《2025年计算高手六年级数学上册苏教版》

计算:$\frac {1}{2}+\frac {3}{4}÷\frac {1}{2}$

答案： $\frac{1}{2}+\frac{3}{4}÷\frac{1}{2}$
$=\frac{1}{2}+\frac{3}{4}×2$
$=\frac{1}{2}+\frac{3}{2}$
$=2$

一、计算下面各题,能简算的要简算。
$84×(\frac {3}{4}-\frac {1}{3})$　　　　$\frac {3}{8}+(\frac {3}{7}+\frac {1}{14})×\frac {2}{3}$　　　　$\frac {11}{12}÷\frac {1}{8}+\frac {13}{12}×8$
$(\frac {3}{8}-\frac {1}{4})÷\frac {3}{8}$　　　　$5×\frac {7}{8}-0.125$　　　　$\frac {3}{4}×\frac {2}{3}÷\frac {3}{4}×\frac {2}{3}$

答案： 1. $84×(\frac {3}{4}-\frac {1}{3})$
解：
$\begin{aligned}&84×(\frac {3}{4}-\frac {1}{3})\\=&84×\frac {3}{4}-84×\frac {1}{3}\\=&63 - 28\\=&35\end{aligned}$
2. $\frac {3}{8}+(\frac {3}{7}+\frac {1}{14})×\frac {2}{3}$
解：
$\begin{aligned}&\frac {3}{8}+(\frac {3}{7}+\frac {1}{14})×\frac {2}{3}\\=&\frac {3}{8}+(\frac {6}{14}+\frac {1}{14})×\frac {2}{3}\\=&\frac {3}{8}+\frac {7}{14}×\frac {2}{3}\\=&\frac {3}{8}+\frac {1}{3}\\=&\frac {9}{24}+\frac {8}{24}\\=&\frac {17}{24}\end{aligned}$
3. $\frac {11}{12}÷\frac {1}{8}+\frac {13}{12}×8$
解：
$\begin{aligned}&\frac {11}{12}÷\frac {1}{8}+\frac {13}{12}×8\\=&\frac {11}{12}×8+\frac {13}{12}×8\\=&(\frac {11}{12}+\frac {13}{12})×8\\=&\frac {24}{12}×8\\=&2×8\\=&16\end{aligned}$
4. $(\frac {3}{8}-\frac {1}{4})÷\frac {3}{8}$
解：
$\begin{aligned}&(\frac {3}{8}-\frac {1}{4})÷\frac {3}{8}\\=&(\frac {3}{8}-\frac {2}{8})÷\frac {3}{8}\\=&\frac {1}{8}÷\frac {3}{8}\\=&\frac {1}{8}×\frac {8}{3}\\=&\frac {1}{3}\end{aligned}$
5. $5×\frac {7}{8}-0.125$
解：
$\begin{aligned}&5×\frac {7}{8}-0.125\\=&\frac {35}{8}-\frac {1}{8}\\=&\frac {34}{8}\\=&\frac {17}{4}\end{aligned}$
6. $\frac {3}{4}×\frac {2}{3}÷\frac {3}{4}×\frac {2}{3}$
解：
$\begin{aligned}&\frac {3}{4}×\frac {2}{3}÷\frac {3}{4}×\frac {2}{3}\\=&\frac {3}{4}÷\frac {3}{4}×\frac {2}{3}×\frac {2}{3}\\=&1×\frac {2}{3}×\frac {2}{3}\\=&\frac {4}{9}\end{aligned}$
综上，答案依次为$35$；$\frac{17}{24}$；$16$；$\frac{1}{3}$；$\frac{17}{4}$；$\frac{4}{9}$。

二、实验班原创 算理探究 桃桃在计算$\frac {2}{5}×(\frac {3}{4}+\frac {1}{2})-\frac {1}{3}$时,她的步骤如下:
①$\frac {2}{5}×\frac {3}{4}= \frac {6}{20}= \frac {3}{10}$ ②$\frac {3}{10}+\frac {1}{2}= \frac {3}{10}+\frac {5}{10}= \frac {8}{10}= \frac {4}{5}$ ③$\frac {4}{5}-\frac {1}{3}= \frac {12}{15}-\frac {5}{15}= \frac {7}{15}$
桃桃的计算结果是否正确？如果错误,那么请用正确顺序重新计算。

答案： 不正确。
$\frac{2}{5}× (\frac{3}{4}+\frac{1}{2})-\frac{1}{3}$
$=\frac{2}{5}× \frac{5}{4}-\frac{1}{3}$
$=\frac{1}{6}$