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5. 用递等式计算。
$18÷\frac {3}{5}×\frac {5}{6}$ $(\frac {3}{4}+\frac {2}{5})÷\frac {2}{5}$ $\frac {19}{20}-(\frac {3}{5}+2×\frac {1}{8})$
$1÷(\frac {2}{7}+\frac {1}{5})$ $3-\frac {2}{7}÷\frac {8}{35}-\frac {3}{4}$ $\frac {39}{28}÷[\frac {1}{2}+(\frac {7}{8}-\frac {5}{6})]$
$18÷\frac {3}{5}×\frac {5}{6}$ $(\frac {3}{4}+\frac {2}{5})÷\frac {2}{5}$ $\frac {19}{20}-(\frac {3}{5}+2×\frac {1}{8})$
$1÷(\frac {2}{7}+\frac {1}{5})$ $3-\frac {2}{7}÷\frac {8}{35}-\frac {3}{4}$ $\frac {39}{28}÷[\frac {1}{2}+(\frac {7}{8}-\frac {5}{6})]$
答案
$1. 18÷\frac{3}{5}×\frac{5}{6}$
$=18×\frac{5}{3}×\frac{5}{6}$
$=30×\frac{5}{6}$
=25
$2. (\frac{3}{4}+\frac{2}{5})÷\frac{2}{5}$
$=(\frac{15}{20}+\frac{8}{20})×\frac{5}{2}$
$=\frac{23}{20}×\frac{5}{2}$
$=\frac{23}{8}$
$3. \frac{19}{20}-(\frac{3}{5}+2×\frac{1}{8})$
$=\frac{19}{20}-(\frac{3}{5}+\frac{1}{4})$
$=\frac{19}{20}-(\frac{12}{20}+\frac{5}{20})$
$=\frac{19}{20}-\frac{17}{20}$
$=\frac{1}{10}$
$4. 1÷(\frac{2}{7}+\frac{1}{5})$
$=1÷(\frac{10}{35}+\frac{7}{35})$
$=1÷\frac{17}{35}$
$=\frac{35}{17}$
$5. 3-\frac{2}{7}÷\frac{8}{35}-\frac{3}{4}$
$=3-\frac{2}{7}×\frac{35}{8}-\frac{3}{4}$
$=3-\frac{5}{4}-\frac{3}{4}$
$=3-(\frac{5}{4}+\frac{3}{4})$
=3-2
=1
$6. \frac{39}{28}÷[\frac{1}{2}+(\frac{7}{8}-\frac{5}{6})]$
$=\frac{39}{28}÷[\frac{1}{2}+(\frac{21}{24}-\frac{20}{24})]$
$=\frac{39}{28}÷[\frac{1}{2}+\frac{1}{24}]$
$=\frac{39}{28}÷[\frac{12}{24}+\frac{1}{24}]$
$=\frac{39}{28}÷\frac{13}{24}$
$=\frac{39}{28}×\frac{24}{13}$
$=\frac{18}{7}$
$=18×\frac{5}{3}×\frac{5}{6}$
$=30×\frac{5}{6}$
=25
$2. (\frac{3}{4}+\frac{2}{5})÷\frac{2}{5}$
$=(\frac{15}{20}+\frac{8}{20})×\frac{5}{2}$
$=\frac{23}{20}×\frac{5}{2}$
$=\frac{23}{8}$
$3. \frac{19}{20}-(\frac{3}{5}+2×\frac{1}{8})$
$=\frac{19}{20}-(\frac{3}{5}+\frac{1}{4})$
$=\frac{19}{20}-(\frac{12}{20}+\frac{5}{20})$
$=\frac{19}{20}-\frac{17}{20}$
$=\frac{1}{10}$
$4. 1÷(\frac{2}{7}+\frac{1}{5})$
$=1÷(\frac{10}{35}+\frac{7}{35})$
$=1÷\frac{17}{35}$
$=\frac{35}{17}$
$5. 3-\frac{2}{7}÷\frac{8}{35}-\frac{3}{4}$
$=3-\frac{2}{7}×\frac{35}{8}-\frac{3}{4}$
