Điền dấu >, <, = thích hợp vào chỗ chấm.

\(\frac{9}{5}\,\, + \,\,\frac{2}{5}\,\,...........\,\,2\)	\(\frac{5}{9}\,\,.........\,\,\frac{1}{2}\,\, + \,\,\frac{2}{3}\)
\(1\,\,.........\,\,\frac{9}{7}\,\, - \,\,\frac{2}{7}\)	\(\frac{7}{9}\,\, \times \,\,1\,\,........\,\,\frac{5}{7}\,\)

\(\frac{9}{5}\,\, + \,\,\frac{2}{5}\, > \,\,2\)

Giải thích:

\(\frac{9}{5}\,\, + \,\,\frac{2}{5}\, = \frac{{9 + 2}}{5} = \frac{{11}}{5}\)

\(2 = \frac{2}{1} = \frac{{2 \times 5}}{{1 \times 5}}\,\, = \,\frac{{10}}{5}\,\)

So sánh: \(\frac{{11}}{5} > \frac{{10}}{5}\)

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

\(\frac{5}{9}\,\, < \,\frac{1}{2}\,\, + \,\,\frac{2}{3}\)

Giải thích:

\(\frac{1}{2} + \frac{2}{3}\,\, = \,\frac{{1 \times 3}}{{2 \times 3}}\, + \frac{{2 \times 2}}{{3 \times 2}} = \frac{1}{6} + \frac{4}{6} = \frac{5}{6}\)

So sánh: hai phân số có cùng tử số, phân số nào có mẫu số lớn hơn thì nhỏ hơn

Vậy: \(\frac{5}{9} < \frac{5}{6}\)

Vậy \(\frac{5}{9}\,\, < \,\frac{1}{2}\,\, + \,\,\frac{2}{3}\)

\(1\,\, = \,\frac{9}{7}\,\, - \,\,\frac{2}{7}\)

\(\frac{9}{7} - \frac{2}{7}\,\, = \,\frac{{9 - 2}}{7}\, = \frac{7}{7} = 1\)

So sánh: 1 = 1

Vậy \(1\,\, = \,\frac{9}{7}\,\, - \,\,\frac{2}{7}\)

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

\(\frac{7}{9}\,\, \times 1\, = \frac{7}{9} = \frac{{7 \times 7}}{{9 \times 7}} = \frac{{49}}{{63}}\)

\(\frac{5}{7} = \frac{{5 \times 9}}{{7 \times 9}}\,\, = \,\frac{{45}}{{63}}\,\)

So sánh: \(\frac{{49}}{{63}} > \frac{{45}}{{63}}\)

Vậy \(\frac{7}{9}\,\, \times \,\,1\,\, > \,\frac{5}{7}\,\)