第30页 - 经纶学典学霸六年级数学上下册【江苏国标】

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$\frac {19}{8×11}=\frac18+\frac {1}{11}$

$=1+\frac12-(\frac12+\frac13)+(\frac13+\frac14)-(\frac14+\frac15)$

$+(\frac15+\frac16)-(\frac16+\frac17)+(\frac17+\frac18)$

$=\frac98$

$=7×(\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac {15}{56})$

$=7×(\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac {15}{56})\ $

$=7×[(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+$

$(\frac{1}{5}+\frac{1}{6})-(\frac{1}{6}+\frac{1}{7})+(\frac{1}{7}+\frac{1}{8})]$

$=7×(\frac{1}{3}+\frac18)$

$=7×\frac{11}{24}$

$=\frac{77}{24}$

$\ \ \ \ \frac{20}{6}-\frac{28}{12}+\frac{36}{20}-\frac{44}{30}+\frac{52}{42}-\frac{60}{56}$

$\ = (\frac{5}{6}-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56})×4\ $

$=(\frac{1}{2}+\frac{1}{3}-\frac{1}{3}-\frac{1}{4}+\frac{1}{4}+\frac{1}{5}-\frac{1}{5}-\frac{1}{6}$

$+\frac{1}{6}+\frac{1}{7}-\frac{1}{7} -\frac{1}{8})×4$

$=(\frac{1}{2}-\frac{1}{8})×4$

$=\frac{3}{8}×4$

$=\frac{3}{2} $