一、解方程。
$x - \frac{1}{6} = \frac{3}{8}$ $3.1x÷2 = 1.24$ $3.6(x÷0.8) = 10.8$
$8.4 + x÷3 = 9.6$ $(0.97 + 4.23)x = 1.872$ $2x + 2.8×2 = 10.4$
$1.5(x + 1.6) = 3.6$ $6x - 12.4 = 54.8$ $1.9x - 1.4x = 27$
$x - \frac{1}{6} = \frac{3}{8}$ $3.1x÷2 = 1.24$ $3.6(x÷0.8) = 10.8$
$8.4 + x÷3 = 9.6$ $(0.97 + 4.23)x = 1.872$ $2x + 2.8×2 = 10.4$
$1.5(x + 1.6) = 3.6$ $6x - 12.4 = 54.8$ $1.9x - 1.4x = 27$
答案
$x=\frac{13}{24}$ $x=0.8$ $x=2.4$ $x=3.6$ $x=0.36$ $x=2.4$ $x=0.8$ $x=11.2$ $x=54$
解析
1. 解:$x = \frac{3}{8} + \frac{1}{6}$
$x = \frac{9}{24} + \frac{4}{24}$
$x = \frac{13}{24}$
2. 解:$3.1x = 1.24×2$
$3.1x = 2.48$
$x = 2.48÷3.1$
$x = 0.8$
3. 解:$x÷0.8 = 10.8÷3.6$
$x÷0.8 = 3$
$x = 3×0.8$
$x = 2.4$
4. 解:$x÷3 = 9.6 - 8.4$
$x÷3 = 1.2$
$x = 1.2×3$
$x = 3.6$
5. 解:$5.2x = 1.872$
$x = 1.872÷5.2$
$x = 0.36$
6. 解:$2x + 5.6 = 10.4$
$2x = 10.4 - 5.6$
$2x = 4.8$
$x = 4.8÷2$
$x = 2.4$
7. 解:$x + 1.6 = 3.6÷1.5$
$x + 1.6 = 2.4$
$x = 2.4 - 1.6$
$x = 0.8$
8. 解:$6x = 54.8 + 12.4$
$6x = 67.2$
$x = 67.2÷6$
$x = 11.2$
9. 解:$0.5x = 27$
$x = 27÷0.5$
$x = 54$
$x = \frac{9}{24} + \frac{4}{24}$
$x = \frac{13}{24}$
2. 解:$3.1x = 1.24×2$
$3.1x = 2.48$
$x = 2.48÷3.1$
$x = 0.8$
3. 解:$x÷0.8 = 10.8÷3.6$
$x÷0.8 = 3$
$x = 3×0.8$
$x = 2.4$
4. 解:$x÷3 = 9.6 - 8.4$
$x÷3 = 1.2$
$x = 1.2×3$
$x = 3.6$
5. 解:$5.2x = 1.872$
$x = 1.872÷5.2$
$x = 0.36$
6. 解:$2x + 5.6 = 10.4$
$2x = 10.4 - 5.6$
$2x = 4.8$
$x = 4.8÷2$
$x = 2.4$
7. 解:$x + 1.6 = 3.6÷1.5$
$x + 1.6 = 2.4$
$x = 2.4 - 1.6$
$x = 0.8$
8. 解:$6x = 54.8 + 12.4$
$6x = 67.2$
$x = 67.2÷6$
$x = 11.2$
9. 解:$0.5x = 27$
$x = 27÷0.5$
$x = 54$
二、计算下面各题,怎样简便就怎样计算。
$21 - \frac{7}{11} - \frac{4}{11}$ $\frac{11}{9} - \frac{7}{12} - \frac{5}{12} + \frac{7}{9}$ $\frac{2}{15} + \frac{27}{30} - \frac{1}{30}$
$\frac{7}{6} - (\frac{7}{10} - \frac{1}{3}) + \frac{1}{6}$ $\frac{18}{11} - (\frac{7}{11} + \frac{3}{8})$ $\frac{13}{49} + \frac{12}{13} - \frac{13}{49} + \frac{14}{13}$
$7.2 - 3.6 + 2.8 - 5.4$ $2.17÷0.25÷4$ $6.27×101 - 6.27$
$(71.2 - 71.2×0.9)÷0.25$ $0.8×(3.2 - 2.99÷2.3)$
$8.4 + (3.5 - 0.75)×0.4$ $3.5×[1.5×(1.07 + 1.93)]$
