四、慎思妙算。
1. 直接写出得数。
$1-\frac{6}{7}=$ $\frac{2}{9}+\frac{4}{9}=$ $\frac{11}{12}-\frac{2}{3}=$ $\frac{3}{10}+\frac{2}{5}=$
$\frac{7}{8}-\frac{1}{4}=$ $\frac{5}{7}-\frac{5}{7}=$ $\frac{1}{6}+\frac{5}{6}=$ $\frac{3}{4}+\frac{5}{12}=$

$1 - \frac{6}{7} = \frac{1}{7}$；
$\frac{2}{9} + \frac{4}{9} = \frac{6}{9} = \frac{2}{3}$；
$\frac{11}{12} - \frac{2}{3} = \frac{11}{12} - \frac{8}{12} = \frac{3}{12} = \frac{1}{4}$；
$\frac{3}{10} + \frac{2}{5} = \frac{3}{10} + \frac{4}{10} = \frac{7}{10}$；
$\frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8}$；
$\frac{5}{7} - \frac{5}{7} = 0$；
$\frac{1}{6} + \frac{5}{6} = 1$；
$\frac{3}{4} + \frac{5}{12} = \frac{9}{12} + \frac{5}{12} = \frac{14}{12} = \frac{7}{6}$。

2. 计算下面各题，能简算的要简算。
$\frac{11}{12}-(\frac{1}{6}+\frac{1}{8})$            $\frac{7}{5}+\frac{4}{9}+\frac{5}{9}+\frac{3}{5}$              $\frac{3}{4}-\frac{1}{3}+\frac{5}{6}$
$\frac{7}{12}-(\frac{3}{4}-\frac{1}{2})$             $\frac{1}{3}+\frac{2}{5}+\frac{3}{4}$                $11-\frac{7}{10}-\frac{3}{10}$

1.
$\begin{aligned}\frac{11}{12}-(\frac{1}{6}+\frac{1}{8})&=\frac{11}{12}-(\frac{4}{24}+\frac{3}{24})\\&=\frac{22}{24}-\frac{7}{24}\\&=\frac{15}{24}\\&=\frac{5}{8}\end{aligned}$
2.
$\begin{aligned}\frac{7}{5}+\frac{4}{9}+\frac{5}{9}+\frac{3}{5}&=(\frac{7}{5}+\frac{3}{5})+(\frac{4}{9}+\frac{5}{9})\\&=\frac{10}{5} + 1\\&=2 + 1\\&=3\end{aligned}$
3.
$\begin{aligned}\frac{3}{4}-\frac{1}{3}+\frac{5}{6}&=\frac{9}{12}-\frac{4}{12}+\frac{10}{12}\\&=\frac{9 - 4+10}{12}\\&=\frac{15}{12}\\&=\frac{5}{4}\end{aligned}$
4.
$\begin{aligned}\frac{7}{12}-(\frac{3}{4}-\frac{1}{2})&=\frac{7}{12}-(\frac{9}{12}-\frac{6}{12})\\&=\frac{7}{12}-\frac{3}{12}\\&=\frac{4}{12}\\&=\frac{1}{3}\end{aligned}$
5.
$\begin{aligned}\frac{1}{3}+\frac{2}{5}+\frac{3}{4}&=\frac{20}{60}+\frac{24}{60}+\frac{45}{60}\\&=\frac{20 + 24+45}{60}\\&=\frac{89}{60}\end{aligned}$
6.
$\begin{aligned}11-\frac{7}{10}-\frac{3}{10}&=11-(\frac{7}{10}+\frac{3}{10})\\&=11 - 1\\&=10\end{aligned}$

3. 解方程。
$\frac{3}{4}-x=\frac{7}{10}$           $\frac{2}{5}+x=\frac{7}{8}$            $3.6x+0.5x=123$
$4.2+2x-3.8=10$                   $8×1.2+4x=36$              $1.5x÷2=60$

解方程：
1. $\frac{3}{4} - x = \frac{7}{10}$
解：$x = \frac{3}{4} - \frac{7}{10}$
$x = \frac{15}{20} - \frac{14}{20}$
$x = \frac{1}{20}$
2. $\frac{2}{5} + x = \frac{7}{8}$
解：$x = \frac{7}{8} - \frac{2}{5}$
$x = \frac{35}{40} - \frac{16}{40}$
$x = \frac{19}{40}$
3. $3.6x + 0.5x = 123$
解：$4.1x = 123$
$x = 123 ÷ 4.1$
$x = 30$
4. $4.2 + 2x - 3.8 = 10$
解：$0.4 + 2x = 10$
$2x = 10 - 0.4$
$2x = 9.6$
$x = 4.8$
5. $8×1.2 + 4x = 36$
解：$9.6 + 4x = 36$
$4x = 36 - 9.6$
$4x = 26.4$
$x = 6.6$
6. $1.5x ÷ 2 = 60$
解：$1.5x = 60×2$
$1.5x = 120$
$x = 120 ÷ 1.5$
$x = 80$