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 `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 (`3<10`).

A fraction is a way to represent division of integer into parts: `n/m` is a fraction where both `n` and `m` are integers.

`n` is called numerator, `m` is called denominator: `(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 `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: `8/4=2`.

Note, that every integer `b` can be represented as a fraction: `color(purple)(b=b/1)`.

For example, `5=5/1`.

In case when numerator and denominators are equal we obtain one as result: `color(red)(m/m=1)`.

For example, `10/10=1`.

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