Question

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

Answer 1

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.

Answer 2

There are infinitly many  ways can we write a fraction that has a numerator of 2 as sum of fraction.

Lets assume we have the fraction

$\rm \dfrac{2}{d}$

We will pick any pairs of integers a & b where b ≠ 0.

Then,

$\rm 2b-ad$ is an integer Therefore, $\rm \dfrac {2b - ad}{bd}$is a fraction.

Consider the fractions,

$\dfrac{a}{b} \& \rm \dfrac {2b - ad}{bd}$

Then their sum will be :-

$\dfrac{a}{b} + \rm \dfrac {2b - ad}{bd}=\dfrac{ad}{bd}+\dfrac{2b - ad}{bd}=\dfrac{2b}{bd}=\dfrac{2}{d}- as \;\rm reqired$

Therefore,there are infinitely many possible solutions.

Learn more about Fractions here : https://brainly.com/question/1301963