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1. 直接写出得数。
$0.2 - \frac{1}{5} =$ $\frac{1}{2} + \frac{1}{5} =$ $\frac{13}{18} + \frac{7}{18} =$
$\frac{3}{2} - \frac{1}{2} =$ $\frac{7}{15} + \frac{8}{15} =$ $1 - \frac{3}{10} - \frac{3}{10} =$
$\frac{3}{4} - \frac{1}{2} =$ $\frac{1}{3} + \frac{1}{6} =$ $\frac{1}{7} - \frac{1}{9} =$
$\frac{2}{3} + \frac{1}{5} =$ $1 - \frac{9}{16} =$ $\frac{2}{9} + \frac{4}{9} =$
$\frac{1}{5} + \frac{1}{3} =$ $\frac{3}{4} - \frac{5}{8} =$ $\frac{8}{9} + \frac{4}{11} + \frac{1}{9} =$
$\frac{1}{5} - \frac{1}{7} =$ $\frac{3}{7} + \frac{1}{4} =$ $\frac{11}{8} - \frac{1}{8} =$
$1 - \frac{1}{6} - \frac{1}{6} =$ $\frac{7}{8} - \frac{3}{8} + \frac{3}{8} =$
$0.2 - \frac{1}{5} =$ $\frac{1}{2} + \frac{1}{5} =$ $\frac{13}{18} + \frac{7}{18} =$
$\frac{3}{2} - \frac{1}{2} =$ $\frac{7}{15} + \frac{8}{15} =$ $1 - \frac{3}{10} - \frac{3}{10} =$
$\frac{3}{4} - \frac{1}{2} =$ $\frac{1}{3} + \frac{1}{6} =$ $\frac{1}{7} - \frac{1}{9} =$
$\frac{2}{3} + \frac{1}{5} =$ $1 - \frac{9}{16} =$ $\frac{2}{9} + \frac{4}{9} =$
$\frac{1}{5} + \frac{1}{3} =$ $\frac{3}{4} - \frac{5}{8} =$ $\frac{8}{9} + \frac{4}{11} + \frac{1}{9} =$
$\frac{1}{5} - \frac{1}{7} =$ $\frac{3}{7} + \frac{1}{4} =$ $\frac{11}{8} - \frac{1}{8} =$
$1 - \frac{1}{6} - \frac{1}{6} =$ $\frac{7}{8} - \frac{3}{8} + \frac{3}{8} =$
答案
0；$\frac{7}{10}$；$\frac{10}{9}$；1；1；$\frac{2}{5}$；$\frac{1}{4}$；$\frac{1}{2}$；$\frac{2}{63}$；$\frac{13}{15}$；$\frac{7}{16}$；$\frac{2}{3}$；$\frac{8}{15}$；$\frac{1}{8}$；$\frac{15}{11}$；$\frac{2}{35}$；$\frac{19}{28}$；$\frac{5}{4}$；$\frac{2}{3}$；$\frac{7}{8}$
解析
1. $0.2-\frac{1}{5}=0.2 - 0.2=0$；
2. $\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}$；
3. $\frac{13}{18}+\frac{7}{18}=\frac{13 + 7}{18}=\frac{20}{18}=\frac{10}{9}$；
4. $\frac{3}{2}-\frac{1}{2}=\frac{3 - 1}{2}=1$；
5. $\frac{7}{15}+\frac{8}{15}=\frac{7 + 8}{15}=1$；
6. $1-\frac{3}{10}-\frac{3}{10}=1-(\frac{3}{10}+\frac{3}{10})=1-\frac{6}{10}=\frac{4}{10}=\frac{2}{5}$；
7. $\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$；
8. $\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$；
9. $\frac{1}{7}-\frac{1}{9}=\frac{9}{63}-\frac{7}{63}=\frac{2}{63}$；
10. $\frac{2}{3}+\frac{1}{5}=\frac{10}{15}+\frac{3}{15}=\frac{13}{15}$；
11. $1-\frac{9}{16}=\frac{16}{16}-\frac{9}{16}=\frac{7}{16}$；
12. $\frac{2}{9}+\frac{4}{9}=\frac{2 + 4}{9}=\frac{6}{9}=\frac{2}{3}$；
13. $\frac{1}{5}+\frac{1}{3}=\frac{3}{15}+\frac{5}{15}=\frac{8}{15}$；
