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a,\(2-\frac{5}{7}+\frac{9}{21}\)
\(=2-\frac{154}{147}\)
\(=\frac{135}{147}\)
b, \(\frac{5}{8}\):\(3+\frac{25}{24}\)
\(=\frac{5}{24}+\frac{25}{24}\)
\(=\frac{30}{24}\)
5/6 + 9/12 : 18/5 = 5/6 + 3/4 : 18/5
= 5/6 + 3/4 x 5/18
= 5/6 + 15/72
= 5/6 + 5/24
= 20/24 + 5/24
= 25/24
5/7 + 9/8 - 15/28 = 40/56 + 63/56 - 30/56
= 103/56 - 30/56
= 73/56
\(\dfrac{5}{6}+\dfrac{9}{12}:\dfrac{18}{5}\)
\(=\dfrac{5}{6}+\dfrac{5}{24}\)
\(=\dfrac{25}{24}\)
\(---\)
\(\dfrac{5}{7}+\dfrac{9}{8}-\dfrac{15}{28}\)
\(=\dfrac{103}{56}-\dfrac{15}{28}\)
\(=\dfrac{73}{56}\)
25/37 - 2/5 + 12/37 = (25/37+12/37)-2/5=37/37-2/5=1-2/5=5/5-2/5=3/5
\(\dfrac{7}{9}+\left(\dfrac{2}{3}-\dfrac{5}{12}\right)\)
\(=\dfrac{7}{9}+\left(\dfrac{8}{12}-\dfrac{5}{12}\right)\)
\(=\dfrac{7}{9}+\dfrac{1}{4}\)
\(=\dfrac{28}{36}+\dfrac{9}{36}=\dfrac{37}{36}\)
\(-------------\)
\(\dfrac{5}{8}+\dfrac{1}{4}\times\dfrac{2}{3}\)
\(=\dfrac{5}{8}+\dfrac{1}{6}\)
\(=\dfrac{15}{24}+\dfrac{4}{24}=\dfrac{19}{24}\)
\(\dfrac{7}{9}+\left(\dfrac{2}{3}-\dfrac{5}{12}\right)=\dfrac{7}{9}+\dfrac{1}{4}=\dfrac{28}{36}+\dfrac{9}{36}=\dfrac{37}{36}\)
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\(\dfrac{5}{8}+\dfrac{1}{4}\times\dfrac{2}{3}=\dfrac{5}{8}+\dfrac{1}{6}=\dfrac{15}{24}+\dfrac{4}{24}=\dfrac{19}{24}\)
\(\frac{12}{25}:\frac{9}{32}\cdot\frac{5}{8}=\frac{12}{25}\cdot\frac{32}{9}\cdot\frac{5}{8}=\frac{12\cdot32\cdot5}{25\cdot9\cdot8}=\frac{3\cdot4\cdot8\cdot4\cdot5}{5\cdot5\cdot3\cdot3\cdot8}=\frac{4\cdot4}{5\cdot3}=\frac{16}{15}\)