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5. 把一批书按$2:3:4或2:4:5$两种方案分给甲、乙、丙三个班,都可以将这批书正好分完,这批书可能有$(\quad)$本。
①$90$ ②$99$ ③$110$
①$90$ ②$99$ ③$110$
答案
②
解析
2+3+4=9，2+4+5=11，9和11的最小公倍数是99，这批书的数量是99的倍数，选项中只有99符合。②
6. 要剪一个面积是$28.26$平方厘米的圆形纸片,至少需要一张面积是$(\quad)$平方厘米的正方形纸片。($\pi取3.14$)
①$28.26$ ②$18$ ③$36$
①$28.26$ ②$18$ ③$36$
答案
③
解析
圆形面积公式：$S = \pi r^2$，已知$S = 28.26$平方厘米，$\pi = 3.14$，则$r^2 = 28.26÷3.14 = 9$，解得$r = 3$厘米。要剪此圆形，正方形边长至少为圆的直径，即$2r = 6$厘米，正方形面积为$6×6 = 36$平方厘米。③
1. 直接写出得数。
$\frac{1}{2}+\frac{1}{3}$ $\frac{4}{9}÷\frac{2}{9}$ $1÷\frac{1}{4}÷\frac{1}{4}$
$\frac{9}{13}×\frac{2}{3}÷\frac{9}{13}×\frac{2}{3}$ $\frac{4}{5}×\frac{3}{4}$ $0×\frac{7}{8}+\frac{1}{4}$
$(\frac{1}{2}+\frac{1}{3})×18$ $\frac{5}{8}÷12.5\%$
$\frac{1}{2}+\frac{1}{3}$ $\frac{4}{9}÷\frac{2}{9}$ $1÷\frac{1}{4}÷\frac{1}{4}$
$\frac{9}{13}×\frac{2}{3}÷\frac{9}{13}×\frac{2}{3}$ $\frac{4}{5}×\frac{3}{4}$ $0×\frac{7}{8}+\frac{1}{4}$
$(\frac{1}{2}+\frac{1}{3})×18$ $\frac{5}{8}÷12.5\%$
答案
$\frac{5}{6}$ 2 16 $\frac{4}{9}$ $\frac{3}{5}$ $\frac{1}{4}$ 15 5
2. 用简便算法计算下面各题。
$8×0.4×12.5×25\%$ $\frac{4}{5}+\frac{2}{3}÷(\frac{5}{6}-\frac{1}{2})$
$1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}$ $(2.7×60\%+7.3×60\%)÷\frac{27}{5}$
$8×0.4×12.5×25\%$ $\frac{4}{5}+\frac{2}{3}÷(\frac{5}{6}-\frac{1}{2})$
$1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}$ $(2.7×60\%+7.3×60\%)÷\frac{27}{5}$
答案
10 $2\frac{4}{5}$ $\frac{2}{3}$ $\frac{10}{9}$
解析
$8×0.4×12.5×25\%$
$=(8×12.5)×(0.4×25\%)$
$=100×0.1$
$=10$
$\frac{4}{5}+\frac{2}{3}÷(\frac{5}{6}-\frac{1}{2})$
$=\frac{4}{5}+\frac{2}{3}÷\frac{1}{3}$
$=\frac{4}{5}+2$
$=2\frac{4}{5}$
$1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}$
$=1-(\frac{1}{2}+\frac{1}{3})+(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+(\frac{1}{5}+\frac{1}{6})$
$=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}$
$=\frac{1}{2}+\frac{1}{6}$
$=\frac{2}{3}$
$(2.7×60\%+7.3×60\%)÷\frac{27}{5}$
$=60\%×(2.7+7.3)÷\frac{27}{5}$
$=0.6×10×\frac{5}{27}$
$=6×\frac{5}{27}$
$=\frac{10}{9}$
$=(8×12.5)×(0.4×25\%)$
$=100×0.1$
$=10$
$\frac{4}{5}+\frac{2}{3}÷(\frac{5}{6}-\frac{1}{2})$
$=\frac{4}{5}+\frac{2}{3}÷\frac{1}{3}$
$=\frac{4}{5}+2$
$=2\frac{4}{5}$
$1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}$
$=1-(\frac{1}{2}+\frac{1}{3})+(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+(\frac{1}{5}+\frac{1}{6})$
$=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}$
$=\frac{1}{2}+\frac{1}{6}$
$=\frac{2}{3}$
$(2.7×60\%+7.3×60\%)÷\frac{27}{5}$
$=60\%×(2.7+7.3)÷\frac{27}{5}$
$=0.6×10×\frac{5}{27}$
$=6×\frac{5}{27}$
$=\frac{10}{9}$
3. 解方程。
$\frac{1}{15}x-\frac{1}{5}= \frac{1}{3}$ $\frac{1}{3}x+\frac{1}{4}x= 28$ $3x-\frac{3}{5}÷\frac{9}{5}= \frac{1}{5}$
$\frac{1}{15}x-\frac{1}{5}= \frac{1}{3}$ $\frac{1}{3}x+\frac{1}{4}x= 28$ $3x-\frac{3}{5}÷\frac{9}{5}= \frac{1}{5}$
答案
$x=8$ $x=48$ $x=\frac{8}{45}$
解析
解：$\frac{1}{15}x - \frac{1}{5} = \frac{1}{3}$
$\frac{1}{15}x = \frac{1}{3} + \frac{1}{5}$
$\frac{1}{15}x = \frac{5}{15} + \frac{3}{15}$
$\frac{1}{15}x = \frac{8}{15}$
$x = 8$
解：$\frac{1}{3}x + \frac{1}{4}x = 28$
$\frac{4}{12}x + \frac{3}{12}x = 28$
$\frac{7}{12}x = 28$
$x = 28 × \frac{12}{7}$
$x = 48$
解：$3x - \frac{3}{5} ÷ \frac{9}{5} = \frac{1}{5}$
$3x - \frac{3}{5} × \frac{5}{9} = \frac{1}{5}$
$3x - \frac{1}{3} = \frac{1}{5}$
$3x = \frac{1}{5} + \frac{1}{3}$
$3x = \frac{3}{15} + \frac{5}{15}$
$3x = \frac{8}{15}$
$x = \frac{8}{45}$
$\frac{1}{15}x = \frac{1}{3} + \frac{1}{5}$
$\frac{1}{15}x = \frac{5}{15} + \frac{3}{15}$
$\frac{1}{15}x = \frac{8}{15}$
$x = 8$
解：$\frac{1}{3}x + \frac{1}{4}x = 28$
$\frac{4}{12}x + \frac{3}{12}x = 28$
$\frac{7}{12}x = 28$
$x = 28 × \frac{12}{7}$
$x = 48$
解：$3x - \frac{3}{5} ÷ \frac{9}{5} = \frac{1}{5}$
$3x - \frac{3}{5} × \frac{5}{9} = \frac{1}{5}$
$3x - \frac{1}{3} = \frac{1}{5}$
$3x = \frac{1}{5} + \frac{1}{3}$
$3x = \frac{3}{15} + \frac{5}{15}$
$3x = \frac{8}{15}$
$x = \frac{8}{45}$