14. $\frac{3}{4}-\frac{5}{8}=\frac{6}{8}-\frac{5}{8}=\frac{1}{8}$；
15. $\frac{8}{9}+\frac{4}{11}+\frac{1}{9}=(\frac{8}{9}+\frac{1}{9})+\frac{4}{11}=1+\frac{4}{11}=\frac{15}{11}$；
16. $\frac{1}{5}-\frac{1}{7}=\frac{7}{35}-\frac{5}{35}=\frac{2}{35}$；
17. $\frac{3}{7}+\frac{1}{4}=\frac{12}{28}+\frac{7}{28}=\frac{19}{28}$；
18. $\frac{11}{8}-\frac{1}{8}=\frac{11 - 1}{8}=\frac{10}{8}=\frac{5}{4}$；
19. $1-\frac{1}{6}-\frac{1}{6}=1-(\frac{1}{6}+\frac{1}{6})=1-\frac{2}{6}=\frac{4}{6}=\frac{2}{3}$；
20. $\frac{7}{8}-\frac{3}{8}+\frac{3}{8}=\frac{7 - 3+3}{8}=\frac{7}{8}$；
2. $\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}$；
3. $\frac{13}{18}+\frac{7}{18}=\frac{13 + 7}{18}=\frac{20}{18}=\frac{10}{9}$；
4. $\frac{3}{2}-\frac{1}{2}=\frac{3 - 1}{2}=1$；
5. $\frac{7}{15}+\frac{8}{15}=\frac{7 + 8}{15}=1$；
6. $1-\frac{3}{10}-\frac{3}{10}=1-(\frac{3}{10}+\frac{3}{10})=1-\frac{6}{10}=\frac{4}{10}=\frac{2}{5}$；
7. $\frac{3}{4}-\frac{1}{2}=\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$；
8. $\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$；
9. $\frac{1}{7}-\frac{1}{9}=\frac{9}{63}-\frac{7}{63}=\frac{2}{63}$；
10. $\frac{2}{3}+\frac{1}{5}=\frac{10}{15}+\frac{3}{15}=\frac{13}{15}$；
11. $1-\frac{9}{16}=\frac{16}{16}-\frac{9}{16}=\frac{7}{16}$；
12. $\frac{2}{9}+\frac{4}{9}=\frac{2 + 4}{9}=\frac{6}{9}=\frac{2}{3}$；
13. $\frac{1}{5}+\frac{1}{3}=\frac{3}{15}+\frac{5}{15}=\frac{8}{15}$；
14. $\frac{3}{4}-\frac{5}{8}=\frac{6}{8}-\frac{5}{8}=\frac{1}{8}$；
15. $\frac{8}{9}+\frac{4}{11}+\frac{1}{9}=(\frac{8}{9}+\frac{1}{9})+\frac{4}{11}=1+\frac{4}{11}=\frac{15}{11}$；
16. $\frac{1}{5}-\frac{1}{7}=\frac{7}{35}-\frac{5}{35}=\frac{2}{35}$；
17. $\frac{3}{7}+\frac{1}{4}=\frac{12}{28}+\frac{7}{28}=\frac{19}{28}$；
18. $\frac{11}{8}-\frac{1}{8}=\frac{11 - 1}{8}=\frac{10}{8}=\frac{5}{4}$；
19. $1-\frac{1}{6}-\frac{1}{6}=1-(\frac{1}{6}+\frac{1}{6})=1-\frac{2}{6}=\frac{4}{6}=\frac{2}{3}$；
20. $\frac{7}{8}-\frac{3}{8}+\frac{3}{8}=\frac{7 - 3+3}{8}=\frac{7}{8}$；
2. 计算。（能简算的要简算。）
$\frac{4}{5} + (\frac{3}{8} - \frac{1}{4})$ $2 - \frac{3}{7} - \frac{4}{7}$
$\frac{5}{8} - \frac{1}{3} + \frac{5}{12}$ $\frac{1}{5} + \frac{1}{2} + \frac{1}{10}$
$\frac{5}{12} - (\frac{1}{2} - \frac{1}{12})$ $\frac{1}{6} + \frac{5}{6} + \frac{1}{6}$
$\frac{7}{12} + \frac{2}{5} + \frac{5}{12}$ $\frac{9}{10} - (\frac{2}{5} + \frac{1}{4})$
$\frac{9}{7} + \frac{1}{8} + \frac{5}{7} + \frac{3}{8}$ $\frac{7}{8} - \frac{4}{5} + \frac{9}{8} - \frac{1}{5}$
