登录
口算
$\frac{1}{16}+\frac{7}{16}=$
$\frac{2}{7}+\frac{1}{5}=$
$\frac{7}{15}-\frac{1}{3}=$
$\frac{1}{4}+\frac{3}{16}=$
$\frac{7}{18}+\frac{3}{18}=$
$\frac{7}{9}-\frac{2}{3}=$
$\frac{5}{6}+\frac{7}{8}=$
$\frac{5}{8}+\frac{3}{8}=$
$\frac{1}{16}+\frac{7}{16}=$
$\frac{2}{7}+\frac{1}{5}=$
$\frac{7}{15}-\frac{1}{3}=$
$\frac{1}{4}+\frac{3}{16}=$
$\frac{7}{18}+\frac{3}{18}=$
$\frac{7}{9}-\frac{2}{3}=$
$\frac{5}{6}+\frac{7}{8}=$
$\frac{5}{8}+\frac{3}{8}=$
答案
$\frac{1}{16}+\frac{7}{16}=\frac{1+7}{16}=\frac{8}{16}=\frac{1}{2}$
$\frac{2}{7}+\frac{1}{5}=\frac{10}{35}+\frac{7}{35}=\frac{17}{35}$
$\frac{7}{15}-\frac{1}{3}=\frac{7}{15}-\frac{5}{15}=\frac{2}{15}$
$\frac{1}{4}+\frac{3}{16}=\frac{4}{16}+\frac{3}{16}=\frac{7}{16}$
$\frac{7}{18}+\frac{3}{18}=\frac{7+3}{18}=\frac{10}{18}=\frac{5}{9}$
$\frac{7}{9}-\frac{2}{3}=\frac{7}{9}-\frac{6}{9}=\frac{1}{9}$
$\frac{5}{6}+\frac{7}{8}=\frac{20}{24}+\frac{21}{24}=\frac{41}{24}$
$\frac{5}{8}+\frac{3}{8}=\frac{5+3}{8}=\frac{8}{8}=1$
$\frac{2}{7}+\frac{1}{5}=\frac{10}{35}+\frac{7}{35}=\frac{17}{35}$
$\frac{7}{15}-\frac{1}{3}=\frac{7}{15}-\frac{5}{15}=\frac{2}{15}$
$\frac{1}{4}+\frac{3}{16}=\frac{4}{16}+\frac{3}{16}=\frac{7}{16}$
$\frac{7}{18}+\frac{3}{18}=\frac{7+3}{18}=\frac{10}{18}=\frac{5}{9}$
$\frac{7}{9}-\frac{2}{3}=\frac{7}{9}-\frac{6}{9}=\frac{1}{9}$
$\frac{5}{6}+\frac{7}{8}=\frac{20}{24}+\frac{21}{24}=\frac{41}{24}$
$\frac{5}{8}+\frac{3}{8}=\frac{5+3}{8}=\frac{8}{8}=1$
4. 找规律，算一算。
$\frac{1}{2}+\frac{1}{4}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}+\frac{1}{1024}=$
$\frac{1}{2}+\frac{1}{4}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}+\frac{1}{1024}=$
答案
4.$\frac{1}{2}+\frac{1}{4}=\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})-\frac{1}{4}=(\frac{1}{2}+\frac{1}{2})-$
$\frac{1}{4}=1-\frac{1}{4}=\frac{3}{4}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}=\frac{1}{2}+\frac{1}{4}+(\frac{1}{8}+\frac{1}{8})-\frac{1}{8}=$
$\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})-\frac{1}{8}=(\frac{1}{2}+\frac{1}{2})-\frac{1}{8}=1-$
$\frac{1}{8}=\frac{7}{8}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+(\frac{1}{16}+\frac{1}{16})-$
$\frac{1}{16}=\frac{1}{2}+\frac{1}{4}+(\frac{1}{8}+\frac{1}{8})-\frac{1}{16}=\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})-$
$\frac{1}{16}=(\frac{1}{2}+\frac{1}{2})-\frac{1}{16}=1-\frac{1}{16}=\frac{15}{16}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=1-\frac{1}{32}=\frac{31}{32}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+$
$\frac{1}{512}+\frac{1}{1024}=1-\frac{1}{1024}=\frac{1023}{1024}$
$\frac{1}{4}=1-\frac{1}{4}=\frac{3}{4}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}=\frac{1}{2}+\frac{1}{4}+(\frac{1}{8}+\frac{1}{8})-\frac{1}{8}=$
$\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})-\frac{1}{8}=(\frac{1}{2}+\frac{1}{2})-\frac{1}{8}=1-$
$\frac{1}{8}=\frac{7}{8}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+(\frac{1}{16}+\frac{1}{16})-$
$\frac{1}{16}=\frac{1}{2}+\frac{1}{4}+(\frac{1}{8}+\frac{1}{8})-\frac{1}{16}=\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})-$
$\frac{1}{16}=(\frac{1}{2}+\frac{1}{2})-\frac{1}{16}=1-\frac{1}{16}=\frac{15}{16}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=1-\frac{1}{32}=\frac{31}{32}$
$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+$
$\frac{1}{512}+\frac{1}{1024}=1-\frac{1}{1024}=\frac{1023}{1024}$
5. 已知$\frac{5}{6}=\frac{1}{2}+\frac{1}{3}$，$\frac{7}{12}=\frac{1}{3}+\frac{1}{4}$，$\frac{9}{20}=\frac{1}{4}+\frac{1}{5}$，……
计算：$1+\frac{1}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}$
计算：$1+\frac{1}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}$
答案
5.$1+\frac{1}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}=1+\frac{1}{2}-$
$(\frac{1}{2}+\frac{1}{3})+(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+$
$(\frac{1}{5}+\frac{1}{6})-(\frac{1}{6}+\frac{1}{7})=1-\frac{1}{7}=\frac{6}{7}$
$(\frac{1}{2}+\frac{1}{3})+(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+$
$(\frac{1}{5}+\frac{1}{6})-(\frac{1}{6}+\frac{1}{7})=1-\frac{1}{7}=\frac{6}{7}$
6. 仔细观察，发现规律。
$\frac{1}{1×2}=1-\frac{1}{2}$ $\frac{1}{2×3}=\frac{1}{2}-\frac{1}{3}$ $\frac{1}{3×4}=\frac{1}{3}-\frac{1}{4}$ $\frac{1}{4×5}=\frac{1}{4}-\frac{1}{5}$
计算：$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}$
$\frac{1}{1×2}=1-\frac{1}{2}$ $\frac{1}{2×3}=\frac{1}{2}-\frac{1}{3}$ $\frac{1}{3×4}=\frac{1}{3}-\frac{1}{4}$ $\frac{1}{4×5}=\frac{1}{4}-\frac{1}{5}$
计算：$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}$
答案
6.$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}=$
$(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+$
$(\frac{1}{4}-\frac{1}{5})+(\frac{1}{5}-\frac{1}{6})+(\frac{1}{6}-\frac{1}{7})+$
$(\frac{1}{7}-\frac{1}{8})+(\frac{1}{8}-\frac{1}{9})=1-\frac{1}{9}=\frac{8}{9}$
$(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+$
$(\frac{1}{4}-\frac{1}{5})+(\frac{1}{5}-\frac{1}{6})+(\frac{1}{6}-\frac{1}{7})+$
$(\frac{1}{7}-\frac{1}{8})+(\frac{1}{8}-\frac{1}{9})=1-\frac{1}{9}=\frac{8}{9}$
