《2025年心算口算巧算六年级上册北师大版》

解方程。$\frac{1}{2}x = \frac{1}{4} - \frac{1}{8}$

答案： 解：右边：$\frac{2}{8} - \frac{1}{8} = \frac{1}{8}$
$x = \frac{1}{8} ÷ \frac{1}{2} = \frac{1}{4}$

$x - \frac{1}{12}x = \frac{11}{20}$

答案： 解：左边：$\frac{11}{12}x$
$\frac{11}{12}x = \frac{11}{20}$
$x = \frac{11}{20} ÷ \frac{11}{12} = \frac{3}{5}$

$\frac{5}{6}x - \frac{5}{12} = 7$

答案： 解：$\frac{5}{6}x = 7 + \frac{5}{12} = \frac{84}{12} + \frac{5}{12} = \frac{89}{12}$
$x = \frac{89}{12} ÷ \frac{5}{6} = \frac{89}{10}$

$x - \frac{3}{5}x = 30$

答案： 解：左边：$\frac{2}{5}x$
$\frac{2}{5}x = 30$
$x = 30 × \frac{5}{2} = 75$

$2.5x + x = \frac{14}{15}$

答案： 解：左边：$3.5x = \frac{7}{2}x$
$\frac{7}{2}x = \frac{14}{15}$
$x = \frac{14}{15} × \frac{2}{7} = \frac{4}{15}$

$\frac{2}{3}x = \frac{1}{7} + \frac{3}{14}$

答案： 解：右边：$\frac{2}{14} + \frac{3}{14} = \frac{5}{14}$
$x = \frac{5}{14} ÷ \frac{2}{3} = \frac{15}{28}$

$x - \frac{3}{7} = \frac{5}{7} × \frac{3}{25}$

答案： 解：右边：$\frac{15}{175} = \frac{3}{35}$
$x = \frac{3}{35} + \frac{3}{7} = \frac{3}{35} + \frac{15}{35} = \frac{18}{35}$

$x - \frac{7}{15} = \frac{4}{15} ÷ \frac{2}{5}$

答案： 解：右边：$\frac{4}{15} × \frac{5}{2} = \frac{2}{3}$
$x = \frac{2}{3} + \frac{7}{15} = \frac{10}{15} + \frac{7}{15} = \frac{17}{15}$

$\frac{3}{4}x + \frac{2}{5} = \frac{4}{5}$

答案： 解：$\frac{3}{4}x = \frac{4}{5} - \frac{2}{5} = \frac{2}{5}$
$x = \frac{2}{5} ÷ \frac{3}{4} = \frac{8}{15}$

$\frac{2}{3}x + \frac{1}{2} = 4 × \frac{3}{8}$

答案： 解：右边：$\frac{12}{8} = \frac{3}{2}$
$\frac{2}{3}x = \frac{3}{2} - \frac{1}{2} = 1$
$x = 1 ÷ \frac{2}{3} = \frac{3}{2}$

$\frac{3}{4}x + \frac{3}{5} = \frac{24}{25} × \frac{5}{3}$

答案： 解：右边：$\frac{120}{75} = \frac{8}{5}$
$\frac{3}{4}x = \frac{8}{5} - \frac{3}{5} = 1$
$x = 1 ÷ \frac{3}{4} = \frac{4}{3}$

$\frac{2}{3}x + \frac{3}{5}x = 19$

答案： 解：左边：$\frac{10}{15}x + \frac{9}{15}x = \frac{19}{15}x$
$\frac{19}{15}x = 19$
$x = 19 × \frac{15}{19} = 15$