Fill up grids such that $\dfrac{\square}{\square \square}+\dfrac{\square}{\square \square} +\dfrac{\square}{\square\square}=1$

In the following grid, fill up the numbers from 1 to 9 (without repetition) such that their sum is $1$.

$\dfrac{\square}{\square \square}+\dfrac{\square}{\square \square} +\dfrac{\square}{\square\square}=1$

Solution provided by Mark, another contributor of this blog:

I would begin with:

$\displaystyle \frac{9}{12}$

since this is the largest addend possible. This leaves $\displaystyle \frac{1}{4}$.

Observing that:

$\displaystyle \frac{1}{4}=\frac{17}{68}=\frac{2\cdot5+7}{68}= \frac{5}{34}+\frac{7}{68}$

We now have:

$\displaystyle \frac{9}{12}+\frac{5}{34}+\frac{7}{68}=1$