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5. 计算下面各题。
$5×1.25×\frac{2}{5}+0.78$
$(\frac{1}{2}-\frac{3}{8})÷\frac{3}{4}$
$\frac{11}{12}÷\frac{2}{3}×\frac{2}{5}×\frac{3}{22}$
$\frac{5}{9}÷(\frac{4}{9}-\frac{2}{5}×\frac{5}{6})$
$0.75÷\frac{3}{8}×(\frac{2}{3}-\frac{1}{6})$
$\frac{1}{8}×[8÷(\frac{1}{8}×8)]$
$5×1.25×\frac{2}{5}+0.78$
$(\frac{1}{2}-\frac{3}{8})÷\frac{3}{4}$
$\frac{11}{12}÷\frac{2}{3}×\frac{2}{5}×\frac{3}{22}$
$\frac{5}{9}÷(\frac{4}{9}-\frac{2}{5}×\frac{5}{6})$
$0.75÷\frac{3}{8}×(\frac{2}{3}-\frac{1}{6})$
$\frac{1}{8}×[8÷(\frac{1}{8}×8)]$
答案
1. $5×1.25×\frac{2}{5}+0.78$
$\begin{aligned}&=5×\frac{2}{5}×1.25 + 0.78\\&=2×1.25 + 0.78\\&=2.5 + 0.78\\&=3.28\end{aligned}$
2. $(\frac{1}{2}-\frac{3}{8})÷\frac{3}{4}$
$\begin{aligned}&=(\frac{4}{8}-\frac{3}{8})×\frac{4}{3}\\&=\frac{1}{8}×\frac{4}{3}\\&=\frac{1}{6}\end{aligned}$
3. $\frac{11}{12}÷\frac{2}{3}×\frac{2}{5}×\frac{3}{22}$
$\begin{aligned}&=\frac{11}{12}×\frac{3}{2}×\frac{2}{5}×\frac{3}{22}\\&=\frac{11×3×2×3}{12×2×5×22}\\&=\frac{3}{40}\end{aligned}$
4. $\frac{5}{9}÷(\frac{4}{9}-\frac{2}{5}×\frac{5}{6})$
$\begin{aligned}&=\frac{5}{9}÷(\frac{4}{9}-\frac{1}{3})\\&=\frac{5}{9}÷(\frac{4}{9}-\frac{3}{9})\\&=\frac{5}{9}÷\frac{1}{9}\\&=5\end{aligned}$
5. $0.75÷\frac{3}{8}×(\frac{2}{3}-\frac{1}{6})$
$\begin{aligned}&=\frac{3}{4}×\frac{8}{3}×(\frac{4}{6}-\frac{1}{6})\\&=2×\frac{1}{2}\\&=1\end{aligned}$
6. $\frac{1}{8}×[8÷(\frac{1}{8}×8)]$
$\begin{aligned}&=\frac{1}{8}×[8÷1]\\&=\frac{1}{8}×8\\&=1\end{aligned}$
$\begin{aligned}&=5×\frac{2}{5}×1.25 + 0.78\\&=2×1.25 + 0.78\\&=2.5 + 0.78\\&=3.28\end{aligned}$
2. $(\frac{1}{2}-\frac{3}{8})÷\frac{3}{4}$
$\begin{aligned}&=(\frac{4}{8}-\frac{3}{8})×\frac{4}{3}\\&=\frac{1}{8}×\frac{4}{3}\\&=\frac{1}{6}\end{aligned}$
3. $\frac{11}{12}÷\frac{2}{3}×\frac{2}{5}×\frac{3}{22}$
$\begin{aligned}&=\frac{11}{12}×\frac{3}{2}×\frac{2}{5}×\frac{3}{22}\\&=\frac{11×3×2×3}{12×2×5×22}\\&=\frac{3}{40}\end{aligned}$
4. $\frac{5}{9}÷(\frac{4}{9}-\frac{2}{5}×\frac{5}{6})$
$\begin{aligned}&=\frac{5}{9}÷(\frac{4}{9}-\frac{1}{3})\\&=\frac{5}{9}÷(\frac{4}{9}-\frac{3}{9})\\&=\frac{5}{9}÷\frac{1}{9}\\&=5\end{aligned}$
5. $0.75÷\frac{3}{8}×(\frac{2}{3}-\frac{1}{6})$
$\begin{aligned}&=\frac{3}{4}×\frac{8}{3}×(\frac{4}{6}-\frac{1}{6})\\&=2×\frac{1}{2}\\&=1\end{aligned}$
6. $\frac{1}{8}×[8÷(\frac{1}{8}×8)]$
$\begin{aligned}&=\frac{1}{8}×[8÷1]\\&=\frac{1}{8}×8\\&=1\end{aligned}$
6. 用简便方法计算下面各题。
$\frac{4}{15}÷7+\frac{11}{15}×\frac{1}{7}$
$(0.375+\frac{1}{27})×8+\frac{19}{27}$
$(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})÷\frac{1}{48}$
$\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×0.8$
$(\frac{1}{3}-\frac{1}{4}+\frac{1}{6})×24$
$\frac{14}{27}×75\%+\frac{13}{27}×\frac{3}{4}$
$\frac{4}{15}÷7+\frac{11}{15}×\frac{1}{7}$
$(0.375+\frac{1}{27})×8+\frac{19}{27}$
$(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})÷\frac{1}{48}$
$\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×0.8$
$(\frac{1}{3}-\frac{1}{4}+\frac{1}{6})×24$
$\frac{14}{27}×75\%+\frac{13}{27}×\frac{3}{4}$
答案
6.
