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(1)(广州期末真题)下面选项中,当$a=(\quad)$时,$a×(\frac{1}{4}+\frac{1}{5})$运用乘法分配律计算简便。
A.9
B.13
C.17
D.20
A.9
B.13
C.17
D.20
答案
(1)D
(2)下列算式中,等号左、右两边不相等的是(
A.$\frac{3}{5}×99=\frac{3}{5}×100 -1$
B.$\frac{3}{5}×99=\frac{3}{5}×100 - \frac{3}{5}$
C.$\frac{3}{5}×(\frac{7}{9}×\frac{8}{11})=(\frac{3}{5}×\frac{7}{9})×\frac{8}{11}$
D.$\frac{3}{5}×99=\frac{3}{5}×(100 -1)$
A
)。A.$\frac{3}{5}×99=\frac{3}{5}×100 -1$
B.$\frac{3}{5}×99=\frac{3}{5}×100 - \frac{3}{5}$
C.$\frac{3}{5}×(\frac{7}{9}×\frac{8}{11})=(\frac{3}{5}×\frac{7}{9})×\frac{8}{11}$
D.$\frac{3}{5}×99=\frac{3}{5}×(100 -1)$
答案
(2)A
2. [教材改编]根据乘法运算律填一填。(○里填符号)
$\frac{5}{6}×\frac{2}{7}×\frac{6}{5}=□×□×\frac{2}{7}$
$(\frac{7}{9}+\frac{11}{12})×36=\frac{7}{9}×36○□○36$
$(\frac{2}{5}×4)×\frac{3}{4}=\frac{2}{5}×(□○□)$
$\frac{9}{11}×\frac{1}{6}-\frac{3}{11}×\frac{1}{6}=(□○□)○□$
$\frac{5}{6}×\frac{2}{7}×\frac{6}{5}=□×□×\frac{2}{7}$
$(\frac{7}{9}+\frac{11}{12})×36=\frac{7}{9}×36○□○36$
$(\frac{2}{5}×4)×\frac{3}{4}=\frac{2}{5}×(□○□)$
$\frac{9}{11}×\frac{1}{6}-\frac{3}{11}×\frac{1}{6}=(□○□)○□$
答案
$\frac{5}{6}×\frac{6}{5}×\frac{2}{7}$
$\frac{7}{9}×36 + \frac{11}{12}×36$
$\frac{2}{5}×(4 × \frac{3}{4})$
$(\frac{9}{11}-\frac{3}{11})×\frac{1}{6}$
$\frac{7}{9}×36 + \frac{11}{12}×36$
$\frac{2}{5}×(4 × \frac{3}{4})$
$(\frac{9}{11}-\frac{3}{11})×\frac{1}{6}$
3. 用简便算法计算下面各题。
$\frac{13}{22}×\frac{2}{7}×\frac{11}{13}$
$(\frac{8}{9}+\frac{4}{29})×29×9$
$\frac{4}{11}×29+\frac{4}{11}×30-\frac{4}{11}×15$
$\frac{13}{22}×\frac{2}{7}×\frac{11}{13}$
$(\frac{8}{9}+\frac{4}{29})×29×9$
$\frac{4}{11}×29+\frac{4}{11}×30-\frac{4}{11}×15$
答案
$\frac{13}{22}×\frac{2}{7}×\frac{11}{13}$
$=\frac{13}{22}×\frac{11}{13}×\frac{2}{7}$
$=\frac{1}{2}×\frac{2}{7}$
$=\frac{1}{7}$
$(\frac{8}{9}+\frac{4}{29})×29×9$
$=\frac{8}{9}×29×9+\frac{4}{29}×29×9$
$=232+36$
$=268$
$\frac{4}{11}×29+\frac{4}{11}×30-\frac{4}{11}×15$
$=\frac{4}{11}×(29+30-15)$
$=\frac{4}{11}×44=16$
