《2025年状元成才路创优作业100分六年级数学上册人教版湖南专版》

1. 选择合适的方法计算,写出过程。
$\frac{7}{24} × \frac{9}{14} = \frac{7}{24} × \frac{9}{14} = ($$\frac{3}{16}$$)$
$1.2 × \frac{4}{5} = 1.2 × 0.8 = ($$0.96$$)$
$0.7 × \frac{2}{3} = \frac{7}{10} × \frac{2}{3} = ($$\frac{7}{15}$$)$
$72 × \frac{5}{18} = ($$20$$)$
$\frac{4}{5} × \frac{7}{3} = ($$\frac{28}{15}$$)$
$2.6 × \frac{8}{13} = ($$1.6$$)$
$\frac{2}{5} × 0.8 = ($$0.32$$)$
$3.6 × \frac{4}{7} = ($$\frac{72}{35}$$)$
$\frac{19}{42} × \frac{35}{38} = ($$\frac{5}{12}$$)$

答案： $\frac{3}{16}
0.96
\frac{7}{15}$
$72×\frac{5}{18}=\frac{72}{1}×\frac{5}{18}=20$
$\frac{4}{5}×\frac{7}{3}=\frac{28}{15}$ $2.6×\frac{8}{13}=2.6×\frac{8}{13}=1.6$
$\frac{2}{5}×0.8=0.4×0.8=0.32$ $3.6×\frac{4}{7}=\frac{18}{5}×\frac{4}{7}=\frac{72}{35}$
$\frac{19}{42}×\frac{35}{38}=\frac{19}{42}×\frac{35}{38}=\frac{5}{12}$

2. 根据给出的图形画图表示出各算式的意思。

答案：

3. 下面的计算对吗？对的画“√”,错的画“×”并改正。
$\frac{7}{12} - \frac{1}{12} × \frac{2}{5} = \frac{1}{2} × \frac{2}{5} = \frac{1}{5}$ (×)
- 改正：$\frac{7}{12}-\frac{1}{12}×\frac{2}{5}=\frac{7}{12}-\frac{1}{30}=\frac{11}{20}$
$\frac{3}{10} × (\frac{5}{3} + \frac{1}{2}) = \frac{3}{10} × \frac{5}{3} + \frac{1}{2} = 1$ (×)
- 改正：$\frac{3}{10}×\left(\frac{5}{3}+\frac{1}{2}\right)=\frac{3}{10}×\frac{13}{6}=\frac{13}{20}$

答案： × $\frac{7}{12}-\frac{1}{12}×\frac{2}{5}=\frac{7}{12}-\frac{1}{30}=\frac{11}{20}$ × $\frac{3}{10}×\left(\frac{5}{3}+\frac{1}{2}\right)=\frac{3}{10}×\frac{13}{6}=\frac{13}{20}$ ​

4. 计算下面各题,能简算的要简算。
$\frac{5}{9} + \frac{4}{15} × \frac{9}{8}$
$\frac{1}{7} × (4 - \frac{2}{5})$
$\frac{4}{9} × \frac{3}{8} + \frac{5}{8}$
$\frac{11}{25} × \frac{3}{8} × \frac{20}{33}$ 
$\frac{7}{10} × \frac{9}{8} + \frac{1}{8} × 0.7$
$\frac{8}{9} × [\frac{3}{4} - (\frac{7}{16} - \frac{1}{4})]$
$(\frac{5}{4} + \frac{3}{5} - \frac{5}{6}) × 60$
$\frac{17}{40} × \frac{29}{27} + \frac{17}{40} × \frac{11}{27}$
$2025\frac{2025}{2026} × \frac{1}{2027}$

答案： $\frac{5}{9}+\frac{4}{15}×\frac{9}{8}= \frac{5}{9} + \frac{3}{10}- = \frac{50 + 27}{90}- = \frac{77}{90}$
$\frac{1}{7} × (4 - \frac{2}{5})- = \frac{1}{7} × \frac{18}{5}- = \frac{18}{35}$
$\frac{4}{9} × \frac{3}{8} + \frac{5}{8}- = \frac{1}{6} + \frac{5}{8}- = \frac{4 + 15}{24} = \frac{19}{24}$
$\frac{11}{25} × \frac{3}{8} × \frac{20}{33}$ $= \frac{11}{25} × \frac{20}{33} × \frac{3}{8}$- $= \frac{4}{15} × \frac{3}{8}$- $= \frac{1}{10}$
$\frac{7}{10} × \frac{9}{8} + \frac{1}{8} × 0.7$-$= \frac{7}{10} × \frac{9}{8} + \frac{7}{10} × \frac{1}{8}$ $= \frac{7}{10} × (\frac{9}{8} + \frac{1}{8})$$= \frac{7}{10} × \frac{10}{8}$$= \frac{7}{8}$
$\frac{8}{9} × [\frac{3}{4} - (\frac{7}{16} - \frac{1}{4})]$$= \frac{8}{9} × [\frac{3}{4} + \frac{1}{4} - \frac{7}{16}]$$= \frac{8}{9} × (1 - \frac{7}{16})$ $= \frac{8}{9} × \frac{9}{16}$$= \frac{1}{2}$
$(\frac{5}{4} + \frac{3}{5} - \frac{5}{6}) × 60$ $= \frac{5}{4} × 60 + \frac{3}{5} × 60 - \frac{5}{6} × 60$ $= 75 + 36 - 50$ $= 61$
 $\frac{17}{40} × \frac{29}{27} + \frac{17}{40} × \frac{11}{27}$$= \frac{17}{40} × (\frac{29}{27} + \frac{11}{27})$$= \frac{17}{40} × \frac{40}{27}$ $= \frac{17}{27}$
$2025\frac{2025}{2026} × \frac{1}{2027}$$= (2026 - \frac{1}{2026}) × \frac{1}{2027}$ $= 2026 × \frac{1}{2027} - \frac{1}{2026} × \frac{1}{2027}$ $= \frac{2026}{2027} - \frac{1}{2026 × 2027}$$= \frac{2026 × 2026 - 1}{2026 × 2027}$ $= \frac{(2026 + 1)(2026 - 1)}{2026 × 2027}$$= \frac{2027 × 2025}{2026 × 2027}$ $= \frac{2025}{2026}$