1. 直接写出得数。
$\boldsymbol{\frac{3}{7} - \frac{3}{14} =}$
$\boldsymbol{\frac{1}{6} + \frac{1}{12} =}$
$\boldsymbol{\frac{3}{7} + \frac{3}{14} =}$
$\boldsymbol{\frac{4}{5} - \frac{3}{10} =}$
$\boldsymbol{\frac{1}{4} + \frac{1}{3} =}$
$\boldsymbol{\frac{3}{5} + \frac{7}{10} =}$
$\boldsymbol{\frac{5}{9} - \frac{1}{3} =}$
$\boldsymbol{\frac{1}{3} + \frac{2}{5} =}$
$\boldsymbol{\frac{3}{7} - \frac{3}{14} =}$
$\boldsymbol{\frac{1}{6} + \frac{1}{12} =}$
$\boldsymbol{\frac{3}{7} + \frac{3}{14} =}$
$\boldsymbol{\frac{4}{5} - \frac{3}{10} =}$
$\boldsymbol{\frac{1}{4} + \frac{1}{3} =}$
$\boldsymbol{\frac{3}{5} + \frac{7}{10} =}$
$\boldsymbol{\frac{5}{9} - \frac{1}{3} =}$
$\boldsymbol{\frac{1}{3} + \frac{2}{5} =}$
答案
$\boldsymbol{\frac{3}{14}}$
$\boldsymbol{\frac{1}{4}}$
$\boldsymbol{\frac{9}{14}}$
$\boldsymbol{\frac{1}{2}}$
$\boldsymbol{\frac{7}{12}}$
$\boldsymbol{\frac{13}{10}}$
$\boldsymbol{\frac{2}{9}}$
$\boldsymbol{\frac{11}{15}}$
$\boldsymbol{\frac{1}{4}}$
$\boldsymbol{\frac{9}{14}}$
$\boldsymbol{\frac{1}{2}}$
$\boldsymbol{\frac{7}{12}}$
$\boldsymbol{\frac{13}{10}}$
$\boldsymbol{\frac{2}{9}}$
$\boldsymbol{\frac{11}{15}}$
2. 计算。
$\frac{1}{6} + (\frac{11}{12} - \frac{1}{6})$
$1 - (\frac{1}{3} + \frac{1}{2})$
$\frac{3}{4} + (\frac{5}{6} + \frac{7}{9})$
$\frac{3}{5} + (\frac{3}{4} - \frac{1}{6})$
$\frac{1}{6} + (\frac{11}{12} - \frac{1}{6})$
$1 - (\frac{1}{3} + \frac{1}{2})$
$\frac{3}{4} + (\frac{5}{6} + \frac{7}{9})$
$\frac{3}{5} + (\frac{3}{4} - \frac{1}{6})$
答案
$=\frac {1}{6}-\frac {1}{6}+\frac {11}{12} $
$=\frac{11}{12}$
$=1-\frac {5}{6}$
$= \frac{1}{6}$
$=\frac {27}{36}+\frac {30}{36}+\frac {28}{36} $
$=\frac{85}{36}$
$=\frac {36}{60}+\frac {45}{60}-\frac {10}{60}$
$= \frac{71}{60}$
$=\frac{11}{12}$
$=1-\frac {5}{6}$
$= \frac{1}{6}$
$=\frac {27}{36}+\frac {30}{36}+\frac {28}{36} $
$=\frac{85}{36}$
$=\frac {36}{60}+\frac {45}{60}-\frac {10}{60}$
$= \frac{71}{60}$
3. 用简便方法计算,说说你的理由。
$\frac{2}{13} + \frac{5}{7} + \frac{11}{13} + \frac{2}{7}$
$\frac{7}{8} - \frac{1}{5} - \frac{2}{5}$
$\frac{8}{19} - \frac{5}{16} + \frac{11}{19} + \frac{5}{16}$
$\frac{26}{49} + \frac{8}{13} + \frac{23}{49}$