$=\frac{13}{22}×\frac{11}{13}×\frac{2}{7}$
$=\frac{1}{2}×\frac{2}{7}$
$=\frac{1}{7}$
$(\frac{8}{9}+\frac{4}{29})×29×9$
$=\frac{8}{9}×29×9+\frac{4}{29}×29×9$
$=232+36$
$=268$
$\frac{4}{11}×29+\frac{4}{11}×30-\frac{4}{11}×15$
$=\frac{4}{11}×(29+30-15)$
$=\frac{4}{11}×44=16$
4. [新情境·环境保护]无患子的果皮含有皂素，自古以来就是天然的清洁剂。自制无患子洗手液，环保又实用。阿芳周末两天收集的无患子质量如下表，若每千克无患子可以制作$\frac{7}{10}$L洗手液，则阿芳一共可以制作多少升洗手液？
答案
$\frac{7}{10}×3+\frac{7}{10}×7=\frac{7}{10}×(3+7)=7(\mathrm{L})$
答:阿芳一共可以制作7 L洗手液。
答:阿芳一共可以制作7 L洗手液。
5. 简算:$41\frac{1}{3}×\frac{3}{4}+51\frac{1}{4}×\frac{4}{5}+61\frac{1}{5}×\frac{5}{6}$
答案
$41\frac{1}{3}×\frac{3}{4}+51\frac{1}{4}×\frac{4}{5}+61\frac{1}{5}×\frac{5}{6}$
$=(40+\frac{4}{3})×\frac{3}{4}+(50+\frac{5}{4})×\frac{4}{5}+(60+\frac{6}{5})×\frac{5}{6}$
$=40×\frac{3}{4}+\frac{4}{3}×\frac{3}{4}+50×\frac{4}{5}+\frac{4}{4}×\frac{5}{5}+60×\frac{5}{6}+\frac{6}{5}×\frac{5}{6}$
$=30+1+40+1+50+1$
$=123$
$=(40+\frac{4}{3})×\frac{3}{4}+(50+\frac{5}{4})×\frac{4}{5}+(60+\frac{6}{5})×\frac{5}{6}$
$=40×\frac{3}{4}+\frac{4}{3}×\frac{3}{4}+50×\frac{4}{5}+\frac{4}{4}×\frac{5}{5}+60×\frac{5}{6}+\frac{6}{5}×\frac{5}{6}$
$=30+1+40+1+50+1$
$=123$
快乐口算
$3.2×(\frac{1}{8}+\frac{1}{2})=$
$\frac{3}{5}×10+\frac{2}{5}=$
$\frac{9}{5}×8×\frac{5}{9}=$
$\frac{3}{5}+\frac{1}{3}×\frac{4}{5}=$
$\frac{5}{21}×63=$
$\frac{34}{39}×\frac{26}{27}=$
$\frac{7}{13}+\frac{7}{13}=$
$1-\frac{1}{6}-\frac{1}{3}=$
$\frac{11}{32}-\frac{7}{32}=$
$\frac{15}{8}×\frac{4}{5}=$
$3.2×(\frac{1}{8}+\frac{1}{2})=$
$\frac{3}{5}×10+\frac{2}{5}=$
$\frac{9}{5}×8×\frac{5}{9}=$
$\frac{3}{5}+\frac{1}{3}×\frac{4}{5}=$
$\frac{5}{21}×63=$
$\frac{34}{39}×\frac{26}{27}=$
$\frac{7}{13}+\frac{7}{13}=$
$1-\frac{1}{6}-\frac{1}{3}=$
$\frac{11}{32}-\frac{7}{32}=$
$\frac{15}{8}×\frac{4}{5}=$
答案
$2$
$6\frac{2}{5}$
$8$
$\frac{13}{15}$
$15$
$\frac{68}{81}$
$\frac{14}{13}$
$\frac{1}{2}$
$\frac{1}{8}$
$1.5$
$6\frac{2}{5}$
$8$
$\frac{13}{15}$
$15$
$\frac{68}{81}$
$\frac{14}{13}$
$\frac{1}{2}$
$\frac{1}{8}$
$1.5$
