Question

6．計算：97$\frac{1}{50}$×$\frac{1}{49}$+77$\frac{1}{40}$×$\frac{1}{39}$+57$\frac{1}{30}$×$\frac{1}{29}$．

Answer 1

分析 97$\frac{1}{50}$=98-$\frac{49}{50}$，77$\frac{1}{40}$=78-$\frac{39}{40}$，57$\frac{1}{30}$=58-$\frac{29}{30}$，然后再根據(jù)乘法分配律進行簡算．

解答 解：97$\frac{1}{50}$×$\frac{1}{49}$+77$\frac{1}{40}$×$\frac{1}{39}$+57$\frac{1}{30}$×$\frac{1}{29}$
=（98-$\frac{49}{50}$）×$\frac{1}{49}$+（78-$\frac{39}{40}$）×$\frac{1}{39}$+（58-$\frac{29}{30}$）×$\frac{1}{29}$
=98×$\frac{1}{49}$-$\frac{49}{50}$×$\frac{1}{49}$+78×$\frac{1}{39}$-$\frac{39}{40}$×$\frac{1}{39}$+58×$\frac{1}{29}$-$\frac{29}{30}$×$\frac{1}{29}$
=2-$\frac{1}{50}$+2-$\frac{1}{40}$+2-$\frac{1}{30}$
=（2+2+2）-（$\frac{1}{50}$+$\frac{1}{40}$+$\frac{1}{30}$）
=6-$\frac{47}{600}$
=5$\frac{553}{600}$．

點評 考查了運算定律與簡便運算，四則混合運算．注意運算順序和運算法則，靈活運用所學的運算定律簡便計算．