三、慎思妙算。
1. 直接写出得数。
$\dfrac{1}{2}+0.5=$ $\dfrac{2}{5}+\dfrac{2}{5}=$ $\dfrac{4}{9}+\dfrac{5}{9}=$ $\dfrac{1}{3}+\dfrac{1}{4}=$
$1-\dfrac{2}{11}=$ $\dfrac{6}{7}-\dfrac{5}{6}=$ $6-\dfrac{7}{8}=$ $1-\dfrac{3}{7}+\dfrac{4}{7}=$

$ \dfrac{1}{2} + 0.5 = 1$；
$ \dfrac{2}{5} + \dfrac{2}{5} = \dfrac{4}{5}$；
$ \dfrac{4}{9} + \dfrac{5}{9} = 1$；
$ \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{7}{12}$；
$1 - \dfrac{2}{11} = \dfrac{9}{11}$；
$ \dfrac{6}{7} - \dfrac{5}{6} = \dfrac{1}{42}$；
$ 6 - \dfrac{7}{8} = \dfrac{41}{8}（或5\dfrac{1}{8}）$；
$ 1 - \dfrac{3}{7} + \dfrac{4}{7} = \dfrac{8}{7} （或1\dfrac{1}{7}）$。

2. 脱式计算。
$\dfrac{3}{4}-\dfrac{5}{8}+\dfrac{5}{12}$ $\dfrac{2}{3}-(\dfrac{1}{4}+\dfrac{1}{8})$
$\dfrac{8}{9}-\dfrac{1}{6}+\dfrac{2}{3}$ $\dfrac{4}{5}+\dfrac{3}{10}-\dfrac{11}{12}$

①$\frac{3}{4} - \frac{5}{8} + \frac{5}{12}$
$=\frac{18}{24} - \frac{15}{24} + \frac{10}{24}$
$=\frac{18 - 15 + 10}{24}$
$=\frac{13}{24}$
②$\frac{2}{3} - (\frac{1}{4} + \frac{1}{8})$
$=\frac{2}{3} - (\frac{2}{8} + \frac{1}{8})$
$=\frac{2}{3} - \frac{3}{8}$
$=\frac{16}{24} - \frac{9}{24}$
$=\frac{7}{24}$
③$\frac{8}{9} - \frac{1}{6} + \frac{2}{3}$
$=\frac{16}{18} - \frac{3}{18} + \frac{12}{18}$
$=\frac{16 - 3 + 12}{18}$
$=\frac{25}{18}$
④$\frac{4}{5} + \frac{3}{10} - \frac{11}{12}$
$=\frac{48}{60} + \frac{18}{60} - \frac{55}{60}$
$=\frac{48 + 18 - 55}{60}$
$=\frac{11}{60}$

3. 计算下面各题，能简算的要简算。
$\dfrac{11}{20}-\dfrac{4}{17}+\dfrac{9}{20}-\dfrac{13}{17}$ $\dfrac{5}{12}+(\dfrac{4}{9}+\dfrac{7}{12})$
$\dfrac{7}{9}-(\dfrac{3}{5}-\dfrac{2}{9})$ $\dfrac{7}{10}-(\dfrac{2}{7}+\dfrac{3}{10})$

第一题：$\dfrac{11}{20}-\dfrac{4}{17}+\dfrac{9}{20}-\dfrac{13}{17}$
$=(\dfrac{11}{20}+\dfrac{9}{20})-(\dfrac{4}{17}+\dfrac{13}{17})$
$=1-1$
$=0$
第二题：$\dfrac{5}{12}+(\dfrac{4}{9}+\dfrac{7}{12})$
$=(\dfrac{5}{12}+\dfrac{7}{12})+\dfrac{4}{9}$
$=1+\dfrac{4}{9}$
$=1\dfrac{4}{9}$
第三题：$\dfrac{7}{9}-(\dfrac{3}{5}-\dfrac{2}{9})$
$=\dfrac{7}{9}-\dfrac{3}{5}+\dfrac{2}{9}$
$=(\dfrac{7}{9}+\dfrac{2}{9})-\dfrac{3}{5}$
$=1-\dfrac{3}{5}$
$=\dfrac{2}{5}$
第四题：$\dfrac{7}{10}-(\dfrac{2}{7}+\dfrac{3}{10})$
$=\dfrac{7}{10}-\dfrac{2}{7}-\dfrac{3}{10}$
$=(\dfrac{7}{10}-\dfrac{3}{10})-\dfrac{2}{7}$
$=\dfrac{4}{10}-\dfrac{2}{7}$
$=\dfrac{2}{5}-\dfrac{2}{7}$
$=\dfrac{14}{35}-\dfrac{10}{35}$
$=\dfrac{4}{35}$

4. 解方程。
$x-\dfrac{1}{5}=\dfrac{17}{20}$ $x+\dfrac{1}{6}=\dfrac{5}{6}$ $x-\dfrac{1}{3}+\dfrac{1}{4}=\dfrac{5}{6}$

解方程
1. $ x - \dfrac{1}{5} = \dfrac{17}{20} $
解：$ x = \dfrac{17}{20} + \dfrac{1}{5} $
$ x = \dfrac{17}{20} + \dfrac{4}{20} $
$ x = \dfrac{21}{20} $
2. $ x + \dfrac{1}{6} = \dfrac{5}{6} $
解：$ x = \dfrac{5}{6} - \dfrac{1}{6} $
$ x = \dfrac{4}{6} $
$ x = \dfrac{2}{3} $
3. $ x - \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{5}{6} $
解：$ x = \dfrac{5}{6} + \dfrac{1}{3} - \dfrac{1}{4} $
$ x = \dfrac{10}{12} + \dfrac{4}{12} - \dfrac{3}{12} $
$ x = \dfrac{11}{12} $