$\frac{4}{3} - \frac{1}{8} + \frac{7}{12}$ $\frac{5}{8} - (\frac{5}{8} - \frac{1}{2})$
$\frac{1}{12} + \frac{3}{8} + \frac{11}{12} + \frac{5}{8}$ $8 - \frac{9}{16} - \frac{7}{16}$
$\frac{7}{8} - \frac{3}{4} + \frac{1}{8}$ $\frac{2}{3} + (\frac{4}{17} + \frac{3}{3})$
$\frac{8}{9} + \frac{7}{15} + \frac{1}{9} - \frac{4}{15}$ $\frac{7}{12} - (\frac{3}{4} - \frac{1}{2})$
$\frac{4}{5} + (\frac{3}{8} - \frac{1}{4})$ $2 - \frac{3}{7} - \frac{4}{7}$
$\frac{5}{8} - \frac{1}{3} + \frac{5}{12}$ $\frac{1}{5} + \frac{1}{2} + \frac{1}{10}$
$\frac{5}{12} - (\frac{1}{2} - \frac{1}{12})$ $\frac{1}{6} + \frac{5}{6} + \frac{1}{6}$
$\frac{7}{12} + \frac{2}{5} + \frac{5}{12}$ $\frac{9}{10} - (\frac{2}{5} + \frac{1}{4})$
$\frac{9}{7} + \frac{1}{8} + \frac{5}{7} + \frac{3}{8}$ $\frac{7}{8} - \frac{4}{5} + \frac{9}{8} - \frac{1}{5}$
$\frac{4}{3} - \frac{1}{8} + \frac{7}{12}$ $\frac{5}{8} - (\frac{5}{8} - \frac{1}{2})$
$\frac{1}{12} + \frac{3}{8} + \frac{11}{12} + \frac{5}{8}$ $8 - \frac{9}{16} - \frac{7}{16}$
$\frac{7}{8} - \frac{3}{4} + \frac{1}{8}$ $\frac{2}{3} + (\frac{4}{17} + \frac{3}{3})$
$\frac{8}{9} + \frac{7}{15} + \frac{1}{9} - \frac{4}{15}$ $\frac{7}{12} - (\frac{3}{4} - \frac{1}{2})$
答案
$\frac{37}{40}$，$1$，$\frac{17}{24}$，$\frac{4}{5}$，$0$，$\frac{7}{6}$，$\frac{7}{5}$，$\frac{1}{4}$，$\frac{5}{2}$，$1$，$\frac{43}{24}$，$\frac{1}{2}$，$2$，$7$，$\frac{1}{4}$，$1\frac{46}{51}$（或 $\frac{97}{51}$），$1\frac{1}{5}$，$\frac{1}{3}$
解析
1. $\frac{4}{5} + (\frac{3}{8} - \frac{1}{4})$
先算括号内：$\frac{3}{8} - \frac{1}{4} = \frac{3}{8} - \frac{2}{8} = \frac{1}{8}$
再算加法：$\frac{4}{5} + \frac{1}{8} = \frac{32}{40} + \frac{5}{40} = \frac{37}{40}$
2. $2 - \frac{3}{7} - \frac{4}{7}$
利用减法结合律：$2 - (\frac{3}{7} + \frac{4}{7}) = 2 - 1 = 1$
3. $\frac{5}{8} - \frac{1}{3} + \frac{5}{12}$
先通分：$\frac{5}{8} = \frac{15}{24}$，$\frac{1}{3} = \frac{8}{24}$，$\frac{5}{12} = \frac{10}{24}$
再计算：$\frac{15}{24} - \frac{8}{24} + \frac{10}{24} = \frac{17}{24}$
4. $\frac{1}{5} + \frac{1}{2} + \frac{1}{10}$
先通分：$\frac{1}{5} = \frac{2}{10}$，$\frac{1}{2} = \frac{5}{10}$
再计算：$\frac{2}{10} + \frac{5}{10} + \frac{1}{10} = \frac{8}{10} = \frac{4}{5}$
5. $\frac{5}{12} - (\frac{1}{2} - \frac{1}{12})$
先算括号内：$\frac{1}{2} - \frac{1}{12} = \frac{6}{12} - \frac{1}{12} = \frac{5}{12}$
再算减法：$\frac{5}{12} - \frac{5}{12} = 0$
6. $\frac{1}{6} + \frac{5}{6} + \frac{1}{6} = \frac{7}{6}$
