Đáp án:

 $4)
a)8\\
b) 5\\
c)-6\\
d)-21\\
e)
\dfrac{-5}{11}\\
f)\dfrac{15}{2}\\
g)\dfrac{-1}{3}\\
h)\dfrac{-80}{9}$

Giải thích các bước giải:

 $4)
a)4\dfrac{1}{3}.\dfrac{4}{9}+13\dfrac{2}{3}.\dfrac{4}{9}
=\dfrac{4}{9}.\left (4\dfrac{1}{3} +13\dfrac{2}{3} \right )\\
=\dfrac{4}{9}.\left (4+13+\dfrac{1}{3} +\dfrac{2}{3} \right )
=\dfrac{4}{9}.\left ( 17+\dfrac{3}{3} \right )
=\dfrac{4}{9}.18
=8\\
b) 5\dfrac{1}{4}.\dfrac{3}{8}+10\dfrac{3}{4}.\dfrac{3}{8}
=\dfrac{3}{8}.\left (5\dfrac{1}{4} +10\dfrac{3}{4} \right )\\
=\dfrac{3}{8}.\left (5+10+\dfrac{1}{4} +\dfrac{3}{4} \right )
=\dfrac{3}{8}.(15+\dfrac{4}{4})
=\dfrac{3}{8}.16
=5\\
c)6\dfrac{1}{5}.\left ( -\dfrac{2}{7} \right )+14\dfrac{4}{5}.\left ( -\dfrac{2}{7} \right )
=\left ( -\dfrac{2}{7} \right ).\left ( 6\dfrac{1}{5} +14\dfrac{4}{5}\right )\\
=\left ( -\dfrac{2}{7} \right ).\left ( 6+14+ \dfrac{1}{5} +\dfrac{4}{5}\right )
=\dfrac{-2}{7}.(20+\dfrac{5}{5})
=\dfrac{-2}{7}.21
=-6\\
d)7\dfrac{1}{6}.\left ( -\dfrac{7}{6} \right )+10\dfrac{5}{6}.\left ( -\dfrac{7}{6} \right )
=\left ( -\dfrac{7}{6} \right ).\left (7\dfrac{1}{6}+10\dfrac{5}{6}  \right )\\
=\left ( -\dfrac{7}{6} \right ).\left (7+10+\dfrac{1}{6}+\dfrac{5}{6}  \right )
=\left ( -\dfrac{7}{6} \right ).(17+\dfrac{6}{6})
=\dfrac{-7}{6}.18
=-21\\
e)
\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}
=\dfrac{5}{7}.\left ( \dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11} \right )\\
=\dfrac{5}{7}.\dfrac{-7}{11}
=\dfrac{-5}{11}\\
f)19\dfrac{5}{8}:\dfrac{7}{12}-15\dfrac{1}{4}:\dfrac{7}{12}
=\left (19\dfrac{5}{8}-15\dfrac{1}{4}  \right ):\dfrac{7}{12}\\
=\left (19-15+\dfrac{5}{8}-\dfrac{1}{4}  \right ).\dfrac{12}{7}
=\left (4+\dfrac{5}{8}-\dfrac{2}{8}  \right ).\dfrac{12}{7}
=(4+\dfrac{3}{8}).\dfrac{12}{7}
=\left(\dfrac{32}{8}+\dfrac{3}{8}\right).\dfrac{12}{7}\\
=\dfrac{35}{8}.\dfrac{12}{7}
=\dfrac{15}{2}\\
g)\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}.\dfrac{1}{3}
=\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{15}.5+\dfrac{3}{5}.\dfrac{1}{3}\\
=\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{3}+\dfrac{3}{5}.\dfrac{1}{3}
=\dfrac{1}{3}.\left ( \dfrac{2}{5}+\dfrac{3}{5} -2\right )
=\dfrac{1}{3}.(1-2)
=\dfrac{-1}{3}\\
h)\dfrac{4}{9}.19\dfrac{1}{3}-\dfrac{4}{9}.39\dfrac{1}{3}
=\dfrac{4}{9}.\left (19\dfrac{1}{3}- 39\dfrac{1}{3} \right )\\
=\dfrac{4}{9}.\left (19-39+\dfrac{1}{3}- \dfrac{1}{3} \right )
=\dfrac{4}{9}.(-20)
=\dfrac{-80}{9}$