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1. 口算。
$\frac{7}{13}+\frac{6}{13}=$
$\frac{3}{8}-\frac{1}{4}=$
$\frac{7}{13}×\frac{26}{21}=$
$\frac{3}{4}÷\frac{6}{7}=$
$\frac{7}{5}×\frac{15}{28}=$
$\frac{14}{39}÷\frac{7}{13}=$
$\frac{1}{7}+\frac{5}{14}=$
$\frac{3}{2}-\frac{7}{10}=$
$\frac{5}{6}+\frac{1}{4}=$
$\frac{7}{13}+\frac{6}{13}=$
1
$\frac{3}{8}-\frac{1}{4}=$
$\frac{1}{8}$
$\frac{7}{13}×\frac{26}{21}=$
$\frac{2}{3}$
$\frac{3}{4}÷\frac{6}{7}=$
$\frac{7}{8}$
$\frac{7}{5}×\frac{15}{28}=$
$\frac{3}{4}$
$\frac{14}{39}÷\frac{7}{13}=$
$\frac{2}{3}$
$\frac{1}{7}+\frac{5}{14}=$
$\frac{1}{2}$
$\frac{3}{2}-\frac{7}{10}=$
$\frac{4}{5}$
$\frac{5}{6}+\frac{1}{4}=$
$\frac{13}{12}$
答案
1. $\frac{7}{13}+\frac{6}{13}=\frac{7 + 6}{13}=\frac{13}{13}=1$
2. $\frac{3}{8}-\frac{1}{4}=\frac{3}{8}-\frac{2}{8}=\frac{3 - 2}{8}=\frac{1}{8}$
3. $\frac{7}{13}×\frac{26}{21}=\frac{7×26}{13×21}=\frac{7×2}{1×21}=\frac{2}{3}$
4. $\frac{3}{4}÷\frac{6}{7}=\frac{3}{4}×\frac{7}{6}=\frac{3×7}{4×6}=\frac{7}{8}$
5. $\frac{7}{5}×\frac{15}{28}=\frac{7×15}{5×28}=\frac{3}{4}$
6. $\frac{14}{39}÷\frac{7}{13}=\frac{14}{39}×\frac{13}{7}=\frac{14×13}{39×7}=\frac{2}{3}$
7. $\frac{1}{7}+\frac{5}{14}=\frac{2}{14}+\frac{5}{14}=\frac{2 + 5}{14}=\frac{1}{2}$
8. $\frac{3}{2}-\frac{7}{10}=\frac{15}{10}-\frac{7}{10}=\frac{15 - 7}{10}=\frac{4}{5}$
9. $\frac{5}{6}+\frac{1}{4}=\frac{10}{12}+\frac{3}{12}=\frac{10+3}{12}=\frac{13}{12}$
2. $\frac{3}{8}-\frac{1}{4}=\frac{3}{8}-\frac{2}{8}=\frac{3 - 2}{8}=\frac{1}{8}$
3. $\frac{7}{13}×\frac{26}{21}=\frac{7×26}{13×21}=\frac{7×2}{1×21}=\frac{2}{3}$
4. $\frac{3}{4}÷\frac{6}{7}=\frac{3}{4}×\frac{7}{6}=\frac{3×7}{4×6}=\frac{7}{8}$
5. $\frac{7}{5}×\frac{15}{28}=\frac{7×15}{5×28}=\frac{3}{4}$
6. $\frac{14}{39}÷\frac{7}{13}=\frac{14}{39}×\frac{13}{7}=\frac{14×13}{39×7}=\frac{2}{3}$
7. $\frac{1}{7}+\frac{5}{14}=\frac{2}{14}+\frac{5}{14}=\frac{2 + 5}{14}=\frac{1}{2}$
8. $\frac{3}{2}-\frac{7}{10}=\frac{15}{10}-\frac{7}{10}=\frac{15 - 7}{10}=\frac{4}{5}$
9. $\frac{5}{6}+\frac{1}{4}=\frac{10}{12}+\frac{3}{12}=\frac{10+3}{12}=\frac{13}{12}$
2. 计算。
$5-\frac{7}{8}×\frac{16}{21}$
$(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
$5-\frac{7}{8}×\frac{16}{21}$
$(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
答案
1. $5-\frac{7}{8}×\frac{16}{21}$
$=5-\frac{2}{3}$
$=\frac{15}{3}-\frac{2}{3}$
$=\frac{13}{3}$
2. $(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$=(\frac{6}{8}-\frac{5}{8})×\frac{9}{5}$
$=\frac{1}{8}×\frac{9}{5}$
$=\frac{9}{40}$
3. $(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$=(\frac{3}{6}+\frac{2}{6})÷\frac{1}{3}$
$=\frac{5}{6}×3$
$=\frac{5}{2}$
4. $\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$=\frac{4}{15}+\frac{2}{5}×\frac{3}{2}$
$=\frac{4}{15}+\frac{3}{5}$