$21 - \frac{7}{11} - \frac{4}{11}$ $\frac{11}{9} - \frac{7}{12} - \frac{5}{12} + \frac{7}{9}$ $\frac{2}{15} + \frac{27}{30} - \frac{1}{30}$
$\frac{7}{6} - (\frac{7}{10} - \frac{1}{3}) + \frac{1}{6}$ $\frac{18}{11} - (\frac{7}{11} + \frac{3}{8})$ $\frac{13}{49} + \frac{12}{13} - \frac{13}{49} + \frac{14}{13}$
$7.2 - 3.6 + 2.8 - 5.4$ $2.17÷0.25÷4$ $6.27×101 - 6.27$
$(71.2 - 71.2×0.9)÷0.25$ $0.8×(3.2 - 2.99÷2.3)$
$8.4 + (3.5 - 0.75)×0.4$ $3.5×[1.5×(1.07 + 1.93)]$
答案
20 1 1 $\frac{29}{30}$ $\frac{5}{8}$ 2 1 2.17 627 28.48 1.52 9.5 15.75
解析
1. $21 - \frac{7}{11} - \frac{4}{11}$
$\begin{aligned}&=21 - \left(\frac{7}{11} + \frac{4}{11}\right)\\&=21 - 1\\&=20\end{aligned}$
2. $\frac{11}{9} - \frac{7}{12} - \frac{5}{12} + \frac{7}{9}$
$\begin{aligned}&=\left(\frac{11}{9} + \frac{7}{9}\right) - \left(\frac{7}{12} + \frac{5}{12}\right)\\&=2 - 1\\&=1\end{aligned}$
3. $\frac{2}{15} + \frac{27}{30} - \frac{1}{30}$
$\begin{aligned}&=\frac{2}{15} + \left(\frac{27}{30} - \frac{1}{30}\right)\\&=\frac{2}{15} + \frac{26}{30}\\&=\frac{2}{15} + \frac{13}{15}\\&=1\end{aligned}$
4. $\frac{7}{6} - \left(\frac{7}{10} - \frac{1}{3}\right) + \frac{1}{6}$
$\begin{aligned}&=\left(\frac{7}{6} + \frac{1}{6}\right) - \left(\frac{21}{30} - \frac{10}{30}\right)\\&=\frac{8}{6} - \frac{11}{30}\\&=\frac{40}{30} - \frac{11}{30}\\&=\frac{29}{30}\end{aligned}$
5. $\frac{18}{11} - \left(\frac{7}{11} + \frac{3}{8}\right)$
$\begin{aligned}&=\frac{18}{11} - \frac{7}{11} - \frac{3}{8}\\&=1 - \frac{3}{8}\\&=\frac{5}{8}\end{aligned}$
6. $\frac{13}{49} + \frac{12}{13} - \frac{13}{49} + \frac{14}{13}$
$\begin{aligned}&=\left(\frac{13}{49} - \frac{13}{49}\right) + \left(\frac{12}{13} + \frac{14}{13}\right)\\&=0 + 2\\&=2\end{aligned}$
7. $7.2 - 3.6 + 2.8 - 5.4$
$\begin{aligned}&=(7.2 + 2.8) - (3.6 + 5.4)\\&=10 - 9\\&=1\end{aligned}$
8. $2.17÷0.25÷4$
$\begin{aligned}&=2.17÷(0.25×4)\\&=2.17÷1\\&=2.17\end{aligned}$
9. $6.27×101 - 6.27$
$\begin{aligned}&=6.27×(101 - 1)\\&=6.27×100\\&=627\end{aligned}$
10. $(71.2 - 71.2×0.9)÷0.25$
$\begin{aligned}&=71.2×(1 - 0.9)÷0.25\\&=71.2×0.1÷0.25\\&=7.12÷0.25\\&=28.48\end{aligned}$
11. $0.8×(3.2 - 2.99÷2.3)$
