Đáp án:
$a) \dfrac{360}{23}\\
b) \dfrac{24}{23}\\
c) \dfrac{-1}{8}\\
d) \dfrac{-23}{66}\\
e) \dfrac{3}{5}\\
f) \dfrac{-1}{14}$
Giải thích các bước giải:
$a) 13\dfrac{2}{5}+\dfrac{15}{23}+1\dfrac{6}{10}\\
=\dfrac{67}{5}+\dfrac{15}{23}+\dfrac{16}{10}\\
=\dfrac{67}{5}+\dfrac{15}{23}+\dfrac{8}{5}\\
=\dfrac{75}{5}+\dfrac{15}{23}\\
=15+\dfrac{15}{23}\\
=\dfrac{345}{23}+\dfrac{15}{23}\\
=\dfrac{360}{23}\\
b) \dfrac{1}{2}-\dfrac{-1}{3}+\dfrac{1}{23}+\dfrac{1}{6}\\
=\dfrac{3}{6}-\dfrac{-2}{6}+\dfrac{1}{6}+\dfrac{1}{23}\\
=\dfrac{6}{6}+\dfrac{1}{23}\\
=\dfrac{23}{23}+\dfrac{1}{23}\\
=\dfrac{24}{23}\\
c) 0,25+\dfrac{3}{5}-\left ( \dfrac{1}{8}-\dfrac{2}{5}+1\dfrac{1}{4} \right )\\
=\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{1}{8}+\dfrac{2}{5}-\dfrac{5}{4}\\
=\left (\dfrac{1}{4}-\dfrac{5}{4} \right )+\left ( \dfrac{3}{5}+\dfrac{2}{5} \right )-\dfrac{1}{8}\\
=\dfrac{-4}{4}+\dfrac{5}{5}-\dfrac{1}{8}\\
=\dfrac{-1}{8}\\
d) \dfrac{-5}{9}.\dfrac{3}{11}+\dfrac{-13}{18}.\dfrac{3}{11}\\
=\dfrac{3}{11}.\left ( \dfrac{-5}{9}+\dfrac{-13}{18} \right )\\
=\dfrac{3}{11}.\left ( \dfrac{-10}{18}+\dfrac{-13}{18} \right )\\
=\dfrac{3}{11}.\dfrac{-23}{18}\\
=\dfrac{-23}{66}\\
e) \dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:1\dfrac{2}{3}\\
=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}:\dfrac{5}{3}\\
=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}\\
=\dfrac{3}{5}.\left ( \dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7} \right )\\
=\dfrac{3}{5}.\dfrac{7}{7}\\
=\dfrac{3}{5}\\
f)
\left ( -\dfrac{4}{5}+\dfrac{5}{7} \right ):\dfrac{2}{3}+\left (\dfrac{-1}{5}+\dfrac{2}{7} \right ).\dfrac{2}{3}\\
=\left ( \dfrac{-4}{5}+\dfrac{5}{7} \right ).\dfrac{3}{2}+\left (\dfrac{-7}{35}+\dfrac{10}{35} \right ).\dfrac{2}{3}\\
= \left (\dfrac{-28}{35}+\dfrac{25}{35} \right ).\dfrac{3}{2}+\dfrac{3}{35}.\dfrac{2}{3}\\
=\dfrac{-3}{35}.\dfrac{3}{2}+\dfrac{2}{35}\\
=\dfrac{-9}{70}+\dfrac{2}{35}\\ =\dfrac{-9}{70}+\dfrac{4}{70}=\dfrac{-5}{70}=\dfrac{-1}{14}\\ $
