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2. 用简便方法计算。
$0.75 + \frac{1}{2} + \frac{1}{4}$
$3\frac{3}{8} - \frac{2}{7} - \frac{5}{7}$
$( \frac{1}{12} + \frac{1}{4} ) + ( \frac{5}{12} + \frac{3}{4} )$
$0.75 + \frac{1}{2} + \frac{1}{4}$
$3\frac{3}{8} - \frac{2}{7} - \frac{5}{7}$
$( \frac{1}{12} + \frac{1}{4} ) + ( \frac{5}{12} + \frac{3}{4} )$
答案
$0.75 + \frac{1}{2} + \frac{1}{4}$
$=0.75 + \frac{1}{4} + \frac{1}{2}$
$=0.75 + 0.25 + 0.5$
$=1 + 0.5$
$=1.5$
$3\frac{3}{8} - \frac{2}{7} - \frac{5}{7}$
$=3\frac{3}{8} - (\frac{2}{7} + \frac{5}{7})$
$=3\frac{3}{8} - 1$
$=2\frac{3}{8}$
$(\frac{1}{12} + \frac{1}{4}) + (\frac{5}{12} + \frac{3}{4})$
$=(\frac{1}{12} + \frac{5}{12}) + (\frac{1}{4} + \frac{3}{4})$
$=\frac{6}{12} + 1$
$=\frac{1}{2} + 1$
$=1\frac{1}{2}$
$=0.75 + \frac{1}{4} + \frac{1}{2}$
$=0.75 + 0.25 + 0.5$
$=1 + 0.5$
$=1.5$
$3\frac{3}{8} - \frac{2}{7} - \frac{5}{7}$
$=3\frac{3}{8} - (\frac{2}{7} + \frac{5}{7})$
$=3\frac{3}{8} - 1$
$=2\frac{3}{8}$
$(\frac{1}{12} + \frac{1}{4}) + (\frac{5}{12} + \frac{3}{4})$
$=(\frac{1}{12} + \frac{5}{12}) + (\frac{1}{4} + \frac{3}{4})$
$=\frac{6}{12} + 1$
$=\frac{1}{2} + 1$
$=1\frac{1}{2}$
3. 用递等式计算。
$\frac{5}{6} - \frac{1}{4} + \frac{1}{3}$
$\frac{7}{8} + \frac{1}{6} - \frac{5}{12}$
$( \frac{2}{3} + \frac{1}{4} ) + \frac{3}{5}$
$\frac{5}{6} - \frac{1}{4} + \frac{1}{3}$
$\frac{7}{8} + \frac{1}{6} - \frac{5}{12}$
$( \frac{2}{3} + \frac{1}{4} ) + \frac{3}{5}$
答案
$\frac{5}{6} - \frac{1}{4} + \frac{1}{3}$
$= \frac{10}{12} - \frac{3}{12} + \frac{4}{12}$
$= \frac{10 - 3 + 4}{12}$
$= \frac{11}{12}$
$\frac{7}{8} + \frac{1}{6} - \frac{5}{12}$
$= \frac{21}{24} + \frac{4}{24} - \frac{10}{24}$
$= \frac{21 + 4 - 10}{24}$
$= \frac{15}{24}$
$= \frac{5}{8}$
$(\frac{2}{3} + \frac{1}{4}) + \frac{3}{5}$
$= (\frac{8}{12} + \frac{3}{12}) + \frac{3}{5}$
$= \frac{11}{12} + \frac{3}{5}$
$= \frac{55}{60} + \frac{36}{60}$
$= \frac{91}{60}$
$= \frac{10}{12} - \frac{3}{12} + \frac{4}{12}$
$= \frac{10 - 3 + 4}{12}$
$= \frac{11}{12}$
$\frac{7}{8} + \frac{1}{6} - \frac{5}{12}$
$= \frac{21}{24} + \frac{4}{24} - \frac{10}{24}$
$= \frac{21 + 4 - 10}{24}$
$= \frac{15}{24}$
$= \frac{5}{8}$
$(\frac{2}{3} + \frac{1}{4}) + \frac{3}{5}$
$= (\frac{8}{12} + \frac{3}{12}) + \frac{3}{5}$
$= \frac{11}{12} + \frac{3}{5}$
$= \frac{55}{60} + \frac{36}{60}$
$= \frac{91}{60}$
4. 解方程。
$\frac{3}{5} + x = \frac{9}{10}$
$\frac{7}{10} + x + \frac{1}{2} = \frac{15}{8}$
$\frac{4}{5} - x + \frac{1}{3} = \frac{4}{7}$
$\frac{3}{5} + x = \frac{9}{10}$
$\frac{7}{10} + x + \frac{1}{2} = \frac{15}{8}$
$\frac{4}{5} - x + \frac{1}{3} = \frac{4}{7}$
答案
解：
$\frac{3}{5} + x = \frac{9}{10}$
$x = \frac{9}{10} - \frac{3}{5}$
$x = \frac{9}{10} - \frac{6}{10}$
$x = \frac{3}{10}$
解：
$\frac{7}{10} + x + \frac{1}{2} = \frac{15}{8}$
$\frac{7}{10} + \frac{5}{10} + x = \frac{15}{8}$
$\frac{6}{5} + x = \frac{15}{8}$
$x = \frac{15}{8} - \frac{6}{5}$
$x = \frac{75}{40} - \frac{48}{40}$
$x = \frac{27}{40}$
解：
$\frac{4}{5} - x + \frac{1}{3} = \frac{4}{7}$
$\frac{12}{15} + \frac{5}{15} - x = \frac{4}{7}$
$\frac{17}{15} - x = \frac{4}{7}$
$x = \frac{17}{15} - \frac{4}{7}$
$x = \frac{119}{105} - \frac{60}{105}$
$x = \frac{59}{105}$
$\frac{3}{5} + x = \frac{9}{10}$
$x = \frac{9}{10} - \frac{3}{5}$
$x = \frac{9}{10} - \frac{6}{10}$
$x = \frac{3}{10}$
解：
$\frac{7}{10} + x + \frac{1}{2} = \frac{15}{8}$
$\frac{7}{10} + \frac{5}{10} + x = \frac{15}{8}$
$\frac{6}{5} + x = \frac{15}{8}$
$x = \frac{15}{8} - \frac{6}{5}$
$x = \frac{75}{40} - \frac{48}{40}$
$x = \frac{27}{40}$
解：
$\frac{4}{5} - x + \frac{1}{3} = \frac{4}{7}$
$\frac{12}{15} + \frac{5}{15} - x = \frac{4}{7}$
$\frac{17}{15} - x = \frac{4}{7}$
$x = \frac{17}{15} - \frac{4}{7}$
$x = \frac{119}{105} - \frac{60}{105}$
$x = \frac{59}{105}$
三、把下面的分数填入相应的圈里。
$\frac{1}{2}$ $\frac{3}{2}$ $\frac{6}{6}$ $\frac{14}{14}$ $\frac{23}{12}$ $\frac{39}{40}$ $\frac{37}{16}$
$\frac{1}{2}$ $\frac{3}{2}$ $\frac{6}{6}$ $\frac{14}{14}$ $\frac{23}{12}$ $\frac{39}{40}$ $\frac{37}{16}$
答案
三、真分数$\frac{1}{2}$ $\frac{39}{40}$
假分数$\frac{3}{2}$ $\frac{6}{6}$ $\frac{14}{14}$ $\frac{23}{12}$ $\frac{37}{16}$
假分数$\frac{3}{2}$ $\frac{6}{6}$ $\frac{14}{14}$ $\frac{23}{12}$ $\frac{37}{16}$
