Đáp án:
$1)
\dfrac{23}{5}\\
2)
\dfrac{38}{5}\\
3)
\dfrac{5}{9}\\
4)
\dfrac{11}{4}\\
5)
\dfrac{2}{5}\\
6)
\dfrac{4}{3}\\
7)
\dfrac{9}{4}\\
8)
\dfrac{5}{4}\\
9)
\dfrac{11}{7}$
Giải thích các bước giải:
$1)
9\dfrac{5}{13}-\left ( \dfrac{2}{5}+4\dfrac{5}{13} \right )=9\dfrac{5}{13}- \dfrac{2}{5}-4\dfrac{5}{13} \\
=9-4+\left ( \dfrac{5}{13}-\dfrac{5}{13} \right )-\dfrac{2}{5}\\
=5-\dfrac{2}{5}=\dfrac{25}{5}-\dfrac{2}{5}=\dfrac{23}{5}\\
2)
\left ( 10\dfrac{2}{9}+2\dfrac{3}{5} \right )-5\dfrac{2}{9}=10\dfrac{2}{9}+2\dfrac{3}{5} -5\dfrac{2}{9}\\
=10-5+\left ( \dfrac{2}{9}-\dfrac{2}{9} \right )+\dfrac{13}{5}\\
=5+\dfrac{13}{5}=\dfrac{25}{5}+\dfrac{13}{5}=\dfrac{38}{5}\\
3)
8\dfrac{2}{7}-\left ( 3\dfrac{4}{9}+4\dfrac{2}{7} \right )=8\dfrac{2}{7}- 3\dfrac{4}{9}-4\dfrac{2}{7}\\
=8-4+\left ( \dfrac{2}{7}-\dfrac{2}{7} \right )-\dfrac{31}{9}\\
=4-\dfrac{31}{9}=\dfrac{36}{9}-\dfrac{31}{9}=\dfrac{5}{9}\\
4)
\dfrac{1}{2}+\dfrac{3}{2}.\left ( 2-\dfrac{1}{2} \right )\\
=\dfrac{1}{2}+\dfrac{3}{2}.\left ( \dfrac{4}{2}-\dfrac{1}{2} \right )\\
=\dfrac{1}{2}+\dfrac{3}{2}.\dfrac{3}{2}\\
=\dfrac{2}{4}+\dfrac{9}{4}=\dfrac{11}{4}\\
5)
7\dfrac{3}{8}-\left ( 2\dfrac{3}{5}+4\dfrac{3}{8} \right )\\
=7\dfrac{3}{8}- 2\dfrac{3}{5}-4\dfrac{3}{8}\\
=7-4+\left ( \dfrac{3}{8}-\dfrac{3}{8} \right )-\dfrac{13}{5}\\
=3-\dfrac{13}{5}=\dfrac{15}{5}-\dfrac{13}{5}=\dfrac{2}{5}\\
6)
6\dfrac{4}{5}-\left ( 1\dfrac{2}{3}+3\dfrac{4}{5} \right )\\
=6\dfrac{4}{5}- 1\dfrac{2}{3}-3\dfrac{4}{5} \\
=6-3+\left ( \dfrac{4}{5}-\dfrac{4}{5} \right )-\dfrac{5}{3}\\
=3-\dfrac{5}{3}=\dfrac{9}{3}-\dfrac{5}{3}=\dfrac{4}{3}\\
7)
6\dfrac{5}{7}-\left ( 1\dfrac{3}{4}+2\dfrac{5}{7} \right )\\
=6\dfrac{5}{7}-\dfrac{3}{4}-2\dfrac{5}{7} \\
=6-2+\left ( \dfrac{5}{7}-\dfrac{5}{7} \right )-\dfrac{7}{4}\\
=4-\dfrac{7}{4}=\dfrac{16}{4}-\dfrac{7}{4}=\dfrac{9}{4}\\
8)
7\dfrac{5}{9}-\left ( 2\dfrac{3}{4}+3\dfrac{5}{9} \right )\\
=7\dfrac{5}{9}- 2\dfrac{3}{4}-3\dfrac{5}{9} \\
=7-3+\left ( \dfrac{5}{9}-\dfrac{5}{9} \right )-\dfrac{11}{4}\\
=4-\dfrac{11}{4}=\dfrac{16}{4}-\dfrac{11}{4}=\dfrac{5}{4}\\
9)
7\dfrac{5}{11}-\left ( 2\dfrac{3}{7}+3\dfrac{5}{11} \right )\\
=7\dfrac{5}{11}-2\dfrac{3}{7}-3\dfrac{5}{11} \\
=7-3+\left ( \dfrac{5}{11} -\dfrac{5}{11}\right )-\dfrac{17}{7}\\
=4-\dfrac{17}{7}=\dfrac{28}{7}-\dfrac{17}{7}=\dfrac{11}{7}$
