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Hướng dẫn giải

a)

\[\frac{3}{4}:\frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{{3 \times 5}}{{4 \times 2}} = \frac{{15}}{8}\]

\[\frac{1}{8}:\frac{1}{7} = \frac{1}{8} \times \frac{7}{1} = \frac{{1 \times 7}}{{8 \times 1}} = \frac{7}{8}\]

Vì \(\frac{{15}}{8} > \frac{7}{8}\)nên \[\frac{3}{4}:\frac{2}{5} > \frac{1}{8}:\frac{1}{7}\]

b)

\[\frac{5}{8}:\frac{5}{4} = \frac{5}{8} \times \frac{4}{5} = \frac{{\bcancel{5} \times \bcancel{4}}}{{\bcancel{4} \times 2 \times \bcancel{5}}} = \frac{1}{2}\]

\[\frac{9}{{12}}:\frac{3}{4} = \frac{9}{{12}} \times \frac{4}{3} = \frac{{\bcancel{3} \times \bcancel{3} \times \bcancel{4}}}{{\bcancel{4} \times \bcancel{3} \times \bcancel{3}}} = 1\]

Vì \(\frac{1}{2} < \)1 nên \[\frac{5}{8}:\frac{5}{4} < \frac{9}{{12}}:\frac{3}{4}\]