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a) \(1\frac{3}{19}+\frac{8}{21}-\frac{3}{19}+0.5+\frac{13}{21}\)
\(=\left(1\frac{3}{19}-\frac{3}{19}\right)+\left(\frac{8}{21}+\frac{13}{21}\right)+0.5\)
\(=1+1+0.5=2.5\)
b) \(\left(-\frac{3}{4}+\frac{2}{7}\right):\frac{3}{7}+\left(\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)
\(=\left(\frac{-3}{4}+\frac{2}{7}+\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)
\(=0:\frac{3}{7}=0\)
\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right).\)
\(=5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+\frac{73}{35}-\frac{5}{6}-8-\frac{2}{7}+\frac{1}{18}\)
\(=\left(5-2-8\right)+\left(\frac{1}{5}+\frac{73}{35}-\frac{2}{7}\right)+\left(-\frac{2}{9}-\frac{5}{6}+\frac{1}{18}\right)+\frac{1}{23}\)
\(=-5+\left(\frac{7}{35}+\frac{73}{35}-\frac{10}{35}\right)+\left(-\frac{4}{18}-\frac{15}{18}+\frac{1}{18}\right)+\frac{1}{23}\)
\(=-5+\frac{70}{35}+\frac{-18}{18}+\frac{1}{23}\)
\(=-5+2+\left(-1\right)+\frac{1}{23}\)
\(=-4+\frac{1}{23}=-\frac{91}{23}\)
Tính nhanh nếu có thể:
\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right)\)
\(=\)\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-\frac{73}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right)\)
\(=\)\(5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+\frac{73}{35}-\frac{5}{6}-8-\frac{2}{7}+\frac{1}{18}\)
\(=\)\(\left(5-2-8\right)+\left(\frac{1}{5}+\frac{73}{35}-\frac{2}{7}\right)+\left(\frac{2}{9}-\frac{5}{6}+\frac{1}{18}\right)+\frac{1}{23}\)
\(=\)\(\left(-5\right)+\left(\frac{7}{35}+\frac{73}{35}-\frac{10}{35}\right)+\left(\frac{4}{18}-\frac{15}{18}+\frac{1}{18}\right)+\frac{1}{23}\)
\(=\)\(\left(-5\right)+2+-\frac{5}{9}+\frac{1}{23}\)
\(=\)\(\left(-3\right)+-\frac{5}{9}+\frac{1}{23}\)
\(=\)\(-\frac{727}{207}\)
a) \(\frac{-1}{24}-\left[\frac{1}{4}-\left(\frac{1}{2}-\frac{7}{8}\right)\right]\)
= \(\frac{-1}{24}-\left[\frac{6}{24}-\left(\frac{12}{24}-\frac{21}{24}\right)\right]\)
= \(\frac{-1}{24}-\left[\frac{6}{24}-\frac{-9}{24}\right]\)
= \(\frac{-1}{24}-\frac{15}{24}\)
= \(\frac{-16}{24}\) = \(\frac{-2}{3}\)
b) \(\left(\frac{5}{7}-\frac{7}{5}\right)-\left[\frac{1}{2}-\left(-\frac{2}{7}-\frac{1}{10}\right)\right]\)
= \(\left(\frac{50}{70}-\frac{98}{70}\right)-\left[\frac{35}{70}-\left(-\frac{20}{70}-\frac{7}{70}\right)\right]\)
= \(\frac{-48}{70}-\left[\frac{35}{70}-\left(-\frac{20}{70}-\frac{7}{70}\right)\right]\)
= \(\frac{-48}{70}-\left[\frac{35}{70}-\frac{-27}{70}\right]\)
= \(\frac{-48}{70}-\frac{62}{70}\)
= \(\frac{-110}{70}=\frac{-11}{7}\)