《2024年数学学习与巩固六年级上册北师大版》

4. 计算。
(1)直接写出得数。
$\frac{2}{3}÷\frac{4}{5}=$$\frac{5}{6}$ $20×\frac{3}{5}=$12 $\frac{5}{6}×\frac{5}{6}=$$\frac{25}{36}$ $\frac{3}{7}÷\frac{8}{11}÷\frac{3}{7}=$$\frac{11}{8}$
$1÷\frac{99}{100}=$$\frac{100}{99}$ $44×\frac{3}{11}=$12 $\frac{2}{5}-\frac{1}{6}=$$\frac{7}{30}$ $\frac{3}{22}×\frac{13}{14}×0=$0
(2)用合适的方法计算。
$\frac{5}{7}÷3-\frac{4}{21}$$\frac{1}{21}$ $17×\frac{3}{4}+2÷\frac{4}{3}+\frac{3}{4}$15
$\frac{1}{4}+\frac{3}{7}×\frac{1}{6}÷\frac{5}{28}$$\frac{13}{20}$ $(\frac{1}{2}-\frac{1}{4}-\frac{1}{5})×20$1
(3)解方程。
$(1-\frac{3}{5})x = 240$$x=600$ $x+\frac{3}{4}x = 21$$x=12$ $x-\frac{5}{7}x= \frac{15}{14}$$x=\frac{15}{4}$
$\frac{5}{12}x= \frac{1}{6}+\frac{1}{8}$$x=\frac{7}{10}$ $3.5x - x = \frac{1}{4}$$x=\frac{1}{10}$ $\frac{3}{8}x= \frac{5}{14}÷\frac{10}{7}$$x=\frac{2}{3}$

答案：
(1)
$\frac{2}{3}÷\frac{4}{5}=\frac{2}{3}×\frac{5}{4}=\frac{5}{6}$
$20×\frac{3}{5}=12$
$\frac{5}{6}×\frac{5}{6}=\frac{25}{36}$
$\frac{3}{7}÷\frac{8}{11}÷\frac{3}{7}=\frac{3}{7}×\frac{11}{8}×\frac{7}{3}=\frac{11}{8}$
$1÷\frac{99}{100}=1×\frac{100}{99}=\frac{100}{99}$
$44×\frac{3}{11}=12$
$\frac{2}{5}-\frac{1}{6}=\frac{12}{30}-\frac{5}{30}=\frac{7}{30}$
$\frac{3}{22}×\frac{13}{14}×0 = 0$
(2)
$\frac{5}{7}÷3-\frac{4}{21}=\frac{5}{7}×\frac{1}{3}-\frac{4}{21}=\frac{5}{21}-\frac{4}{21}=\frac{1}{21}$
$17×\frac{3}{4}+2÷\frac{4}{3}+\frac{3}{4}=17×\frac{3}{4}+2×\frac{3}{4}+\frac{3}{4}=(17 + 2+1)×\frac{3}{4}=20×\frac{3}{4}=15$
$\frac{1}{4}+\frac{3}{7}×\frac{1}{6}÷\frac{5}{28}=\frac{1}{4}+\frac{1}{14}×\frac{28}{5}=\frac{1}{4}+\frac{2}{5}=\frac{5}{20}+\frac{8}{20}=\frac{13}{20}$
$(\frac{1}{2}-\frac{1}{4}-\frac{1}{5})×20=\frac{1}{2}×20-\frac{1}{4}×20-\frac{1}{5}×20=10 - 5-4=1$
(3)
$(1-\frac{3}{5})x = 240$
$\frac{2}{5}x=240$
$x=240×\frac{5}{2}=600$
$x+\frac{3}{4}x = 21$
$\frac{7}{4}x=21$
$x=21×\frac{4}{7}=12$
$x-\frac{5}{7}x=\frac{15}{14}$
$\frac{2}{7}x=\frac{15}{14}$
$x=\frac{15}{14}×\frac{7}{2}=\frac{15}{4}$
$\frac{5}{12}x=\frac{1}{6}+\frac{1}{8}$
$\frac{5}{12}x=\frac{4 + 3}{24}=\frac{7}{24}$
$x=\frac{7}{24}×\frac{12}{5}=\frac{7}{10}$
$3.5x - x=\frac{1}{4}$
$2.5x=\frac{1}{4}$
$x=\frac{1}{4}÷2.5=\frac{1}{4}×\frac{2}{5}=\frac{1}{10}$
$\frac{3}{8}x=\frac{5}{14}÷\frac{10}{7}$
$\frac{3}{8}x=\frac{5}{14}×\frac{7}{10}=\frac{1}{4}$
$x=\frac{1}{4}×\frac{8}{3}=\frac{2}{3}$