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1. 填一填。
(1) 计算$2+\frac {5}{8}×\frac {7}{10}÷\frac {7}{24}$时,应先算(
(2)$\frac {13}{25}×99=\frac {13}{25}×100-\frac {13}{25}$,这是运用了(
(3) 若$a+b=420$,则$a÷\frac {7}{5}+b×\frac {5}{7}=$(
(1) 计算$2+\frac {5}{8}×\frac {7}{10}÷\frac {7}{24}$时,应先算(
乘
)法,再算(除
)法,最后算(加
)法。(2)$\frac {13}{25}×99=\frac {13}{25}×100-\frac {13}{25}$,这是运用了(
乘法分配
)律,使计算简便。(3) 若$a+b=420$,则$a÷\frac {7}{5}+b×\frac {5}{7}=$(
300
)。答案
1. (1) 乘 除 加 (2) 乘法分配 (3) 300
2. 根据要求给下面的算式添上小括号。
最后一步求积：
$\frac {5}{8}÷\frac {1}{4}+\frac {3}{5}×\frac {7}{6}$
第一步求和：
$\frac {5}{8}÷\frac {1}{4}+\frac {3}{5}×\frac {7}{6}$
最后一步求积：
$\frac {5}{8}÷\frac {1}{4}+\frac {3}{5}×\frac {7}{6}$
第一步求和：
$\frac {5}{8}÷\frac {1}{4}+\frac {3}{5}×\frac {7}{6}$
答案
2. $\frac {5}{8}÷(\frac {1}{4}+\frac {3}{5})×\frac {7}{6}$ $\frac {5}{8}÷(\frac {1}{4}+\frac {3}{5})×\frac {7}{6}$
(第1道算式答案不唯一)
(第1道算式答案不唯一)
3. 直接写出得数。
$\frac {4}{7}÷\frac {3}{14}=$
$\frac {3}{5}×\frac {5}{9}÷\frac {3}{5}×\frac {5}{9}=$
$\frac {1}{3}×\frac {4}{15}=$
$5÷\frac {5}{6}-\frac {5}{6}÷5=$
$\frac {4}{7}÷\frac {3}{14}=$
$\frac {3}{5}×\frac {5}{9}÷\frac {3}{5}×\frac {5}{9}=$
$\frac {1}{3}×\frac {4}{15}=$
$5÷\frac {5}{6}-\frac {5}{6}÷5=$
答案
3. $\frac {8}{3}$ $\frac {25}{81}$ $\frac {4}{45}$ $5\frac {5}{6}$
4. (苏州真题)计算下面各题,能简算的要简算。
$4.7×102-4.7×2$
$\frac {1}{12}+\frac {8}{9}÷\frac {5}{6}×\frac {5}{8}$
$7-(\frac {6}{7}÷\frac {3}{14}+\frac {13}{18})$
$\frac {7}{20}×8×12.5$
$\frac {4}{7}×\frac {5}{6}+\frac {3}{7}×\frac {5}{6}$
$36×(\frac {5}{6}-\frac {1}{12}+\frac {2}{3})$
$4.7×102-4.7×2$
$\frac {1}{12}+\frac {8}{9}÷\frac {5}{6}×\frac {5}{8}$
$7-(\frac {6}{7}÷\frac {3}{14}+\frac {13}{18})$
$\frac {7}{20}×8×12.5$
$\frac {4}{7}×\frac {5}{6}+\frac {3}{7}×\frac {5}{6}$
$36×(\frac {5}{6}-\frac {1}{12}+\frac {2}{3})$
答案
4. $4.7×102-4.7×2$
$=4.7×(102-2)$
$=4.7×100$
$=470$
![img alt=4]
$=4.7×(102-2)$
$=4.7×100$
$=470$
![img alt=4]
5. 下面(
A.5
B.$\frac {1}{5}$
C.$\frac {5}{6}$
D.$\frac {6}{5}$
C
)填在算式$\frac {6}{11}×\frac {6}{5}+\frac {5}{11}÷□$的□中,这道算式就能简便计算。A.5
B.$\frac {1}{5}$
C.$\frac {5}{6}$
D.$\frac {6}{5}$
答案
5. C
解析
要使算式$\frac{6}{11} × \frac{6}{5} + \frac{5}{11} ÷ □$能简便计算，需将除法转化为乘法后提取公因式。设$□$中的数为$x$，则$\frac{5}{11} ÷ x = \frac{5}{11} × \frac{1}{x}$。要与$\frac{6}{11} × \frac{6}{5}$有相同因数，需$\frac{1}{x} = \frac{6}{5}$，即$x = \frac{5}{6}$。此时算式为$\frac{6}{11} × \frac{6}{5} + \frac{5}{11} × \frac{6}{5} = \frac{6}{5} × (\frac{6}{11} + \frac{5}{11}) = \frac{6}{5} × 1 = \frac{6}{5}$，可简便计算。
C
C
6. (五育并举)周末的劳动实践中,六年级的同学摘了$\frac {2}{5}$吨梨,摘的草莓的质量恰好是梨的$\frac {5}{8}$,六年级的同学摘了多少吨草莓?摘的草莓比梨少多少吨?
答案
6. $\frac {2}{5}×\frac {5}{8}=\frac {1}{4}$(吨) $\frac {2}{5}-\frac {1}{4}=\frac {3}{20}$(吨)
7. 李爷爷熬制了1千克糖稀来制作糖人,他先制作了12个小猫糖人,再用剩下的糖稀正好制作了6个小兔糖人,已知每个小猫糖人需要$\frac {1}{20}$千克糖稀,则每个小兔糖人需要多少千克糖稀?
答案
7. $(1-12×\frac {1}{20})÷6=\frac {1}{15}$(千克)
8. (算法探究)用简便方法计算。
$(\frac {12}{13}+\frac {12}{17}+\frac {12}{19})÷(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})$
$(\frac {12}{13}+\frac {12}{17}+\frac {12}{19})÷(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})$
答案
8. $(\frac {12}{13}+\frac {12}{17}+\frac {12}{19})÷(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})$
$=3×(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})÷(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})$
$=3$
$=3×(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})÷(\frac {4}{13}+\frac {4}{17}+\frac {4}{19})$
$=3$
