《2025年心算口算巧算六年级上册北师大版》

计算下面各题。$(\frac{5}{4} + \frac{5}{4}) ÷ (\frac{5}{4} × \frac{5}{4})$

答案： 解：分子：$\frac{10}{4} = \frac{5}{2}$，分母：$\frac{25}{16}$
$\frac{5}{2} ÷ \frac{25}{16} = \frac{5}{2} × \frac{16}{25} = \frac{8}{5}$

$(\frac{2}{3} - \frac{2}{9} × \frac{1}{2}) ÷ \frac{1}{2}$

答案： 解：括号内：$\frac{2}{3} - \frac{1}{9} = \frac{6}{9} - \frac{1}{9} = \frac{5}{9}$
$\frac{5}{9} × 2 = \frac{10}{9}$

$\frac{3}{5} × \frac{7}{15} + \frac{8}{15} ÷ \frac{5}{3}$

答案： 解：$\frac{3}{5} × \frac{7}{15} + \frac{8}{15} × \frac{3}{5} = \frac{3}{5} × (\frac{7}{15} + \frac{8}{15}) = \frac{3}{5} × 1 = \frac{3}{5}$

$\frac{1}{5} × \frac{5}{6} + \frac{9}{8} × \frac{8}{9}$

答案： 解：$\frac{1}{6} + 1 = \frac{7}{6}$

$\frac{7}{13} ÷ \frac{1}{10} + \frac{2}{13}$

答案： 解：$\frac{7}{13} × 10 + \frac{2}{13} = \frac{70}{13} + \frac{2}{13} = \frac{72}{13}$

$\frac{7}{10} ÷ (\frac{4}{3} - \frac{1}{3}) × \frac{6}{5}$

答案： 解：括号内：$\frac{3}{3} = 1$
$\frac{7}{10} ÷ 1 × \frac{6}{5} = \frac{42}{50} = \frac{21}{25}$

$\frac{7}{8} × \frac{5}{6} + \frac{1}{8} ÷ \frac{6}{5}$

答案： 解：$\frac{7}{8} × \frac{5}{6} + \frac{1}{8} × \frac{5}{6} = \frac{5}{6} × (\frac{7}{8} + \frac{1}{8}) = \frac{5}{6} × 1 = \frac{5}{6}$

$36 × (\frac{2}{3} + \frac{1}{6} - \frac{3}{4})$

答案： 解：$36 × \frac{2}{3} + 36 × \frac{1}{6} - 36 × \frac{3}{4} = 24 + 6 - 27 = 3$

$(\frac{2}{3} + \frac{4}{15} × \frac{5}{6}) ÷ \frac{20}{21}$

答案： 解：括号内：$\frac{2}{3} + \frac{2}{9} = \frac{6}{9} + \frac{2}{9} = \frac{8}{9}$
$\frac{8}{9} × \frac{21}{20} = \frac{14}{15}$

$\frac{4}{5} ÷ (\frac{3}{5} + \frac{1}{10}) × 2$

答案： 解：括号内：$\frac{6}{10} + \frac{1}{10} = \frac{7}{10}$
$\frac{4}{5} ÷ \frac{7}{10} × 2 = \frac{4}{5} × \frac{10}{7} × 2 = \frac{16}{7}$

$\frac{2}{3} ÷ \frac{4}{11} × (\frac{1}{8} + \frac{3}{4})$

答案： 解：括号内：$\frac{1}{8} + \frac{6}{8} = \frac{7}{8}$
$\frac{2}{3} × \frac{11}{4} × \frac{7}{8} = \frac{77}{48}$

$3 ÷ \frac{3}{4} - \frac{3}{4} ÷ 3$

答案： 解：$4 - \frac{1}{4} = \frac{15}{4}$