How many different way can you write a fraction that has a numerator of 2 as a sum of fractions?

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

Even though it looks like it would because you're adding straight across, it doesn't apply for the denominator. Because if we were to actually add those two fractions together, we would get 1 instead of 2/9.

How many different ways, you ask? It depends. For me, I see infinitely manyways to do this.

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.

the first option is the answer.