Question

17．算一算．
①$\frac{1}{6}+$$\frac{1}{20}+$$\frac{1}{30}+$ $\frac{1}{42}$    ②$\frac{1}{2}$+$\frac{1}{4}$+$\frac{1}{8}$+$\frac{1}{16}$+$\frac{1}{32}$+$\frac{1}{64}$．

Answer 1

分析 （1）利用拆分法進(jìn)行計(jì)算；
（2）采用拆分法將式子變形進(jìn)行簡(jiǎn)算．

解答 解：（1）$\frac{1}{6}+$$\frac{1}{20}+$$\frac{1}{30}+$ $\frac{1}{42}$  
=$\frac{1}{6}$+（$\frac{1}{4}$$-\frac{1}{5}$）+（$\frac{1}{5}$$-\frac{1}{6}$）+（$\frac{1}{6}$$-\frac{1}{7}$）
=$\frac{1}{6}$$+\frac{1}{4}$$-\frac{1}{7}$
=$\frac{14}{84}$$+\frac{21}{84}$$-\frac{12}{84}$
=$\frac{23}{84}$

（2）$\frac{1}{2}$+$\frac{1}{4}$+$\frac{1}{8}$+$\frac{1}{16}$+$\frac{1}{32}$+$\frac{1}{64}$
=$\frac{1}{2}$$+\frac{1}{2}$$-\frac{1}{4}$$+\frac{1}{4}$$-\frac{1}{8}$$+\frac{1}{8}$$-\frac{1}{16}$$+\frac{1}{16}$$-\frac{1}{32}$$+\frac{1}{32}$$-\frac{1}{64}$
=1-$\frac{1}{64}$
=$\frac{63}{64}$

點(diǎn)評(píng) 考查學(xué)生對(duì)于加法運(yùn)算定律和分?jǐn)?shù)拆分法的應(yīng)用．