\(\frac{4}{9}\,\, + \,\frac{4}{5}\,\, < \,\,2\)

Giải thích:

\(\frac{4}{9}\,\, + \,\frac{4}{5}\, = \,\frac{{4 \times 5}}{{9 \times 5}} + \frac{{4 \times 9}}{{5 \times 9}} = \frac{{20}}{{45}} + \frac{{36}}{{45}} = \frac{{56}}{{45}}\)

\(\,2 = \frac{2}{1} = \frac{{2 \times 45}}{{1 \times 45}} = \frac{{90}}{{45}}\)

So sánh: \[\frac{{56}}{{45}} < \frac{{90}}{{45}}\]

Vậy \(\frac{4}{9}\,\, + \,\frac{4}{5}\, < 2\)

\(\frac{5}{7}\,\, - \,\,\frac{2}{3}\, < \,\,\frac{5}{6}\)

Giải thích:

\(\frac{5}{7}\,\, - \,\,\frac{2}{3}\,\, = \,\frac{{5 \times 6}}{{7 \times 6}} - \frac{{2 \times 14}}{{3 \times 14}} = \frac{{30}}{{42}} - \frac{{28}}{{42}} = \frac{2}{{42}}\)

\(\frac{5}{6} = \frac{{5 \times 7}}{{6 \times 7}} = \frac{{35}}{{42}}\)

So sánh: \[\frac{2}{{42}} < \frac{{35}}{{42}}\]

Vậy \(\frac{5}{7}\,\, - \,\,\frac{2}{3}\, < \,\frac{5}{6}\)

\(\frac{5}{7}\,\, \times \,\,9\,\, > \,\frac{3}{5}\)

Giải thích:

\(\frac{5}{7}\,\, \times \,\,9\,\, = \frac{5}{7} \times \frac{9}{1} = \frac{{5 \times 9}}{{7 \times 1}} = \frac{{45}}{7}\)

So sánh:

\[\frac{{45}}{7} > 1\] do tử số lớn hơn mẫu số

\[\frac{3}{5} < 1\] do tửi số nhỏ hơn mẫu số

Vậy \(\frac{5}{7}\,\, \times \,\,9\, > \,\,\frac{3}{5}\)

\(\frac{4}{9}\,\,:\,\,\frac{{16}}{{81}}\,\, = \,\frac{9}{4}\)

Giải thích:

\(\frac{4}{9}\,\,:\,\,\frac{{16}}{{81}}\,\, = \,\,\frac{4}{9} \times \frac{{81}}{{16}} = \frac{{\not 4}}{{\not 9}} \times \frac{{\not 9 \times 9}}{{\not 4 \times 4}} = \frac{9}{4}\)

So sánh \(\frac{9}{4}\,\, = \,\,\frac{9}{4}\)

Vậy \(\frac{9}{4}\,\,:\,\,\frac{{16}}{{81}} = \frac{9}{4}\)

Hình vẽ bên có: