# What is Fraction

So, 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.