Почему именно есть найбільшим дробом? Срочно! Пожалуйста!

Решите задачу:

$\frac{66}{77}= \frac{66:11}{77:11}= \frac{6}{7}\\\\ \frac{555}{666}= \frac{555:111}{666:111}= \frac{5}{6}\\\\ \frac{4444}{5555}= \frac{4444:1111}{5555:1111}= \frac{4}{5}\\\\ \frac{7}{8};\frac{6}{7}; \frac{5}{6}; \frac{4}{5}\\\\HOD(5;6;7;8)=2*3*4*5*7=840\\\\\frac{7}{8}= \frac{7*105}{840}= \frac{735}{840}\\\\\frac{6}{7}= \frac{6*120}{840}= \frac{720}{840}\\\\\frac{5}{6}= \frac{5*140}{840}= \frac{700}{840}\\\\ \frac{4}{5}= \frac{4*168}{840}= \frac{672}{840}\\\\735\ \textgreater \ 720\ \textgreater \ 700\ \textgreater \ 672$

$\frac{7}{8}\ \textgreater \ \frac{6}{7}\ \textgreater \ \frac{5}{6}\ \textgreater \ \frac{4}{5}$