How many different ways can you write a fraction that has a numerator of 2 as sum of fraction

There are very many ways to do it ...

Let's say we have the fraction 2/9.

We can split this one fraction into two by modifying the numerator, like so: 2/9 = 1/9 + 1/9

This works because since both fractions have a numerator of 9, you can easily add the numerators to give 2, and that will give 2/9 in return. However, you can't separate the denominators.

2/9 is NOT equal to 2/6 + 2/3

2/9 = 1/9 + 1/9

2/9 = 0.5/9 + 1.5/9 (which simplifies to 1/18 + 3/18, also giving 2/9)

2/9 = 0.5/9 + 0.5/9 + 0.5/9 + 0.5/9 = 1/18 + 1/18 + 1/18 + 1/18

I basically split it up into more and more fractions that add up to give 2/9. So, in short, there are infinitely many ways to do it.