frac{{8}}{{4}}={2}$$$.

Note, that every integer $$${b}$$$ can be represented as a fraction: $$$\color{purple}{{{b}=\frac{{b}}{{1}}}}$$$.

For example, $$${5}=\frac{{5}}{{1}}$$$.

In case when numerator and denominators are equal we obtain one as result: $$$\color{red}{{\frac{{m}}{{m}}={1}}}$$$.

For example, $$$\frac{{10}}{{10}}={1}$$$.

Really, we divide a cake into 10 pieces and eat all 10 pieces - so we eat all cake.