Question

Сравните дроби с 2/47 и 4/89; 4/33 и 12/69; 12/13 и 13/12; 24/7 и 27/9 постарайтесь побыстрее )

Answer 1

$\frac{2}{47} ... \frac{4}{89} \\ \\ \frac{2}{47} = \frac{4}{47*2} = \frac{4}{94} \\ \\ \frac{4}{94} \ \textless \ \frac{4}{89}$ 
следовательно $\frac{2}{47} \ \textless \ \frac{4}{89}$

$\frac{4}{33} ... \frac{12}{69} \\ \\ \frac{4}{33} = \frac{12}{33*3} = \frac{12}{99} \\ \\ \frac{12}{99} \ \textless \ \frac{12}{69}$
следовательно $\frac{4}{33} \ \textless \ \frac{12}{69}$

$\frac{12}{13} ... \frac{13}{12} \\ \\ \frac{12}{13} = \frac{12*12}{156} = \frac{144}{156} \\ \\ \frac{13}{12} = \frac{13*13}{156} = \frac{169}{156} \\ \\ \frac{144}{156} \ \textless \ \frac{169}{156}$
следовательно $\frac{12}{13} \ \textless \ \frac{13}{12}$

$\frac{24}{7} ... \frac{27}{9} \\ \\ \frac{24}{7} = \frac{24*9}{63} = \frac{216}{63} \\ \\ \frac{27}{9} = \frac{27*7}{63} = \frac{189}{63} \\ \\ \frac{216}{63} \ \textgreater \ \frac{189}{63}$
следовательно $\frac{24}{7} \ \textgreater \ \frac{27}{9}$