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

Giải thích:

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

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

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: \(\frac{1}{3}\,\, < \,1\)

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

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

Giải thích:

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

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

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

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

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

Giải thích:

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

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

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

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

40 m² 80 dm² = 408 000 cm²

Giải thích:

40 m² 80 dm²

= 40 × 10 000 cm² + 80 × 100 cm²

= 400 000 cm² + 8 000 cm²

= 408 000 cm²

9 050 mm² = 90 cm² 50 mm²

Giải thích:

9 050 mm² = 9 000 mm² + 50 mm²

= \(\frac{{9\,\,000}}{{100}}\) cm² + 50 mm²

= 90 cm² + 50 mm²

6 dm² 35 mm² = 60 035 mm²

Giải thích:

6 dm² 35 mm²

= 6 × 10 000 mm² + 35 mm²

= 60 000 mm² + 35 mm²

= 60 035 mm²

60 900 cm² = 6 m² + 9 dm²

Giải thích:

60 900 cm²

= 60 000 cm² + 900 cm²

= \(\frac{{60\,\,000}}{{10\,\,000}}\) cm² + \(\frac{{900}}{{100}}\) cm²

= 6 m² + 9 dm²