$=3-\frac{5}{4}-\frac{3}{4}$
$=3-(\frac{5}{4}+\frac{3}{4})$
=3-2
=1
$6. \frac{39}{28}÷[\frac{1}{2}+(\frac{7}{8}-\frac{5}{6})]$
$=\frac{39}{28}÷[\frac{1}{2}+(\frac{21}{24}-\frac{20}{24})]$
$=\frac{39}{28}÷[\frac{1}{2}+\frac{1}{24}]$
$=\frac{39}{28}÷[\frac{12}{24}+\frac{1}{24}]$
$=\frac{39}{28}÷\frac{13}{24}$
$=\frac{39}{28}×\frac{24}{13}$
$=\frac{18}{7}$
6. 用简便方法计算。
$(\frac {7}{8}+\frac {13}{16})÷\frac {13}{16}$ $12÷\frac {14}{5}÷\frac {5}{7}$ $\frac {18}{23}÷\frac {8}{5}+\frac {18}{23}×\frac {3}{8}$
$\frac {3}{7}×2.5+\frac {4}{7}×250\%$ $3.65×7+6.35÷\frac {1}{7}$
$(\frac {7}{8}+\frac {13}{16})÷\frac {13}{16}$ $12÷\frac {14}{5}÷\frac {5}{7}$ $\frac {18}{23}÷\frac {8}{5}+\frac {18}{23}×\frac {3}{8}$
$\frac {3}{7}×2.5+\frac {4}{7}×250\%$ $3.65×7+6.35÷\frac {1}{7}$
答案
$1. (\frac{7}{8}+\frac{13}{16})÷\frac{13}{16}$
$=(\frac{7}{8}+\frac{13}{16})×\frac{16}{13}$
$=\frac{7}{8}×\frac{16}{13}+\frac{13}{16}×\frac{16}{13}$
$=\frac{14}{13}+1$
$=\frac{27}{13}$
$2. 12÷\frac{14}{5}÷\frac{5}{7}$
$=12×\frac{5}{14}×\frac{7}{5}$
$=12×(\frac{5}{14}×\frac{7}{5})$
$=12×\frac{1}{2}$
=6
$3. \frac{18}{23}÷\frac{8}{5}+\frac{18}{23}×\frac{3}{8}$
$=\frac{18}{23}×\frac{5}{8}+\frac{18}{23}×\frac{3}{8}$
$=\frac{18}{23}×(\frac{5}{8}+\frac{3}{8})$
$=\frac{18}{23}×1$
$=\frac{18}{23}$
$4. \frac{3}{7}×2.5+\frac{4}{7}×250\%$
$=\frac{3}{7}×2.5+\frac{4}{7}×2.5$
$=2.5×(\frac{3}{7}+\frac{4}{7})$
=2.5×1
=2.5
$5. 3.65×7+6.35÷\frac{1}{7}$
=3.65×7+6.35×7
=7×(3.65+6.35)
=7×10
=70
$=(\frac{7}{8}+\frac{13}{16})×\frac{16}{13}$
$=\frac{7}{8}×\frac{16}{13}+\frac{13}{16}×\frac{16}{13}$
$=\frac{14}{13}+1$
$=\frac{27}{13}$
$2. 12÷\frac{14}{5}÷\frac{5}{7}$
$=12×\frac{5}{14}×\frac{7}{5}$
$=12×(\frac{5}{14}×\frac{7}{5})$
$=12×\frac{1}{2}$
=6
$3. \frac{18}{23}÷\frac{8}{5}+\frac{18}{23}×\frac{3}{8}$
$=\frac{18}{23}×\frac{5}{8}+\frac{18}{23}×\frac{3}{8}$
$=\frac{18}{23}×(\frac{5}{8}+\frac{3}{8})$
$=\frac{18}{23}×1$
$=\frac{18}{23}$
$4. \frac{3}{7}×2.5+\frac{4}{7}×250\%$
$=\frac{3}{7}×2.5+\frac{4}{7}×2.5$
$=2.5×(\frac{3}{7}+\frac{4}{7})$
=2.5×1
=2.5
$5. 3.65×7+6.35÷\frac{1}{7}$
=3.65×7+6.35×7
=7×(3.65+6.35)
=7×10
=70
