1 计算下面各题，并找出得数的规律。
$ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = $$ $$ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} = $
$ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} = $

1 $\frac{7}{8}$ $\frac{15}{16}$ $\frac{31}{32}$

2 应用上面的规律，直接写出下面算式的得数。
$ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} = $

2 $\frac{127}{128}$

1 计算下面各题。
$ \frac{1}{6}+\frac{4}{7}+\frac{5}{6} $
$ \frac{5}{12}-\frac{7}{18}+\frac{2}{9} $
$ \frac{5}{9}-(\frac{1}{6}+\frac{1}{4}) $
$ \frac{7}{8}-(\frac{1}{2}-\frac{1}{3}) $

1. $\frac{1}{6}+\frac{4}{7}+\frac{5}{6}$
$=(\frac{1}{6}+\frac{5}{6})+\frac{4}{7}$
$=1+\frac{4}{7}$
$=1\frac{4}{7}$
2. $\frac{5}{12}-\frac{7}{18}+\frac{2}{9}$
$=\frac{15}{36}-\frac{14}{36}+\frac{8}{36}$
$=\frac{15-14+8}{36}$
$=\frac{9}{36}$
$=\frac{1}{4}$
3. $\frac{5}{9}-(\frac{1}{6}+\frac{1}{4})$
$=\frac{5}{9}-(\frac{2}{12}+\frac{3}{12})$
$=\frac{5}{9}-\frac{5}{12}$
$=\frac{20}{36}-\frac{15}{36}$
$=\frac{5}{36}$
4. $\frac{7}{8}-(\frac{1}{2}-\frac{1}{3})$
$=\frac{7}{8}-(\frac{3}{6}-\frac{2}{6})$
$=\frac{7}{8}-\frac{1}{6}$
$=\frac{21}{24}-\frac{4}{24}$
$=\frac{17}{24}$

2 列式计算。
(1)$$\frac{1}{2}$$与$$\frac{1}{3}$$的和比它们的差多多少？
(2)$$\frac{4}{5}$$加上$$\frac{4}{5}$$与$$\frac{2}{3}$$的差，和是多少？
(3)一个数比$$\frac{4}{9}$$与$$\frac{5}{12}$$的和大$$\frac{7}{12}$$，这个数是多少？

(1)
$(\frac{1}{2} + \frac{1}{3}) - (\frac{1}{2} - \frac{1}{3})$
$= (\frac{3}{6} + \frac{2}{6}) - (\frac{3}{6} - \frac{2}{6})$
$= \frac{5}{6} - \frac{1}{6}$
$= \frac{4}{6} = \frac{2}{3}$
(2)
$\frac{4}{5} + (\frac{4}{5} - \frac{2}{3})$
$= \frac{4}{5} + (\frac{12}{15} - \frac{10}{15})$
$= \frac{4}{5} + \frac{2}{15}$
$= \frac{12}{15} + \frac{2}{15} = \frac{14}{15}$
(3)
$\frac{4}{9} + \frac{5}{12} + \frac{7}{12}$
$= \frac{4}{9} + (\frac{5}{12} + \frac{7}{12})$
$= \frac{4}{9} + 1 = 1\frac{4}{9}$