1. $\frac{4}{15}÷7+\frac{11}{15}×\frac{1}{7}$
$=\frac{4}{15}×\frac{1}{7}+\frac{11}{15}×\frac{1}{7}$
$=(\frac{4}{15}+\frac{11}{15})×\frac{1}{7}$
$=1×\frac{1}{7}$
$=\frac{1}{7}$
2. $(0.375+\frac{1}{27})×8+\frac{19}{27}$
$=\frac{3}{8}×8+\frac{1}{27}×8+\frac{19}{27}$
$=3+(\frac{8}{27}+\frac{19}{27})$
$=3+1$
$=4$
3. $(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})÷\frac{1}{48}$
$=(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})×48$
$=\frac{5}{6}×48-\frac{3}{8}×48+\frac{11}{24}×48$
$=40-18+22$
$=44$
4. $\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×0.8$
$=\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×\frac{4}{5}$
$=\frac{4}{5}×(\frac{9}{8}-\frac{1}{8})$
$=\frac{4}{5}×1$
$=\frac{4}{5}$
5. $(\frac{1}{3}-\frac{1}{4}+\frac{1}{6})×24$
$=\frac{1}{3}×24-\frac{1}{4}×24+\frac{1}{6}×24$
$=8-6+4$
$=6$
6. $\frac{14}{27}×75\%+\frac{13}{27}×\frac{3}{4}$
$=\frac{14}{27}×\frac{3}{4}+\frac{13}{27}×\frac{3}{4}$
$=(\frac{14}{27}+\frac{13}{27})×\frac{3}{4}$
$=1×\frac{3}{4}$
$=\frac{3}{4}$
1. $\frac{4}{15}÷7+\frac{11}{15}×\frac{1}{7}$
$=\frac{4}{15}×\frac{1}{7}+\frac{11}{15}×\frac{1}{7}$
$=(\frac{4}{15}+\frac{11}{15})×\frac{1}{7}$
$=1×\frac{1}{7}$
$=\frac{1}{7}$
2. $(0.375+\frac{1}{27})×8+\frac{19}{27}$
$=\frac{3}{8}×8+\frac{1}{27}×8+\frac{19}{27}$
$=3+(\frac{8}{27}+\frac{19}{27})$
$=3+1$
$=4$
3. $(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})÷\frac{1}{48}$
$=(\frac{5}{6}-\frac{3}{8}+\frac{11}{24})×48$
$=\frac{5}{6}×48-\frac{3}{8}×48+\frac{11}{24}×48$
$=40-18+22$
$=44$
4. $\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×0.8$
$=\frac{4}{5}×\frac{9}{8}-\frac{1}{8}×\frac{4}{5}$
$=\frac{4}{5}×(\frac{9}{8}-\frac{1}{8})$
$=\frac{4}{5}×1$
$=\frac{4}{5}$
5. $(\frac{1}{3}-\frac{1}{4}+\frac{1}{6})×24$
$=\frac{1}{3}×24-\frac{1}{4}×24+\frac{1}{6}×24$
$=8-6+4$
$=6$
6. $\frac{14}{27}×75\%+\frac{13}{27}×\frac{3}{4}$
$=\frac{14}{27}×\frac{3}{4}+\frac{13}{27}×\frac{3}{4}$
$=(\frac{14}{27}+\frac{13}{27})×\frac{3}{4}$
$=1×\frac{3}{4}$
$=\frac{3}{4}$