$\frac{1}{8} - \frac{3}{7} + \frac{7}{8} - \frac{4}{7}$
$\frac{11}{12} + \frac{2}{9} + \frac{7}{9}$
$\frac{2}{13} + \frac{5}{7} + \frac{11}{13} + \frac{2}{7}$
$\frac{7}{8} - \frac{1}{5} - \frac{2}{5}$
$\frac{8}{19} - \frac{5}{16} + \frac{11}{19} + \frac{5}{16}$
$\frac{26}{49} + \frac{8}{13} + \frac{23}{49}$
$\frac{1}{8} - \frac{3}{7} + \frac{7}{8} - \frac{4}{7}$
$\frac{11}{12} + \frac{2}{9} + \frac{7}{9}$
答案
$\frac{2}{13}+\frac{5}{7}+\frac{11}{13}+\frac{2}{7}$
$ =(\frac{2}{13}+\frac{11}{13})+(\frac{5}{7}+\frac{2}{7})$
=1+1
=2
理由:利用加法交换律和结合律,将同分母分数结合,简化计算。
$\frac{7}{8}-\frac{1}{5}-\frac{2}{5}$
$ =\frac{7}{8}-(\frac{1}{5}+\frac{2}{5})$
$ =\frac{7}{8}-\frac{3}{5}$
$ =\frac{35}{40}-\frac{24}{40}$
$ =\frac{11}{40}$
理由:利用减法的性质,连续减去两个数等于减去这两个数的和,简化计算。
$\frac{8}{19}-\frac{5}{16}+\frac{11}{19}+\frac{5}{16}$
$ =(\frac{8}{19}+\frac{11}{19})+(\frac{5}{16}-\frac{5}{16})$
=1+0
=1
$\frac{26}{49}+\frac{8}{13}+\frac{23}{49}$
$ =(\frac{26}{49}+\frac{23}{49})+\frac{8}{13}$
$ =1+\frac{8}{13}$
$ =\frac{21}{13}$
$\frac{1}{8}-\frac{3}{7}+\frac{7}{8}-\frac{4}{7}$
$ =(\frac{1}{8}+\frac{7}{8})-(\frac{3}{7}+\frac{4}{7})$
=1-1
=0
$\frac{11}{12}+\frac{2}{9}+\frac{7}{9}$
$ =\frac{11}{12}+(\frac{2}{9}+\frac{7}{9})$
$ =\frac{11}{12}+1$
$ =\frac{23}{12}$
$ =(\frac{2}{13}+\frac{11}{13})+(\frac{5}{7}+\frac{2}{7})$
=1+1
=2
理由:利用加法交换律和结合律,将同分母分数结合,简化计算。
$\frac{7}{8}-\frac{1}{5}-\frac{2}{5}$
$ =\frac{7}{8}-(\frac{1}{5}+\frac{2}{5})$
$ =\frac{7}{8}-\frac{3}{5}$
$ =\frac{35}{40}-\frac{24}{40}$
$ =\frac{11}{40}$
理由:利用减法的性质,连续减去两个数等于减去这两个数的和,简化计算。
$\frac{8}{19}-\frac{5}{16}+\frac{11}{19}+\frac{5}{16}$
$ =(\frac{8}{19}+\frac{11}{19})+(\frac{5}{16}-\frac{5}{16})$
=1+0
=1
$\frac{26}{49}+\frac{8}{13}+\frac{23}{49}$
$ =(\frac{26}{49}+\frac{23}{49})+\frac{8}{13}$
$ =1+\frac{8}{13}$
$ =\frac{21}{13}$
$\frac{1}{8}-\frac{3}{7}+\frac{7}{8}-\frac{4}{7}$
$ =(\frac{1}{8}+\frac{7}{8})-(\frac{3}{7}+\frac{4}{7})$
=1-1
=0
$\frac{11}{12}+\frac{2}{9}+\frac{7}{9}$
$ =\frac{11}{12}+(\frac{2}{9}+\frac{7}{9})$
$ =\frac{11}{12}+1$
$ =\frac{23}{12}$
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