1. 能简便的用简便方法计算。
$10\dfrac{3}{7} - 5.89 + \dfrac{4}{7} - 3.11$
$\dfrac{5}{8} + \dfrac{3}{8}×\dfrac{2}{15}$
$\dfrac{3}{5} + 7.91 + \dfrac{9}{100} + 3.4$
$\dfrac{7}{9} + \dfrac{4}{11} - (\dfrac{4}{9} - \dfrac{7}{11})$
$(\dfrac{7}{18} + \dfrac{5}{27})×\dfrac{9}{35}$
$\dfrac{97}{100}×99$
$1\dfrac{3}{4}×4\dfrac{1}{6}÷\dfrac{5}{8}$
$3\dfrac{1}{3}÷1.5×2\dfrac{1}{4}$
$2.6×99 + 2.6$
$80.7×8.7 + 8.07×13$
$\dfrac{17}{24}×\dfrac{1}{5} + \dfrac{7}{24}÷5 + \dfrac{1}{5}$
$255÷255\dfrac{255}{256}$
$3.46×1.3 + 3.46×9.7 - 3.46$
$0.45×6\dfrac{11}{25} + 3.56÷2\dfrac{2}{9}$
$19.75 - (1.75×\dfrac{8}{13} + 1\dfrac{3}{4}×\dfrac{5}{13})$
$17÷51 + (\dfrac{1}{68} + \dfrac{2}{51})×17$
$1.25×9.1×0.7 + 1.25×9.1×0.1$
$76×(\dfrac{1}{23} - \dfrac{1}{53}) + 23×(\dfrac{1}{53} + \dfrac{1}{76}) - 53×(\dfrac{1}{23} - \dfrac{1}{76})$

1. $10\dfrac{3}{7} - 5.89 + \dfrac{4}{7} - 3.11$
$=(10\dfrac{3}{7} + \dfrac{4}{7}) - (5.89 + 3.11)$
$=11 - 9$
$=2$
2. $\dfrac{5}{8} + \dfrac{3}{8}×\dfrac{2}{15}$
$=\dfrac{5}{8} + \dfrac{1}{20}$
$=\dfrac{25}{40} + \dfrac{2}{40}$
$=\dfrac{27}{40}$
3. $\dfrac{3}{5} + 7.91 + \dfrac{9}{100} + 3.4$
$=(0.6 + 3.4) + (7.91 + 0.09)$
$=4 + 8$
$=12$
4. $\dfrac{7}{9} + \dfrac{4}{11} - (\dfrac{4}{9} - \dfrac{7}{11})$
$=\dfrac{7}{9} - \dfrac{4}{9} + \dfrac{4}{11} + \dfrac{7}{11}$
$=\dfrac{1}{3} + 1$
$=\dfrac{4}{3}$
5. $(\dfrac{7}{18} + \dfrac{5}{27})×\dfrac{9}{35}$
$=\dfrac{7}{18}×\dfrac{9}{35} + \dfrac{5}{27}×\dfrac{9}{35}$
$=\dfrac{1}{10} + \dfrac{1}{21}$
$=\dfrac{31}{210}$
6. $\dfrac{97}{100}×99$
$=\dfrac{97}{100}×(100 - 1)$
$=97 - \dfrac{97}{100}$
$=96\dfrac{3}{100}$
7. $1\dfrac{3}{4}×4\dfrac{1}{6}÷\dfrac{5}{8}$
$=\dfrac{7}{4}×\dfrac{25}{6}×\dfrac{8}{5}$
$=\dfrac{35}{3}$
8. $3\dfrac{1}{3}÷1.5×2\dfrac{1}{4}$
$=\dfrac{10}{3}×\dfrac{2}{3}×\dfrac{9}{4}$
$=5$
9. $2.6×99 + 2.6$
$=2.6×(99 + 1)$
$=2.6×100$
$=260$
10. $80.7×8.7 + 8.07×13$
$=80.7×8.7 + 80.7×1.3$
$=80.7×(8.7 + 1.3)$
$=80.7×10$
$=807$
11. $\dfrac{17}{24}×\dfrac{1}{5} + \dfrac{7}{24}÷5 + \dfrac{1}{5}$
$=\dfrac{17}{24}×\dfrac{1}{5} + \dfrac{7}{24}×\dfrac{1}{5} + 1×\dfrac{1}{5}$
$=(\dfrac{17}{24} + \dfrac{7}{24} + 1)×\dfrac{1}{5}$
$=2×\dfrac{1}{5}$
$=\dfrac{2}{5}$
12. $255÷255\dfrac{255}{256}$
$=255÷\dfrac{255×256 + 255}{256}$
$=255×\dfrac{256}{255×257}$
$=\dfrac{256}{257}$
13. $3.46×1.3 + 3.46×9.7 - 3.46$
$=3.46×(1.3 + 9.7 - 1)$
$=3.46×10$
$=34.6$
14. $0.45×6\dfrac{11}{25} + 3.56÷2\dfrac{2}{9}$
$=0.45×6.44 + 3.56×0.45$
$=0.45×(6.44 + 3.56)$
$=0.45×10$
$=4.5$
15. $19.75 - (1.75×\dfrac{8}{13} + 1\dfrac{3}{4}×\dfrac{5}{13})$
$=19.75 - [1.75×(\dfrac{8}{13} + \dfrac{5}{13})]$
$=19.75 - 1.75$
$=18$
16. $17÷51 + (\dfrac{1}{68} + \dfrac{2}{51})×17$
$=\dfrac{1}{3} + \dfrac{1}{4} + \dfrac{2}{3}$
$=(\dfrac{1}{3} + \dfrac{2}{3}) + \dfrac{1}{4}$
$=1 + \dfrac{1}{4}$
$=\dfrac{5}{4}$
17. $1.25×9.1×0.7 + 1.25×9.1×0.1$
$=1.25×9.1×(0.7 + 0.1)$
$=1.25×0.8×9.1$
$=1×9.1$
$=9.1$
18. $76×(\dfrac{1}{23} - \dfrac{1}{53}) + 23×(\dfrac{1}{53} + \dfrac{1}{76}) - 53×(\dfrac{1}{23} - \dfrac{1}{76})$
$=\dfrac{76}{23} - \dfrac{76}{53} + \dfrac{23}{53} + \dfrac{23}{76} - \dfrac{53}{23} + \dfrac{53}{76}$
$=(\dfrac{76}{23} - \dfrac{53}{23}) + (-\dfrac{76}{53} + \dfrac{23}{53}) + (\dfrac{23}{76} + \dfrac{53}{76})$
$=1 - 1 + 1$
$=1$