Tính (1/4-1/4+1/9/1/9):(2/3+7/15/2/5-1/6)

Bài 1: Tính

\(\text{1)}\) \(\dfrac{5}{8}.\dfrac{7}{30}-\dfrac{5}{2}.\dfrac{1}{8}\)

\(=\dfrac{5}{8}.\dfrac{7}{30}-\dfrac{5}{8}.\dfrac{1}{2}\)

\(=\dfrac{5}{8}.\left(\dfrac{7}{30}-\dfrac{1}{2}\right)\)

\(=\dfrac{5}{8}.\dfrac{-4}{15}\)

\(=\dfrac{-1}{6}\)

\(\text{2)}\) \(\dfrac{21}{10}.\dfrac{3}{4}-\dfrac{21}{10}-\dfrac{3}{4}\)

\(=\dfrac{63}{40}-\dfrac{21}{10}-\dfrac{3}{4}\)

\(=\dfrac{-21}{40}-\dfrac{3}{4}\)

\(=\dfrac{-51}{40}\)

\(\text{3)}\) \(\dfrac{-4}{11}:\dfrac{-6}{11}\)

\(=\dfrac{-4}{11}.\dfrac{11}{-6}\)

\(=\dfrac{4}{6}\)

\(\text{4)}\) \(\dfrac{2}{7}.\dfrac{14}{3}-1\)

\(=\dfrac{4}{3}-1\)

\(=\dfrac{1}{3}\)

\(\text{5)}\) \(\dfrac{4}{7}:\left(\dfrac{1}{5}.\dfrac{4}{7}\right)\)

\(=\dfrac{4}{7}:\dfrac{1}{5}:\dfrac{4}{7}\)

\(=1:\dfrac{1}{5}\)

\(=5\)

\(\text{6)}\) \(\dfrac{12}{7}.\dfrac{7}{4}+\dfrac{35}{11}:\dfrac{245}{121}\)

\(=3+\dfrac{35}{11}.\dfrac{121}{245}\)

\(=3+\dfrac{11}{7}\)

\(=3\dfrac{11}{7}=\dfrac{32}{7}\)

\(\text{7)}\) \(\left(\dfrac{4}{3}+\dfrac{8}{3}\right).\left(\dfrac{7}{4}-\dfrac{6}{4}\right):\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\left(\dfrac{7}{4}-\dfrac{6}{4}\right):\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\dfrac{1}{4}:\left(\dfrac{6}{5}+\dfrac{12}{5}+\dfrac{1}{5}\right)\)

\(=4.\dfrac{1}{4}:\dfrac{19}{5}\)

\(=1:\dfrac{19}{5}\)

\(=\dfrac{5}{19}\)

\(\text{8)}\) \(\left(\dfrac{1}{4}-\dfrac{1}{4}+\dfrac{\dfrac{1}{9}}{\dfrac{1}{9}}\right):\left(\dfrac{2}{3}+\dfrac{\dfrac{7}{15}}{\dfrac{2}{5}}-\dfrac{1}{6}\right)\)

\(=\left(0+1\right):\left(\dfrac{2}{3}+\dfrac{7}{15}:\dfrac{2}{5}-\dfrac{1}{6}\right)\)

\(=1:\left(\dfrac{2}{3}+\dfrac{7}{6}-\dfrac{1}{6}\right)\)

\(=1:\left(\dfrac{2}{3}+1\right)\)

\(=1:\dfrac{5}{3}\)

\(=\dfrac{3}{5}\)
\(\text{9)}\)

\(\left[\left(\dfrac{2}{193}-\dfrac{3}{389}\right).\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left[\dfrac{199}{75077}.\dfrac{193}{17}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\left[\dfrac{199}{6613}+\dfrac{33}{34}\right]:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\left(\dfrac{7}{1931}-\dfrac{11}{3862}\right).\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\dfrac{3}{3862}.\dfrac{1931}{25}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\left[\dfrac{3}{50}+\dfrac{9}{2}\right]\)

\(=\dfrac{13235}{13226}:\dfrac{114}{25}\)

\(=\dfrac{330875}{1507764}\)