Tính

a) \[\frac{3}{4}:\frac{9}{{20}} = \frac{{.....}}{{.....}} \times \frac{{.....}}{{.....}} = \frac{{..... \times .....}}{{..... \times .....}} = \frac{{.....}}{{.....}}\]

\[\frac{7}{6} \times \frac{3}{{14}} = \frac{{..... \times .....}}{{..... \times .....}} = \frac{{.....}}{{.....}}\]

Hướng dẫn giải

Đáp án đúng là: B

\(\frac{7}{5}:\frac{7}{{12}} = \frac{7}{5} \times \frac{{12}}{7} = \frac{{\bcancel{7} \times 12}}{{5 \times \bcancel{7}}} = \frac{{12}}{5}\)

Phân số \[\frac{7}{5}\] gấp phân số \[\frac{7}{{12}}\] là: \(\frac{{12}}{5}\) lần.

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 \[\frac{5}{8}:\frac{5}{4} < \frac{9}{{12}}:\frac{3}{4}\]