a) $\dfrac{1}{12}-(-\dfrac{1}{6}-\dfrac{1}{4})$

$=\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{4}$

$=\dfrac{1}{12}+\dfrac{2}{12}+\dfrac{3}{12}$

$=\dfrac{1}{2}$

b) $\dfrac{3}{7}+(\dfrac{-5}{2}+(\dfrac{-3}{5})$

$=\dfrac{30}{70}+\dfrac{-175}{70}+\dfrac{-42}{70}$

$=\dfrac{-187}{70}$

c) $\dfrac{4}{5}+\dfrac{2}{7}-\dfrac{7}{10}$

$=\dfrac{56}{70}+\dfrac{20}{70}-\dfrac{49}{70}$

$=\dfrac{3}{10}$

d) $\dfrac{2}{5}+(\dfrac{-4}{3})+(\dfrac{-1}{2})$

$=\dfrac{12}{30}-\dfrac{40}{30}-\dfrac{15}{30}$

$=\dfrac{-43}{30}$

e) $\dfrac{1}{24}-[\dfrac{1}{4}-(\dfrac{1}{2}-\dfrac{7}{8})]$

$=\dfrac{1}{24}-\dfrac{1}{4}+\dfrac{1}{2}-\dfrac{7}{8}$

$=\dfrac{1}{24}-\dfrac{6}{24}+\dfrac{12}{24}-\dfrac{21}{24}$

$=-\dfrac{7}{12}$

f) $(\dfrac{5}{7}-\dfrac{7}{5}-[\dfrac{1}{2}-(-\dfrac{2}{7}-\dfrac{1}{10})]$

$=\dfrac{5}{7}-\dfrac{7}{5}-\dfrac{1}{2}-\dfrac{2}{7}-\dfrac{1}{10}$

$=(\dfrac{5}{7}-\dfrac{2}{7})+(-\dfrac{7}{5}-\dfrac{1}{10})-\dfrac{1}{2}$

$=\dfrac{3}{7}-\dfrac{3}{2}-\dfrac{1}{2}$

$=\dfrac{3}{7}-\dfrac{14}{7}$

$=-\dfrac{11}{7}$

Đáp án: a ) $\frac{1}{2}$ 

             b ) $\frac{-187}{70}$ 

             c ) $\frac{27}{70}$             

             d ) $\frac{-43}{30}$ 

             e ) $\frac{-7}{12}$

              f ) $\frac{-11}{7}$ 

Giải thích các bước giải:

Bài 4 : 

 a ) $\frac{1}{12}$ - ( $\frac{-1}{6}$ - $\frac{1}{4}$ )

= $\frac{1}{12}$ + $\frac{1}{6}$ + $\frac{1}{4}$ 

= $\frac{1}{12}$ + $\frac{2}{12}$ + $\frac{3}{12}$ 

= $\frac{6}{12}$ 

= $\frac{1}{2}$ 

b ) $\frac{3}{7}$ + ( $\frac{-5}{2}$ ) + ( $\frac{-3}{5}$ )

= $\frac{30}{70}$ + ( $\frac{-175}{70}$ ) + ( $\frac{-42}{70}$ )

= $\frac{-187}{70}$ 

c ) $\frac{4}{5}$ + $\frac{2}{7}$ - $\frac{7}{10}$ 

= $\frac{56}{70}$ + $\frac{20}{70}$ - $\frac{49}{70}$ 

= $\frac{27}{70}$ 

d ) $\frac{2}{5}$ + ( $\frac{-4}{3}$ ) + ( $\frac{-1}{2}$ )

= $\frac{12}{30}$ + ( $\frac{-40}{30}$ ) + ( $\frac{-15}{30}$ )

= $\frac{-43}{30}$ 

e ) -$\frac{1}{24}$ - [ $\frac{1}{4}$ - ( $\frac{1}{2}$ - $\frac{7}{8}$ ) ]

= -$\frac{1}{24}$ - [ $\frac{6}{24}$ - ( $\frac{12}{24}$ - $\frac{21}{24}$ ) ]

= -$\frac{1}{24}$ - ( $\frac{6}{24}$ - $\frac{-9}{24}$ )

= -$\frac{1}{24}$ - $\frac{15}{24}$

= $\frac{-14}{24}$

= $\frac{-7}{12}$

f ) ( $\frac{5}{7}$ - $\frac{7}{5}$ ) - [ $\frac{1}{2}$ - ( - $\frac{2}{7}$ - $\frac{1}{10}$ ) ]

= ( $\frac{50}{70}$ - $\frac{98}{70}$ ) - [ $\frac{35}{70}$ - ( -$\frac{20}{70}$ - $\frac{7}{70}$ ) ]

= $\frac{-48}{70}$ - ( $\frac{35}{70}$ - $\frac{-27}{70}$ )

= $\frac{-48}{70}$ - $\frac{62}{70}$

= $\frac{-110}{70}$

= $\frac{-11}{7}$