Question

1. Tính nhanh

\(\frac{1}{2}\)x \(\frac{2}{3}\)x \(\frac{3}{4}\)x\(\frac{4}{5}\)x \(\frac{5}{6}\)x\(\frac{6}{7}\)x \(\frac{6}{7}\)x \(\frac{7}{8}\)x\(\frac{8}{9}\text{ }\)x \(\frac{9}{10}\)

\(\frac{1}{2}\): \(\frac{3}{2}\): \(\frac{5}{4}\)\(\frac{6}{5}\):\(\frac{7}{6}\):\(\frac{8}{7}\)

Answer 1

\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)

\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)

\(=\frac{1}{24}\)

Answer 2

\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)

\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)

\(=\frac{1}{10}\)

Answer 3

\(\frac{1.2.3.4.5.6.6.7.8.9}{2.3.4.5.6.7.7.8.9.10}=\frac{1.6}{7.10}=\frac{3}{35}\)

Answer 4

\(\frac{1}{2}.\frac{2}{3}.\frac{4}{5}.\frac{5}{6}.\frac{6}{7}.\frac{7}{8}=\frac{1.2.4.5.6.7}{2.3.5.6.7.8}=\frac{1.4}{3.8}=\frac{1}{6}\)