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a) \[\frac{5}{7} - \frac{3}{{14}}\,\,...\,\,1\]                                  b) \[\frac{6}{5} - \frac{3}{{10}}\,\,...\,\,1\]

c) \[\frac{7}{6} + \frac{5}{3}\,\,...\,\,\frac{1}{2} + \frac{7}{{12}}\]               d) \[\frac{6}{5} + \frac{3}{4}\,\,...\,\,\frac{3}{2} + \frac{{17}}{{20}}\]

e) \[\frac{9}{4} - \frac{1}{5}\,\,...\,\,\frac{3}{{10}} + \frac{{17}}{{20}}\]               f) \[\frac{5}{4} - \frac{1}{2}\,\,...\,\,\frac{2}{3} + \frac{5}{6}\]

a)

\[\frac{5}{7} - \frac{3}{{14}} = \frac{{10}}{{14}} - \frac{3}{{14}} = \frac{7}{{14}} = \frac{1}{2}\]

So sánh: \[\frac{1}{2} < 1\]

Vậy: \[\frac{5}{7} - \frac{3}{{14}}\,\, < \,\,1\]                                

b)

\[\frac{6}{5} - \frac{3}{{10}} = \frac{{12}}{{10}} - \frac{3}{{10}} = \frac{9}{{10}}\]

So sánh: \[\frac{9}{{10}} < 1\]

Vậy: \[\frac{6}{5} - \frac{3}{{10}}\,\, < \,\,1\]

c)

\[\frac{7}{6} + \frac{5}{3}\, = \frac{7}{6} + \frac{{10}}{6} = \frac{{17}}{6} = \frac{{34}}{{12}}\]

\[\frac{1}{2} + \frac{7}{{12}} = \frac{6}{{12}} + \frac{7}{{12}} = \frac{{13}}{{12}}\]

So sánh: \[\frac{{34}}{{12}} > \frac{{13}}{{12}}\]

Vậy: \[\frac{7}{6} + \frac{5}{3}\,\, > \,\,\frac{1}{2} + \frac{7}{{12}}\]              

d)

\[\frac{6}{5} + \frac{3}{4} = \frac{{24}}{{20}} + \frac{{15}}{{20}} = \frac{{39}}{{20}}\]

\[\frac{3}{2} + \frac{{17}}{{20}} = \frac{{30}}{{20}} + \frac{{17}}{{20}} = \frac{{47}}{{20}}\]

So sánh: \[\frac{{39}}{{20}} < \frac{{47}}{{20}}\]

Vậy: \[\frac{6}{5} + \frac{3}{4}\,\, < \,\,\frac{3}{2} + \frac{{17}}{{20}}\]

e)

\[\frac{9}{4} - \frac{1}{5} = \frac{{45}}{{20}} - \frac{4}{{20}} = \frac{{41}}{{20}}\]

\[\frac{3}{{10}} + \frac{{17}}{{20}} = \frac{6}{{20}} + \frac{{17}}{{20}} = \frac{{23}}{{20}}\]

So sánh: \[\frac{{41}}{{20}} > \frac{{23}}{{20}}\]

Vậy: \[\frac{9}{4} - \frac{1}{5}\,\, > \,\,\frac{3}{{10}} + \frac{{17}}{{20}}\]     

f)

\[\frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} = \frac{9}{{12}}\]

\[\frac{2}{3} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{{18}}{{12}}\]

So sánh: \[\frac{9}{{12}} < \frac{{18}}{{12}}\]

Vậy: \[\frac{5}{4} - \frac{1}{2}\,\, < \,\,\frac{2}{3} + \frac{5}{6}\]