Question

2．计算：$\frac{1\frac{2}{3}+2\frac{3}{4}+3\frac{4}{5}+…+28\frac{29}{30}}{3\frac{1}{3}+5\frac{2}{4}+7\frac{3}{5}+…+57\frac{28}{30}}$．

Answer 1

分析 把带分数化成假分数，分子$\frac{5}{3}$+$\frac{11}{4}$+$\frac{19}{5}$+…+$\frac{869}{30}$，分母$\frac{10}{3}$+$\frac{22}{4}$+$\frac{38}{5}$+…+$\frac{1738}{30}$=$\frac{5}{3}$×2+$\frac{11}{4}$×2+$\frac{19}{5}$×2+…+$\frac{869}{30}$×2=（$\frac{5}{3}$+$\frac{11}{4}$+$\frac{19}{5}$+…+$\frac{869}{30}$）×2，然后再约分计算．

解答 解：$\frac{1\frac{2}{3}+2\frac{3}{4}+3\frac{4}{5}+…+28\frac{29}{30}}{3\frac{1}{3}+5\frac{2}{4}+7\frac{3}{5}+…+57\frac{28}{30}}$
=$\frac{\frac{5}{3}+\frac{11}{4}+\frac{19}{5}+…+\frac{869}{30}}{\frac{10}{3}+\frac{22}{4}+\frac{38}{5}+…+\frac{1738}{30}}$
=$\frac{\frac{5}{3}+\frac{11}{4}+\frac{19}{5}+…+\frac{869}{30}}{\frac{5}{3}×2+\frac{11}{4}×2+\frac{19}{5}×2+…+\frac{869}{30}×2}$
=$\frac{\frac{5}{3}+\frac{11}{4}+\frac{19}{5}+…+\frac{869}{30}}{（\frac{5}{3}+\frac{11}{4}+\frac{19}{5}+…+\frac{869}{30}）×2}$
=$\frac{1}{2}$．

点评 本题关键是把带分数化成假分数，再找出分子与分母之间的倍数关系，然后再约分解答．