7. $\frac{7}{12} + \frac{2}{5} + \frac{5}{12}$
利用加法交换律：$\frac{7}{12} + \frac{5}{12} + \frac{2}{5} = 1 + \frac{2}{5} = \frac{7}{5}$
8. $\frac{9}{10} - (\frac{2}{5} + \frac{1}{4})$
先算括号内：$\frac{2}{5} + \frac{1}{4} = \frac{8}{20} + \frac{5}{20} = \frac{13}{20}$
再算减法：$\frac{9}{10} - \frac{13}{20} = \frac{18}{20} - \frac{13}{20} = \frac{5}{20} = \frac{1}{4}$
9. $\frac{9}{7} + \frac{1}{8} + \frac{5}{7} + \frac{3}{8}$
利用加法交换律和结合律：$(\frac{9}{7} + \frac{5}{7}) + (\frac{1}{8} + \frac{3}{8}) = 2 + \frac{1}{2} = \frac{5}{2}$
10. $\frac{7}{8} - \frac{4}{5} + \frac{9}{8} - \frac{1}{5}$
利用加法交换律和结合律以及减法性质：$(\frac{7}{8} + \frac{9}{8}) - (\frac{4}{5} + \frac{1}{5}) = 2 - 1 = 1$
11. $\frac{4}{3} - \frac{1}{8} + \frac{7}{12}$
先通分：$\frac{4}{3} = \frac{32}{24}$，$\frac{1}{8} = \frac{3}{24}$，$\frac{7}{12} = \frac{14}{24}$
再计算：$\frac{32}{24} - \frac{3}{24} + \frac{14}{24} = \frac{43}{24}$
12. $\frac{5}{8} - (\frac{5}{8} - \frac{1}{2}) = \frac{1}{2}$
13. $\frac{1}{12} + \frac{3}{8} + \frac{11}{12} + \frac{5}{8}$
利用加法交换律和结合律：$(\frac{1}{12} + \frac{11}{12}) + (\frac{3}{8} + \frac{5}{8}) = 1 + 1 = 2$
14. $8 - \frac{9}{16} - \frac{7}{16}$
利用减法结合律：$8 - (\frac{9}{16} + \frac{7}{16}) = 8 - 1 = 7$
15. $\frac{7}{8} - \frac{3}{4} + \frac{1}{8}$
利用加法交换律：$\frac{7}{8} + \frac{1}{8} - \frac{3}{4} = 1 - \frac{3}{4} = \frac{1}{4}$
16. $\frac{2}{3} + (\frac{4}{17} + \frac{3}{3}) = \frac{2}{3} + 1 + \frac{4}{17} = 1\frac{2}{3} + \frac{4}{17} = \frac{85}{51} + \frac{12}{51} = \frac{97}{51} = 1\frac{46}{51}$（或写为$\frac{97}{51}$，但通常化为带分数）
但考虑到简化，可直接写为：$\frac{2}{3} + 1 + \frac{4}{17} = \frac{97}{51}$ 或 $1\frac{46}{51}$
17. $\frac{8}{9} + \frac{7}{15} + \frac{1}{9} - \frac{4}{15}$
利用加法交换律和结合律以及减法性质：$(\frac{8}{9} + \frac{1}{9}) + (\frac{7}{15} - \frac{4}{15}) = 1 + \frac{3}{15} = 1\frac{1}{5}$
18. $\frac{7}{12} - (\frac{3}{4} - \frac{1}{2})$
先算括号内：$\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$
再算减法：$\frac{7}{12} - \frac{1}{4} = \frac{7}{12} - \frac{3}{12} = \frac{4}{12} = \frac{1}{3}$
先算括号内：$\frac{3}{8} - \frac{1}{4} = \frac{3}{8} - \frac{2}{8} = \frac{1}{8}$
再算加法：$\frac{4}{5} + \frac{1}{8} = \frac{32}{40} + \frac{5}{40} = \frac{37}{40}$
2. $2 - \frac{3}{7} - \frac{4}{7}$
利用减法结合律：$2 - (\frac{3}{7} + \frac{4}{7}) = 2 - 1 = 1$
3. $\frac{5}{8} - \frac{1}{3} + \frac{5}{12}$
先通分：$\frac{5}{8} = \frac{15}{24}$，$\frac{1}{3} = \frac{8}{24}$，$\frac{5}{12} = \frac{10}{24}$
再计算：$\frac{15}{24} - \frac{8}{24} + \frac{10}{24} = \frac{17}{24}$