$\begin{aligned}&=0.8×(3.2 - 1.3)\\&=0.8×1.9\\&=1.52\end{aligned}$
12. $8.4 + (3.5 - 0.75)×0.4$
$\begin{aligned}&=8.4 + 2.75×0.4\\&=8.4 + 1.1\\&=9.5\end{aligned}$
13. $3.5×[1.5×(1.07 + 1.93)]$
$\begin{aligned}&=3.5×[1.5×3]\\&=3.5×4.5\\&=15.75\end{aligned}$
$\begin{aligned}&=21 - \left(\frac{7}{11} + \frac{4}{11}\right)\\&=21 - 1\\&=20\end{aligned}$
2. $\frac{11}{9} - \frac{7}{12} - \frac{5}{12} + \frac{7}{9}$
$\begin{aligned}&=\left(\frac{11}{9} + \frac{7}{9}\right) - \left(\frac{7}{12} + \frac{5}{12}\right)\\&=2 - 1\\&=1\end{aligned}$
3. $\frac{2}{15} + \frac{27}{30} - \frac{1}{30}$
$\begin{aligned}&=\frac{2}{15} + \left(\frac{27}{30} - \frac{1}{30}\right)\\&=\frac{2}{15} + \frac{26}{30}\\&=\frac{2}{15} + \frac{13}{15}\\&=1\end{aligned}$
4. $\frac{7}{6} - \left(\frac{7}{10} - \frac{1}{3}\right) + \frac{1}{6}$
$\begin{aligned}&=\left(\frac{7}{6} + \frac{1}{6}\right) - \left(\frac{21}{30} - \frac{10}{30}\right)\\&=\frac{8}{6} - \frac{11}{30}\\&=\frac{40}{30} - \frac{11}{30}\\&=\frac{29}{30}\end{aligned}$
5. $\frac{18}{11} - \left(\frac{7}{11} + \frac{3}{8}\right)$
$\begin{aligned}&=\frac{18}{11} - \frac{7}{11} - \frac{3}{8}\\&=1 - \frac{3}{8}\\&=\frac{5}{8}\end{aligned}$
6. $\frac{13}{49} + \frac{12}{13} - \frac{13}{49} + \frac{14}{13}$
$\begin{aligned}&=\left(\frac{13}{49} - \frac{13}{49}\right) + \left(\frac{12}{13} + \frac{14}{13}\right)\\&=0 + 2\\&=2\end{aligned}$
7. $7.2 - 3.6 + 2.8 - 5.4$
$\begin{aligned}&=(7.2 + 2.8) - (3.6 + 5.4)\\&=10 - 9\\&=1\end{aligned}$
8. $2.17÷0.25÷4$
$\begin{aligned}&=2.17÷(0.25×4)\\&=2.17÷1\\&=2.17\end{aligned}$
9. $6.27×101 - 6.27$
$\begin{aligned}&=6.27×(101 - 1)\\&=6.27×100\\&=627\end{aligned}$
10. $(71.2 - 71.2×0.9)÷0.25$
$\begin{aligned}&=71.2×(1 - 0.9)÷0.25\\&=71.2×0.1÷0.25\\&=7.12÷0.25\\&=28.48\end{aligned}$
11. $0.8×(3.2 - 2.99÷2.3)$
$\begin{aligned}&=0.8×(3.2 - 1.3)\\&=0.8×1.9\\&=1.52\end{aligned}$
12. $8.4 + (3.5 - 0.75)×0.4$
$\begin{aligned}&=8.4 + 2.75×0.4\\&=8.4 + 1.1\\&=9.5\end{aligned}$
13. $3.5×[1.5×(1.07 + 1.93)]$
$\begin{aligned}&=3.5×[1.5×3]\\&=3.5×4.5\\&=15.75\end{aligned}$
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