《2025年小学学霸作业本六年级数学上册苏教版江苏专版》

(1)计算$23-\frac {8}{9}×\frac {3}{4}÷\frac {1}{27}$时,应先算(乘)法,再算(除)法,最后算(减)法。

答案： 乘 除 减

(2)$35×\frac {4}{9}×\frac {9}{4}= 35×(\frac {4}{9}×\frac {9}{4})= 35$,这是运用了乘法结合律。

答案： 乘法结合

(3)把$\frac {4}{3}-\frac {1}{2}= \frac {5}{6},\frac {1}{3}+\frac {7}{6}= \frac {3}{2},\frac {5}{6}÷\frac {3}{2}= \frac {5}{9}$合并成一个综合算式是$\left( \dfrac{4}{3}-\dfrac{1}{2}\right)÷\left( \dfrac{1}{3}+\dfrac{7}{6}\right)=\dfrac{5}{9}$。

答案： $\left( \dfrac{4}{3}-\dfrac{1}{2}\right)÷\left( \dfrac{1}{3}+\dfrac{7}{6}\right)=\dfrac{5}{9}$

2. 脱式计算。
$5÷\frac {5}{6}-\frac {5}{6}÷5$ $(\frac {7}{11}×\frac {11}{14}-\frac {1}{3})×\frac {1}{5}$
$\frac {2}{5}+\frac {3}{5}×\frac {3}{4}÷\frac {3}{2}$ $\frac {9}{8}÷[(\frac {2}{5}+\frac {1}{10})×\frac {3}{4}]$

答案： $5÷\dfrac{5}{6}-\dfrac{5}{6}÷5$ $\left( \dfrac{7}{11}×\dfrac{11}{14}-\dfrac{1}{3}\right)×\dfrac{1}{5}$
$=5×\dfrac{6}{5}-\dfrac{5}{6}×\dfrac{1}{5}$ $=\left( \dfrac{1}{2}-\dfrac{1}{3}\right)×\dfrac{1}{5}$
$=6-\dfrac{1}{6}$ $=\dfrac{1}{6}×\dfrac{1}{5}$
$=5\dfrac{5}{6}$ $=\dfrac{1}{30}$
$\dfrac{2}{5}+\dfrac{3}{5}×\dfrac{3}{4}÷\dfrac{3}{2}$ $\dfrac{9}{8}÷\left \lbrack \left( \dfrac{2}{5}+\dfrac{1}{10}\right)×\dfrac{3}{4}\right\rbrack$
$=\dfrac{2}{5}+\dfrac{3}{5}×\dfrac{3}{4}×\dfrac{2}{3}$ $=\dfrac{9}{8}÷\left \lbrack \dfrac{1}{2}×\dfrac{3}{4}\right\rbrack$
$=\dfrac{2}{5}+\dfrac{3}{10}$ $=\dfrac{9}{8}÷\dfrac{3}{8}$
$=\dfrac{7}{10}$ $=3$

3. 计算下面各题,注意使用简便算法。
$(\frac {3}{4}+\frac {7}{12})×24$ $\frac {11}{10}÷8+\frac {11}{10}×\frac {7}{8}$
$(\frac {2}{11}+\frac {1}{13})×11×13$ $\frac {19}{14}-(\frac {2}{7}÷\frac {4}{5}+\frac {1}{3})$

答案： $\left( \dfrac{3}{4}+\dfrac{7}{12}\right)×24$ $\dfrac{11}{10}÷8+\dfrac{11}{10}×\dfrac{7}{8}$
$=\dfrac{3}{4}×24+\dfrac{7}{12}×24$ $=\dfrac{11}{10}×\dfrac{1}{8}+\dfrac{11}{10}×\dfrac{7}{8}$
$=18+14$ $=\dfrac{11}{10}×\left( \dfrac{1}{8}+\dfrac{7}{8}\right)$
$=32$ $=\dfrac{11}{10}×1$
$=\dfrac{11}{10}$
$\left( \dfrac{2}{11}+\dfrac{1}{13}\right)×11×13$ $\dfrac{19}{14}-\left( \dfrac{2}{7}÷\dfrac{4}{5}+\dfrac{1}{3}\right)$
$=\dfrac{2}{11}×11×13+\dfrac{1}{13}×11×13$ $=\dfrac{19}{14}-\left( \dfrac{5}{14}+\dfrac{1}{3}\right)$
$=26+11$ $=\dfrac{19}{14}-\dfrac{5}{14}-\dfrac{1}{3}$
$=37$ $=\dfrac{2}{3}$

4. 超市里有两种包装的牛奶,小盒牛奶$\frac {1}{4}$升,大盒牛奶的容量是小盒牛奶的$\frac {5}{2}$,1小盒牛奶和1大盒牛奶共多少升?

答案： $\dfrac{1}{4}×\dfrac{5}{2}+\dfrac{1}{4}=\dfrac{7}{8}$(升)
答:1小盒牛奶和1大盒牛奶共$\dfrac{7}{8}$升。

5. 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,每个小兔糖人需要多少千克糖稀?

答案： $\left( 1-12×\dfrac{1}{20}\right)÷6=\dfrac{1}{15}$(千克)
答:每个小兔糖人需要$\dfrac{1}{15}$千克糖稀。

6. 彤彤在计算$\frac {5}{6}×(□+\frac {4}{5})$时错看成了$\frac {5}{6}×□+\frac {4}{5}$,这样得到的结果与正确答案相比是多了还是少了? 两者相差多少?
得到的结果与正确答案相比多了，两者相差$\dfrac{2}{15}$。

答案： $\dfrac{5}{6}×\left( □+\dfrac{4}{5}\right)=\dfrac{5}{6}×□+\dfrac{5}{6}×\dfrac{4}{5}=\dfrac{5}{6}×□+\dfrac{2}{3}$
$\dfrac{4}{5}＞\dfrac{2}{3}$ $\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{2}{15}$
答:得到的结果与正确答案相比多了,两者相差$\dfrac{2}{15}$。
解析:在计算$\dfrac{5}{6}×\left( □+\dfrac{4}{5}\right)$时,可以使用乘法分配律将式子变形,得到$\dfrac{5}{6}×□+\dfrac{2}{3}$,与$\dfrac{5}{6}×□+\dfrac{4}{5}$相比,只需要比较$\dfrac{4}{5}$和$\dfrac{2}{3}$的大小,$\dfrac{4}{5}＞\dfrac{2}{3}$,即错误结果与正确答案相比是多了,两个分数的差值即为所求。