Đáp án:
$a)0\\
b)\dfrac{5}{7}\\
c)0\\
d)
\dfrac{3}{4}\\
e)
\dfrac{7}{5}\\
f)
\dfrac{-6}{5}\\
g)
\dfrac{27}{5}\\
h)\dfrac{3}{7}\\
i) \dfrac{95}{11}$
Giải thích các bước giải:
$a) \dfrac{-5}{11}+\left ( \dfrac{-6}{11}+1 \right )=\dfrac{-5}{11}+\dfrac{-6}{11}+1 \\
=\left (\dfrac{-5}{11} +\dfrac{-6}{11}\right )+1 =-1+1=0\\
b)\dfrac{2}{3}+\left ( \dfrac{5}{7}+\dfrac{-2}{3} \right )=\dfrac{2}{3}+\dfrac{5}{7}+\dfrac{-2}{3}\\
= \left (\dfrac{2}{3}+\dfrac{-2}{3} \right )+\dfrac{5}{7}=\dfrac{5}{7}\\
c)\left ( \dfrac{-1}{4}+\dfrac{5}{8} \right )+\dfrac{-3}{8}\\
= \dfrac{-2}{8}+\dfrac{5}{8} +\dfrac{-3}{8}\\
=\dfrac{0}{8}=0\\
d)
\dfrac{3}{4}.\dfrac{7}{25}+\dfrac{3}{4}.\dfrac{18}{25}\\
=\dfrac{3}{4}.\left ( \dfrac{7}{25}+\dfrac{18}{25} \right )\\
=\dfrac{3}{4}.\dfrac{25}{25}\\
=\dfrac{3}{4}\\
e)
\dfrac{7}{5}.\dfrac{8}{19}+\dfrac{7}{5}.\dfrac{12}{19}-\dfrac{7}{5}.\dfrac{1}{19}\\
=\dfrac{7}{5}.\left ( \dfrac{8}{19}+\dfrac{12}{19}-\dfrac{1}{19} \right )\\
=\dfrac{7}{5}.\left ( \dfrac{8}{19}+\dfrac{12}{19}-\dfrac{1}{19} \right )\\
=\dfrac{7}{5}.\dfrac{19}{19}=\dfrac{7}{5}\\
f)
\dfrac{-3}{5}.\dfrac{5}{7}+\dfrac{-3}{5}.\dfrac{3}{7}+\dfrac{-3}{5}.\dfrac{6}{7}\\
=\dfrac{-3}{5}.\left ( \dfrac{5}{7}+\dfrac{3}{7}+\dfrac{6}{7} \right )\\
=\dfrac{-3}{5}.\dfrac{14}{7}\\
=\dfrac{-3}{5}.2=\dfrac{-6}{5}\\
g)
10\dfrac{2}{9}+\left ( 2\dfrac{2}{5}-7\dfrac{2}{9} \right )\\
=10\dfrac{2}{9}+ 2\dfrac{2}{5}-7\dfrac{2}{9} \\
=(10-7)+\left ( \dfrac{2}{9}-\dfrac{2}{9} \right )+\dfrac{12}{5}\\
=3+\dfrac{12}{5}\\
=\dfrac{15}{5}+\dfrac{12}{5}=\dfrac{27}{5}\\
h)6\dfrac{3}{10}-\left ( 3\dfrac{4}{7}+2\dfrac{3}{10} \right )\\
=6\dfrac{3}{10}- 3\dfrac{4}{7}-2\dfrac{3}{10} \\
=(6-2)+\left ( \dfrac{3}{10}-\dfrac{3}{10} \right )-\dfrac{25}{7}\\
=4-\dfrac{25}{7}\\
=\dfrac{28}{7}-\dfrac{25}{7}=\dfrac{3}{7}\\
i) \left ( 7\dfrac{4}{9}+4\dfrac{7}{11} \right )-3\dfrac{4}{9}\\
= 7\dfrac{4}{9}+4\dfrac{7}{11} -3\dfrac{4}{9}\\
=(7-3)+\left ( \dfrac{4}{9}-\dfrac{4}{9} \right )+\dfrac{51}{11}\\
=4+\dfrac{51}{11}\\
=\dfrac{44}{11}+\dfrac{51}{11}\\
=\dfrac{95}{11}$
