Question

Solve $\cfrac{\left\lceil\cfrac{17}{7}-\left\lceil\cfrac{27}{17}\right\rceil\right\rceil}{\left\lceil\cfrac{27}{7}+\left\lceil\cfrac{7\cdot17}{27}\right\rceil\right\rceil}$

Answer 1

$\bf \cfrac{\left\lceil \frac{17}{7}-\left\lceil \frac{27}{17} \right\rceil \right\rceil}{\left\lceil \frac{27}{7}+\left\lceil \frac{7\cdot 17}{27}\right\rceil\right\rceil}\qquad \begin{cases} \left\lceil \frac{27}{17} \right\rceil=\left\lceil 1\frac{10}{17} \right\rceil\\ \qquad\qquad 2\\ \hrulefill\\[0.5em] \left\lceil \frac{7\cdot 17}{27}\right\rceil=\left\lceil 4\frac{11}{27} \right\rceil\\ \qquad \qquad 5 \end{cases}$

$\bf \cfrac{\left\lceil \frac{17}{7}-2 \right\rceil}{\left\lceil \frac{27}{7}+5\right\rceil} \implies \cfrac{\left\lceil \frac{3}{7} \right\rceil}{\left\lceil \frac{62}{7}\right\rceil}\implies \cfrac{1}{\left\lceil 8\frac{6}{7} \right\rceil}\implies \cfrac{1}{9}$