Nine Digits, the Unit Fractions

Using each of the nine digits $1$ to $9$ exactly once, some in the numerator and the rest in the denominator, write a fraction equal to $\frac12$. Then do the same for $\frac13$, $\frac14$, $\frac15$, $\frac16$, $\frac17$, $\frac18$ and $\frac19$.

Solution

One solution for each, though there are others: $$\begin{aligned} \frac12 &= \frac{6729}{13458}, & \frac13 &= \frac{5832}{17496}, & \frac14 &= \frac{3942}{15768},\\[0.4em] \frac15 &= \frac{2697}{13485}, & \frac16 &= \frac{2943}{17658}, & \frac17 &= \frac{2394}{16758},\\[0.4em] \frac18 &= \frac{3187}{25496}, & \frac19 &= \frac{6381}{57429}. & & \end{aligned}$$ In each, the four-digit numerator times the whole number on the left gives the five-digit denominator, and between numerator and denominator the digits $1$ to $9$ each appear once. For instance $6729 \times 2 = 13458$ and $6381 \times 9 = 57429$.