4. $\frac{1}{5} + \frac{1}{2} + \frac{1}{10}$
先通分：$\frac{1}{5} = \frac{2}{10}$，$\frac{1}{2} = \frac{5}{10}$
再计算：$\frac{2}{10} + \frac{5}{10} + \frac{1}{10} = \frac{8}{10} = \frac{4}{5}$
5. $\frac{5}{12} - (\frac{1}{2} - \frac{1}{12})$
先算括号内：$\frac{1}{2} - \frac{1}{12} = \frac{6}{12} - \frac{1}{12} = \frac{5}{12}$
再算减法：$\frac{5}{12} - \frac{5}{12} = 0$
6. $\frac{1}{6} + \frac{5}{6} + \frac{1}{6} = \frac{7}{6}$
7. $\frac{7}{12} + \frac{2}{5} + \frac{5}{12}$
利用加法交换律：$\frac{7}{12} + \frac{5}{12} + \frac{2}{5} = 1 + \frac{2}{5} = \frac{7}{5}$
8. $\frac{9}{10} - (\frac{2}{5} + \frac{1}{4})$
先算括号内：$\frac{2}{5} + \frac{1}{4} = \frac{8}{20} + \frac{5}{20} = \frac{13}{20}$
再算减法：$\frac{9}{10} - \frac{13}{20} = \frac{18}{20} - \frac{13}{20} = \frac{5}{20} = \frac{1}{4}$
9. $\frac{9}{7} + \frac{1}{8} + \frac{5}{7} + \frac{3}{8}$
利用加法交换律和结合律：$(\frac{9}{7} + \frac{5}{7}) + (\frac{1}{8} + \frac{3}{8}) = 2 + \frac{1}{2} = \frac{5}{2}$
10. $\frac{7}{8} - \frac{4}{5} + \frac{9}{8} - \frac{1}{5}$
利用加法交换律和结合律以及减法性质：$(\frac{7}{8} + \frac{9}{8}) - (\frac{4}{5} + \frac{1}{5}) = 2 - 1 = 1$
11. $\frac{4}{3} - \frac{1}{8} + \frac{7}{12}$
先通分：$\frac{4}{3} = \frac{32}{24}$，$\frac{1}{8} = \frac{3}{24}$，$\frac{7}{12} = \frac{14}{24}$
再计算：$\frac{32}{24} - \frac{3}{24} + \frac{14}{24} = \frac{43}{24}$
12. $\frac{5}{8} - (\frac{5}{8} - \frac{1}{2}) = \frac{1}{2}$
13. $\frac{1}{12} + \frac{3}{8} + \frac{11}{12} + \frac{5}{8}$
利用加法交换律和结合律：$(\frac{1}{12} + \frac{11}{12}) + (\frac{3}{8} + \frac{5}{8}) = 1 + 1 = 2$
14. $8 - \frac{9}{16} - \frac{7}{16}$
利用减法结合律：$8 - (\frac{9}{16} + \frac{7}{16}) = 8 - 1 = 7$
15. $\frac{7}{8} - \frac{3}{4} + \frac{1}{8}$
利用加法交换律：$\frac{7}{8} + \frac{1}{8} - \frac{3}{4} = 1 - \frac{3}{4} = \frac{1}{4}$
16. $\frac{2}{3} + (\frac{4}{17} + \frac{3}{3}) = \frac{2}{3} + 1 + \frac{4}{17} = 1\frac{2}{3} + \frac{4}{17} = \frac{85}{51} + \frac{12}{51} = \frac{97}{51} = 1\frac{46}{51}$（或写为$\frac{97}{51}$，但通常化为带分数）
但考虑到简化，可直接写为：$\frac{2}{3} + 1 + \frac{4}{17} = \frac{97}{51}$ 或 $1\frac{46}{51}$
17. $\frac{8}{9} + \frac{7}{15} + \frac{1}{9} - \frac{4}{15}$
利用加法交换律和结合律以及减法性质：$(\frac{8}{9} + \frac{1}{9}) + (\frac{7}{15} - \frac{4}{15}) = 1 + \frac{3}{15} = 1\frac{1}{5}$
18. $\frac{7}{12} - (\frac{3}{4} - \frac{1}{2})$
先算括号内：$\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$
再算减法：$\frac{7}{12} - \frac{1}{4} = \frac{7}{12} - \frac{3}{12} = \frac{4}{12} = \frac{1}{3}$
