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计算：$1-\frac{1}{2}=$() $1-\frac{1}{2}-\frac{1}{4}=$() $1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}=$()
你发现了什么规律？根据发现的规律，直接写出下面两题的得数。
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{32}=$() $1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{64}=$()
你发现了什么规律？根据发现的规律，直接写出下面两题的得数。
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{32}=$() $1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{64}=$()
答案
$1-\frac{1}{2}=\frac{1}{2}$
$1-\frac{1}{2}-\frac{1}{4}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$
$1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{32}=\frac{1}{32}$
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{64}=\frac{1}{64}$
$1-\frac{1}{2}-\frac{1}{4}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$
$1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{32}=\frac{1}{32}$
$1-\frac{1}{2}-\frac{1}{4}-\dots-\frac{1}{64}=\frac{1}{64}$
1. 直接写出得数。
$\frac{2}{9}+\frac{5}{9}=$
$\frac{18}{19}-\frac{15}{19}=$
$\frac{5}{13}+\frac{12}{13}=$
$\frac{8}{15}-\frac{2}{5}=$
$\frac{9}{13}-\frac{9}{26}=$
$\frac{5}{18}+\frac{5}{6}=$
$\frac{7}{4}-\frac{3}{8}=$
$\frac{4}{5}+\frac{1}{10}=$
$\frac{2}{9}+\frac{5}{9}=$
$\frac{18}{19}-\frac{15}{19}=$
$\frac{5}{13}+\frac{12}{13}=$
$\frac{8}{15}-\frac{2}{5}=$
$\frac{9}{13}-\frac{9}{26}=$
$\frac{5}{18}+\frac{5}{6}=$
$\frac{7}{4}-\frac{3}{8}=$
$\frac{4}{5}+\frac{1}{10}=$
答案
$\frac{2}{9}+\frac{5}{9}=\frac{7}{9}$
$\frac{18}{19}-\frac{15}{19}=\frac{3}{19}$
$\frac{5}{13}+\frac{12}{13}=\frac{17}{13}$
$\frac{8}{15}-\frac{2}{5}=\frac{8}{15}-\frac{6}{15}=\frac{2}{15}$
$\frac{9}{13}-\frac{9}{26}=\frac{18}{26}-\frac{9}{26}=\frac{9}{26}$
$\frac{5}{18}+\frac{5}{6}=\frac{5}{18}+\frac{15}{18}=\frac{20}{18}=\frac{10}{9}$
$\frac{7}{4}-\frac{3}{8}=\frac{14}{8}-\frac{3}{8}=\frac{11}{8}$
$\frac{4}{5}+\frac{1}{10}=\frac{8}{10}+\frac{1}{10}=\frac{9}{10}$
$\frac{18}{19}-\frac{15}{19}=\frac{3}{19}$
$\frac{5}{13}+\frac{12}{13}=\frac{17}{13}$
$\frac{8}{15}-\frac{2}{5}=\frac{8}{15}-\frac{6}{15}=\frac{2}{15}$
$\frac{9}{13}-\frac{9}{26}=\frac{18}{26}-\frac{9}{26}=\frac{9}{26}$
$\frac{5}{18}+\frac{5}{6}=\frac{5}{18}+\frac{15}{18}=\frac{20}{18}=\frac{10}{9}$
$\frac{7}{4}-\frac{3}{8}=\frac{14}{8}-\frac{3}{8}=\frac{11}{8}$
$\frac{4}{5}+\frac{1}{10}=\frac{8}{10}+\frac{1}{10}=\frac{9}{10}$
2. 判断。(对的在括号里画“√”，错的画“×”。)
(1)整数加法的交换律、结合律对分数加法不适用。 ($\quad$)
(2)$1-\frac{2}{5}-\frac{3}{5}=0$ ($\quad$)
(3)$\frac{1}{3}+\frac{1}{4}+\frac{5}{12}=1$ ($\quad$)
(1)整数加法的交换律、结合律对分数加法不适用。 ($\quad$)
(2)$1-\frac{2}{5}-\frac{3}{5}=0$ ($\quad$)
(3)$\frac{1}{3}+\frac{1}{4}+\frac{5}{12}=1$ ($\quad$)
答案
(1) ×
(2) $1-\frac{2}{5}-\frac{3}{5}=1-(\frac{2}{5}+\frac{3}{5})=1-1=0$，√
(3) $\frac{1}{3}+\frac{1}{4}+\frac{5}{12}=\frac{4}{12}+\frac{3}{12}+\frac{5}{12}=1$，√
(2) $1-\frac{2}{5}-\frac{3}{5}=1-(\frac{2}{5}+\frac{3}{5})=1-1=0$，√
(3) $\frac{1}{3}+\frac{1}{4}+\frac{5}{12}=\frac{4}{12}+\frac{3}{12}+\frac{5}{12}=1$，√
3. 计算下面各题。
$\frac{8}{19}-(\frac{8}{19}-\frac{2}{9})$
$1\frac{5}{6}+\frac{5}{11}+\frac{1}{6}+\frac{6}{11}$
$\frac{17}{12}-(\frac{5}{8}+\frac{5}{12})$
$\frac{8}{19}-(\frac{8}{19}-\frac{2}{9})$
$1\frac{5}{6}+\frac{5}{11}+\frac{1}{6}+\frac{6}{11}$
$\frac{17}{12}-(\frac{5}{8}+\frac{5}{12})$
答案
$\frac{8}{19}-(\frac{8}{19}-\frac{2}{9})$
$=\frac{8}{19}-\frac{8}{19}+\frac{2}{9}$
$=0+\frac{2}{9}$
$=\frac{2}{9}$
$1\frac{5}{6}+\frac{5}{11}+\frac{1}{6}+\frac{6}{11}$
$=(1\frac{5}{6}+\frac{1}{6})+(\frac{5}{11}+\frac{6}{11})$
$=2+1$
$=3$
$\frac{17}{12}-(\frac{5}{8}+\frac{5}{12})$
$=\frac{17}{12}-\frac{5}{12}-\frac{5}{8}$
$=1-\frac{5}{8}$
$=\frac{3}{8}$
$=\frac{8}{19}-\frac{8}{19}+\frac{2}{9}$
$=0+\frac{2}{9}$
$=\frac{2}{9}$
$1\frac{5}{6}+\frac{5}{11}+\frac{1}{6}+\frac{6}{11}$
$=(1\frac{5}{6}+\frac{1}{6})+(\frac{5}{11}+\frac{6}{11})$
$=2+1$
$=3$
$\frac{17}{12}-(\frac{5}{8}+\frac{5}{12})$
$=\frac{17}{12}-\frac{5}{12}-\frac{5}{8}$
$=1-\frac{5}{8}$
$=\frac{3}{8}$
