a: \(=5+\dfrac{1}{5}-\dfrac{2}{9}+\dfrac{2}{23}-\dfrac{3}{35}-\dfrac{5}{6}-8-\dfrac{2}{7}+\dfrac{1}{18}\)

\(=-3+\left(-\dfrac{2}{9}-\dfrac{5}{6}+\dfrac{1}{18}\right)+\left(\dfrac{1}{5}+\dfrac{2}{23}-\dfrac{3}{35}-\dfrac{2}{7}\right)\)

\(=-3+\dfrac{-12-45+1}{18}+\dfrac{7-10-3}{35}+\dfrac{2}{23}\)

\(=3-\dfrac{28}{9}+\dfrac{-6}{35}+\dfrac{2}{23}=\dfrac{-1417}{7245}\)

a: \(\left(5+\frac15-\frac29\right)-\left(2-\frac{1}{23}-\frac{3}{35}+\frac56\right)-\left(8+\frac27-\frac{1}{18}\right)\)

\(=5+\frac15-\frac29-2+\frac{1}{23}+\frac{3}{35}-\frac56-8-\frac27+\frac{1}{18}\)

\(=\left(5-2-8\right)+\left(\frac15+\frac{3}{35}-\frac27\right)+\left(-\frac29-\frac56+\frac{1}{18}\right)+\frac{1}{23}\)

\(=\left(-5\right)+\left(\frac{7}{35}+\frac{3}{35}-\frac{10}{35}\right)+\left(-\frac{4}{18}-\frac{15}{18}+\frac{1}{18}\right)+\frac{1}{23}\)

\(=-5+\left(-\frac{18}{18}\right)+\frac{1}{23}=-6+\frac{1}{23}=-\frac{138}{23}+\frac{1}{23}=-\frac{137}{23}\)

c: \(-\frac57-\left(-\frac{5}{67}\right)+\frac{13}{10}+\frac12+\left(-\frac16\right)+1\frac{3}{14}-\left(-\frac25\right)\)

\(=-\frac57+\frac{5}{67}+\frac{13}{10}+\frac12-\frac16+\frac{17}{14}+\frac25\)

\(=\left(-\frac57+\frac{17}{14}+\frac12\right)+\left(\frac{13}{10}+\frac25-\frac16\right)+\frac{5}{67}\)

\(=\left(-\frac{10}{14}+\frac{17}{14}+\frac12\right)+\left(\frac{13}{10}+\frac{4}{10}-\frac16\right)+\frac{5}{67}\)

\(=\left(\frac{7}{14}+\frac12\right)+\left(\frac{17}{10}-\frac16\right)+\frac{5}{67}=1+\frac{5}{67}+\frac{51}{30}-\frac{5}{30}\)

\(=\frac{72}{67}+\frac{46}{30}=\frac{72}{67}+\frac{23}{15}=\frac{2621}{1005}\)

d: \(\frac35:\left(-\frac{1}{15}-\frac16\right)+\frac35:\left(-\frac13-1\frac{1}{15}\right)\)

\(=\frac35:\left(-\frac{2}{30}-\frac{5}{30}\right)+\frac35:\left(-\frac{5}{15}-\frac{16}{15}\right)\)

\(=\frac35:\left(-\frac{7}{30}\right)+\frac35:\left(-\frac{21}{15}\right)\)

\(=\frac35\cdot\frac{-30}{7}+\frac35\cdot\frac{-5}{7}=\frac35\cdot\left(-\frac{30}{7}-\frac57\right)\)

\(=\frac35\cdot\left(-\frac{35}{7}\right)=\frac35\cdot\left(-5\right)=-3\)

\(=5+\dfrac{1}{5}-\dfrac{2}{9}-2+\dfrac{1}{23}+\dfrac{73}{35}-\dfrac{5}{6}-8-\dfrac{2}{7}+\dfrac{1}{18}\)

\(=-5+\left(\dfrac{1}{5}-\dfrac{2}{7}+\dfrac{73}{35}\right)+\left(\dfrac{-2}{9}-\dfrac{5}{6}+\dfrac{1}{18}\right)+\dfrac{1}{23}\)

\(=-5+\dfrac{7-10+73}{35}+\dfrac{-4-15+1}{18}+\dfrac{1}{23}\)

\(=-5+2-1+\dfrac{1}{23}=-4+\dfrac{1}{23}=-\dfrac{91}{23}\)

a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]

= -1/24 - [ 1/4 +3/8 ]

= -1/24 - 5/8

= -2/3.

a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]

= -1/24 - [ 1/4 +3/8 ]

= -1/24 - 5/8

= -2/3.

\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right).\)

\(=5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+\frac{73}{35}-\frac{5}{6}-8-\frac{2}{7}+\frac{1}{18}\)

\(=\left(5-2-8\right)+\left(\frac{1}{5}+\frac{73}{35}-\frac{2}{7}\right)+\left(-\frac{2}{9}-\frac{5}{6}+\frac{1}{18}\right)+\frac{1}{23}\)

\(=-5+\left(\frac{7}{35}+\frac{73}{35}-\frac{10}{35}\right)+\left(-\frac{4}{18}-\frac{15}{18}+\frac{1}{18}\right)+\frac{1}{23}\)

\(=-5+\frac{70}{35}+\frac{-18}{18}+\frac{1}{23}\)

\(=-5+2+\left(-1\right)+\frac{1}{23}\)

\(=-4+\frac{1}{23}=-\frac{91}{23}\)

Tính nhanh nếu có thể:

\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right)\)

\(=\)\(\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-\frac{73}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right)\)

\(=\)\(5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+\frac{73}{35}-\frac{5}{6}-8-\frac{2}{7}+\frac{1}{18}\)

\(=\)\(\left(5-2-8\right)+\left(\frac{1}{5}+\frac{73}{35}-\frac{2}{7}\right)+\left(\frac{2}{9}-\frac{5}{6}+\frac{1}{18}\right)+\frac{1}{23}\)

\(=\)\(\left(-5\right)+\left(\frac{7}{35}+\frac{73}{35}-\frac{10}{35}\right)+\left(\frac{4}{18}-\frac{15}{18}+\frac{1}{18}\right)+\frac{1}{23}\)

\(=\)\(\left(-5\right)+2+-\frac{5}{9}+\frac{1}{23}\)

\(=\)\(\left(-3\right)+-\frac{5}{9}+\frac{1}{23}\)

\(=\)\(-\frac{727}{207}\)