Tính bằng cách thuận tiện. (1 điểm)

\(\frac{4}{5}\,\, \times \,\,\frac{6}{7}\,\, + \,\,\frac{4}{5}\,\, \times \,\,\frac{3}{7}\) …………………………………….. …………………………………….. …………………………………….. …………………………………….. …………………………………….. ……………………………………..

\(\frac{5}{9}\,\, + \,\,\frac{5}{7}\,\, + \,\,\frac{9}{7}\,\, + \,\,\frac{4}{9}\) …………………………………….. …………………………………….. …………………………………….. …………………………………….. …………………………………….. ……………………………………..

\(\frac{1}{4}\,\, < \,\frac{7}{{24}}\,\, + \,\,\frac{9}{{24}}\)

Giải thích:

\(\frac{1}{4}\, = \frac{{1 \times 6}}{{4 \times 6}}\,\, = \,\frac{6}{{24}}\)

\(\,\frac{7}{{24}}\,\, + \,\,\frac{9}{{24}} = \frac{{7 + 9}}{{24}} = \frac{{16}}{{24}}\)

So sánh: \(\,\frac{6}{{24}}\,\, < \,\frac{{16}}{{24}}\)

Vậy \(\frac{1}{4}\,\, < \,\frac{7}{{24}}\,\, + \,\,\frac{9}{{24}}\)

\(\frac{8}{{21}}\,\, \times \,\,\frac{{14}}{{16}}\,\,\,..............\,\,1\)

Giải thích:

\(\frac{8}{{21}}\,\, \times \,\,\frac{{14}}{{16}}\, = \frac{{\not 8}}{{3 \times \not 7}} \times \frac{{\not 2 \times \not 7}}{{\not 8 \times \not 2}} = \frac{1}{3}\)

So sánh: phân số có tử số nhỏ hơn mẫu số thì nhỏ hơn 1.

Do đó \(\frac{1}{3}\,\, < \,1\)

Vậy \(\frac{8}{{21}}\,\, \times \frac{{14}}{{16}}\,\, < \,\frac{9}{{24}}\)

\(2\,\,:\,\,\frac{5}{9}\,\,..........\,\,\frac{{36}}{{10}}\)

Giải thích:

\(2\,\,:\,\,\frac{5}{9}\,\, = \frac{2}{1} \times \frac{9}{5} = \frac{{2 \times 9}}{{1 \times 5}} = \frac{{18}}{5}\)

\(\frac{{36}}{{10}} = \frac{{36:2}}{{10:2}} = \frac{{18}}{5}\)

So sánh: \(\,\frac{{18}}{5}\,\, = \frac{{18}}{5}\)

Vậy \(2:\frac{5}{9}\,\, = \frac{{36}}{{10}}\,\)

\(\frac{4}{5}\,\,...........\,\,\frac{{37}}{{40}}\,\, - \,\,\frac{{21}}{{40}}\)

Giải thích:

\(\,\frac{{37}}{{40}}\,\, - \,\,\frac{{21}}{{40}} = \frac{{37 - 21}}{{40}} = \frac{{16}}{{40}}\)

\(\frac{4}{5}\, = \frac{{4 \times 8}}{{5 \times 8}}\, = \,\frac{{32}}{{40}}\)

So sánh: \(\,\frac{{16}}{{40}}\,\, < \frac{{32}}{{40}}\)

Vậy \(\frac{4}{5}\,\, < \frac{{37}}{{40}}\, - \frac{{21}}{{40}}\)