Question

9．計(jì)算$\frac{1}{3}+\frac{3}{4}+\frac{2}{5}+\frac{5}{7}+\frac{7}{8}+\frac{9}{20}+\frac{10}{21}+\frac{11}{24}+\frac{18}{35}$．

Answer 1

分析 $\frac{9}{20}$=$\frac{1}{4}$+$\frac{1}{5}$，$\frac{10}{21}$=$\frac{1}{3}$+$\frac{1}{7}$，$\frac{11}{24}$=$\frac{1}{3}$+$\frac{1}{8}$，$\frac{18}{35}$=$\frac{19}{35}$-$\frac{1}{35}$=$\frac{2}{5}$+$\frac{1}{7}$-$\frac{1}{35}$，然后再根據(jù)加法交換律和結(jié)合律進(jìn)行簡算．

解答 解：$\frac{1}{3}+\frac{3}{4}+\frac{2}{5}+\frac{5}{7}+\frac{7}{8}+\frac{9}{20}+\frac{10}{21}+\frac{11}{24}+\frac{18}{35}$
=$\frac{1}{3}$+$\frac{3}{4}$+$\frac{2}{5}$+$\frac{5}{7}$+$\frac{7}{8}$+（$\frac{1}{4}$+$\frac{1}{5}$）+（$\frac{1}{3}$+$\frac{1}{7}$）+（$\frac{1}{3}$+$\frac{1}{8}$）+（$\frac{2}{5}$+$\frac{1}{7}$-$\frac{1}{35}$）
=（$\frac{1}{3}$+$\frac{1}{3}$+$\frac{1}{3}$）+（$\frac{3}{4}$+$\frac{1}{4}$）+（$\frac{5}{7}+\frac{1}{7}+\frac{1}{7}$）+（$\frac{2}{5}+\frac{1}{5}+\frac{2}{5}$）+（$\frac{7}{8}+\frac{1}{8}$）-$\frac{1}{35}$
=1+1+1+1+1-$\frac{1}{35}$
=5-$\frac{1}{35}$
=4$\frac{34}{35}$．

點(diǎn)評 此題考查了簡便運(yùn)算，靈活運(yùn)用運(yùn)算技巧或運(yùn)算定律進(jìn)行簡便計(jì)算．