$=\frac{4}{15}+\frac{9}{15}$
$=\frac{13}{15}$
5. $\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$=\frac{7}{8}÷[1-(\frac{3}{12}+\frac{8}{12})]$
$=\frac{7}{8}÷[1-\frac{11}{12}]$
$=\frac{7}{8}÷\frac{1}{12}$
$=\frac{7}{8}×12$
$=\frac{21}{2}$
6. $(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
$=(\frac{2}{12}+\frac{9}{12})×\frac{4}{11}$
$=\frac{11}{12}×\frac{4}{11}$
$=\frac{1}{3}$
$=5-\frac{2}{3}$
$=\frac{15}{3}-\frac{2}{3}$
$=\frac{13}{3}$
2. $(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$=(\frac{6}{8}-\frac{5}{8})×\frac{9}{5}$
$=\frac{1}{8}×\frac{9}{5}$
$=\frac{9}{40}$
3. $(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$=(\frac{3}{6}+\frac{2}{6})÷\frac{1}{3}$
$=\frac{5}{6}×3$
$=\frac{5}{2}$
4. $\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$=\frac{4}{15}+\frac{2}{5}×\frac{3}{2}$
$=\frac{4}{15}+\frac{3}{5}$
$=\frac{4}{15}+\frac{9}{15}$
$=\frac{13}{15}$
5. $\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$=\frac{7}{8}÷[1-(\frac{3}{12}+\frac{8}{12})]$
$=\frac{7}{8}÷[1-\frac{11}{12}]$
$=\frac{7}{8}÷\frac{1}{12}$
$=\frac{7}{8}×12$
$=\frac{21}{2}$
6. $(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
$=(\frac{2}{12}+\frac{9}{12})×\frac{4}{11}$
$=\frac{11}{12}×\frac{4}{11}$
$=\frac{1}{3}$
解析
$5-\frac{7}{8}×\frac{16}{21}$
$=5-\frac{2}{3}$
$=\frac{13}{3}$
$(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$=(\frac{6}{8}-\frac{5}{8})×\frac{9}{5}$
$=\frac{1}{8}×\frac{9}{5}$
$=\frac{9}{40}$
$(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$=(\frac{3}{6}+\frac{2}{6})÷\frac{1}{3}$
$=\frac{5}{6}×3$
$=\frac{5}{2}$
$\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$=\frac{4}{15}+\frac{2}{5}×\frac{3}{2}$
$=\frac{4}{15}+\frac{3}{5}$
$=\frac{4}{15}+\frac{9}{15}$
$=\frac{13}{15}$
$\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$=\frac{7}{8}÷[1-(\frac{3}{12}+\frac{8}{12})]$
$=\frac{7}{8}÷[1-\frac{11}{12}]$
$=\frac{7}{8}÷\frac{1}{12}$
$=\frac{7}{8}×12$
$=\frac{21}{2}$
$(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
$=(\frac{2}{12}+\frac{9}{12})×\frac{4}{11}$
$=\frac{11}{12}×\frac{4}{11}$
$=\frac{1}{3}$
$=5-\frac{2}{3}$
$=\frac{13}{3}$
$(\frac{3}{4}-\frac{5}{8})÷\frac{5}{9}$
$=(\frac{6}{8}-\frac{5}{8})×\frac{9}{5}$
$=\frac{1}{8}×\frac{9}{5}$
$=\frac{9}{40}$
$(\frac{1}{2}+\frac{1}{3})÷(\frac{2}{3}-\frac{1}{3})$
$=(\frac{3}{6}+\frac{2}{6})÷\frac{1}{3}$
$=\frac{5}{6}×3$
$=\frac{5}{2}$
$\frac{2}{5}×\frac{2}{3}+\frac{2}{5}÷\frac{2}{3}$
$=\frac{4}{15}+\frac{2}{5}×\frac{3}{2}$
$=\frac{4}{15}+\frac{3}{5}$
$=\frac{4}{15}+\frac{9}{15}$
$=\frac{13}{15}$
$\frac{7}{8}÷[1-(\frac{1}{4}+\frac{2}{3})]$
$=\frac{7}{8}÷[1-(\frac{3}{12}+\frac{8}{12})]$
$=\frac{7}{8}÷[1-\frac{11}{12}]$
$=\frac{7}{8}÷\frac{1}{12}$
$=\frac{7}{8}×12$
