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\(\frac{2}{3}.....\frac{{13}}{{12}} - \frac{5}{{12}}\) \(\frac{1}{5} + \frac{6}{5}.....\frac{{29}}{{20}} - \frac{9}{{20}}\)

\(\frac{4}{9}.....\frac{{11}}{{27}} + \frac{{13}}{{27}}\) \(\frac{{11}}{6} - \frac{7}{6}.....\frac{3}{5} + \frac{7}{{30}}\)

\(\frac{2}{3} = \frac{{13}}{{12}} - \frac{5}{{12}}\)

Giải thích:

\(\frac{{13}}{{12}} - \frac{5}{{12}} = \frac{{13 - 5}}{{12}} = \frac{8}{{12}} = \frac{2}{3}\)

\(\frac{1}{5} + \frac{6}{5} > \frac{{29}}{{20}} - \frac{9}{{20}}\)

Giải thích:

\(\frac{1}{5} + \frac{6}{5} = \frac{{1 + 6}}{5} = \frac{7}{5}\)

\(\frac{{29}}{{20}} - \frac{9}{{20}} = \frac{{29 - 9}}{{20}} = \frac{{20}}{{20}} = 1\)

Ta có: \(\frac{7}{5} > 1\) nên \(\frac{1}{5} + \frac{6}{5} > \frac{{29}}{{20}} - \frac{9}{{20}}\)

\(\frac{4}{9} < \frac{{11}}{{27}} + \frac{{13}}{{27}}\)

Giải thích:

\(\frac{{11}}{{27}} + \frac{{13}}{{27}} = \frac{{11 + 13}}{{27}} = \frac{{24}}{{27}}\)

\(\frac{4}{9} = \frac{{4 \times 3}}{{9 \times 3}} = \frac{{12}}{{27}}\)

Ta có: \(\frac{{12}}{{27}} < \frac{{24}}{{27}}\) nên \(\frac{4}{9} < \frac{{11}}{{27}} + \frac{{13}}{{27}}\)

\(\frac{{11}}{6} - \frac{7}{6} < \frac{3}{5} + \frac{7}{{30}}\)

Giải thích:

\(\frac{{11}}{6} - \frac{7}{6} = \frac{{11 - 7}}{6} = \frac{4}{6}\)

\(\frac{3}{5} + \frac{7}{{30}} = \frac{{18}}{{30}} + \frac{7}{{30}} = \frac{{18 + 7}}{{30}} = \frac{{25}}{{30}} = \frac{5}{6}\)

Ta có: \(\frac{4}{6} < \frac{5}{6}\) nên \(\frac{{11}}{6} - \frac{7}{6} < \frac{3}{5} + \frac{7}{{30}}\)