$=\frac{21}{2}$
$(\frac{1}{6}+\frac{3}{4})×(\frac{5}{11}-\frac{1}{11})$
$=(\frac{2}{12}+\frac{9}{12})×\frac{4}{11}$
$=\frac{11}{12}×\frac{4}{11}$
$=\frac{1}{3}$
3. 按要求改变$\frac{2}{9}÷2+\frac{1}{6}×\frac{3}{4}$的运算顺序,并计算。
(1)加法→除法→乘法
(2)乘法→加法→除法
(3)加法→乘法→除法
(1)加法→除法→乘法
(2)乘法→加法→除法
(3)加法→乘法→除法
答案
(1) $2/9÷(2 + 1/6)×3/4$
$=2/9÷13/6×3/4$
$=2/9×6/13×3/4$
$=12/117×3/4$
$=36/468$
$=1/13$
(2) $2/9÷(2 + 1/6×3/4)$
$=2/9÷(2 + 1/8)$
$=2/9÷17/8$
$=2/9×8/17$
$=16/153$
(3) $2/9÷[(2 + 1/6)×3/4]$
$=2/9÷[13/6×3/4]$
$=2/9÷13/8$
$=2/9×8/13$
$=16/117$
$=2/9÷13/6×3/4$
$=2/9×6/13×3/4$
$=12/117×3/4$
$=36/468$
$=1/13$
(2) $2/9÷(2 + 1/6×3/4)$
$=2/9÷(2 + 1/8)$
$=2/9÷17/8$
$=2/9×8/17$
$=16/153$
(3) $2/9÷[(2 + 1/6)×3/4]$
$=2/9÷[13/6×3/4]$
$=2/9÷13/8$
$=2/9×8/13$
$=16/117$
解析
(1)$\frac{2}{9}÷(2+\frac{1}{6})×\frac{3}{4}=\frac{2}{9}÷\frac{13}{6}×\frac{3}{4}=\frac{2}{9}×\frac{6}{13}×\frac{3}{4}=\frac{1}{13}$
(2)$\frac{2}{9}÷(2+\frac{1}{6}×\frac{3}{4})=\frac{2}{9}÷(2+\frac{1}{8})=\frac{2}{9}÷\frac{17}{8}=\frac{16}{153}$
(3)$\frac{2}{9}÷[(2+\frac{1}{6})×\frac{3}{4}]=\frac{2}{9}÷[\frac{13}{6}×\frac{3}{4}]=\frac{2}{9}÷\frac{13}{8}=\frac{16}{117}$
4. 列式计算。
(1)一袋米的$\frac{5}{7}$是40kg,这袋米的$\frac{3}{8}$是多少千克？
(2)四(2)班人数的$\frac{1}{4}比它的\frac{5}{6}$少28,四(2)班有多少人？
(1)一袋米的$\frac{5}{7}$是40kg,这袋米的$\frac{3}{8}$是多少千克？
(2)四(2)班人数的$\frac{1}{4}比它的\frac{5}{6}$少28,四(2)班有多少人？
答案
(1)21千克；(2)48人。
解析
(1)
设这袋米有$x$千克。
$\frac{5}{7}x = 40$
$x=40÷\frac{5}{7}$
$x = 56$
$56×\frac{3}{8}=21$（千克）
(2)
设四（2）班有$x$人。
$\frac{5}{6}x-\frac{1}{4}x = 28$
$\frac{10}{12}x-\frac{3}{12}x=28$
$\frac{7}{12}x = 28$
$x=28÷\frac{7}{12}$
$x = 48$
设这袋米有$x$千克。
$\frac{5}{7}x = 40$
$x=40÷\frac{5}{7}$
$x = 56$
$56×\frac{3}{8}=21$（千克）
(2)
设四（2）班有$x$人。
$\frac{5}{6}x-\frac{1}{4}x = 28$
$\frac{10}{12}x-\frac{3}{12}x=28$
$\frac{7}{12}x = 28$
$x=28÷\frac{7}{12}$
$x = 48$
5. 怎样简便怎样算。
$(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4})×(\frac{1}{2}+\frac{1}{3}+\frac{1}{4})-(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5})×(\frac{1}{2}+\frac{1}{3}+\frac{1}{4})$
$(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4})×(\frac{1}{2}+\frac{1}{3}+\frac{1}{4})-(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5})×(\frac{1}{2}+\frac{1}{3}+\frac{1}{4})$
答案
设$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=A$，
原式$=(1 + A)×(A)-(A+\frac{1}{5})× A$
$=A + A^{2}-A^{2}-\frac{1}{5}A$
$=\frac{4}{5}A$
把$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{6 + 4+3}{12}=\frac{13}{12}$代入$\frac{4}{5}A$，
可得$\frac{4}{5}×\frac{13}{12}=\frac{13}{15}$。
原式$=(1 + A)×(A)-(A+\frac{1}{5})× A$
$=A + A^{2}-A^{2}-\frac{1}{5}A$
$=\frac{4}{5}A$
把$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{6 + 4+3}{12}=\frac{13}{12}$代入$\frac{4}{5}A$，
可得$\frac{4}{5}×\frac{13}{12}=\frac{13}{15}$。
