分数加减运算难题解析试题

分数加减运算难题解析试题一、填空题1.计算(frac{1}{2}+frac{1}{3}frac{1}{6})的结果是________。2.计算(frac{5}{6}frac{1}{4}+frac{1}{3})的结果是________。3.计算(1frac{1}{2}+frac{1}{3}frac{1}{6})的结果是________。4.计算(frac{1}{2}+frac{1}{3}+frac{1}{6}+frac{1}{12}+frac{1}{24})的结果是________。5.计算(frac{1}{2}frac{1}{3}+frac{1}{4}frac{1}{5}+frac{1}{6}frac{1}{7})的结果是________。二、选择题1.下列计算正确的是________。A.(frac{1}{2}+frac{1}{3}=frac{2}{5})B.(frac{5}{6}frac{1}{3}=frac{1}{2})C.(frac{1}{4}+frac{1}{5}=frac{1}{9})D.(frac{3}{4}frac{1}{2}=frac{1}{4})2.计算(frac{1}{2}frac{1}{3}+frac{1}{4}frac{1}{5})的结果与下列哪个分数最接近________？A.(frac{1}{10})B.(frac{1}{8})C.(frac{1}{6})D.(frac{1}{4})3.如果(a=frac{1}{2}+frac{1}{3}frac{1}{4})，(b=frac{1}{3}+frac{1}{4}frac{1}{5})，那么(a)与(b)的关系是________。A.(a>b)B.(a<b)C.(a=b)D.无法确定4.计算(frac{1}{1times2}+frac{1}{2times3}+frac{1}{3times4}+frac{1}{4times5})的结果是________。A.(frac{4}{5})B.(frac{5}{4})C.(1)D.(frac{6}{5})5.计算(frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+frac{1}{42})的结果是________。A.(frac{3}{4})B.(frac{5}{6})C.(frac{2}{3})D.(frac{1}{2})三、解答题1.计算(frac{1}{2}+frac{2}{3}frac{3}{4}+frac{4}{5}frac{5}{6})。2.计算(frac{1}{1times2}+frac{1}{2times3}+frac{1}{3times4}+cdots+frac{1}{99times100})。3.计算(frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+frac{1}{42}+frac{1}{56}+frac{1}{72}+frac{1}{90}+frac{1}{105})。4.一个分数的分子和分母都是三位数，且分子比分母小49，这个分数化简后是(frac{5}{7})，求这个分数。5.甲、乙两人分别从A、B两地同时出发，相向而行。甲的速度是每小时(frac{3}{5})千米，乙的速度是每小时(frac{2}{3})千米。他们相遇后，甲又走了2小时，此时甲离B地还有(frac{2}{3})千米。求A、B两地之间的距离。答案及解析一、填空题1.(frac{1}{2}+frac{1}{3}frac{1}{6}=frac{3}{6}+frac{2}{6}frac{1}{6}=frac{4}{6}=frac{2}{3})2.(frac{5}{6}frac{1}{4}+frac{1}{3}=frac{10}{12}frac{3}{12}+frac{4}{12}=frac{11}{12})3.(1frac{1}{2}+frac{1}{3}frac{1}{6}=frac{6}{6}frac{3}{6}+frac{2}{6}frac{1}{6}=frac{4}{6}=frac{2}{3})4.(frac{1}{2}+frac{1}{3}+frac{1}{6}+frac{1}{12}+frac{1}{24}=frac{12}{24}+frac{8}{24}+frac{4}{24}+frac{2}{24}+frac{1}{24}=frac{27}{24}=frac{9}{8})5.(frac{1}{2}frac{1}{3}+frac{1}{4}frac{1}{5}+frac{1}{6}frac{1}{7}=frac{6}{12}frac{4}{12}+frac{3}{12}frac{2}{10}+frac{2}{12}frac{1}{7}=frac{7}{12}frac{1}{7}=frac{49}{84}frac{12}{84}=frac{37}{84})二、选择题1.BA.(frac{1}{2}+frac{1}{3}=frac{3}{6}+frac{2}{6}=frac{5}{6})B.(frac{5}{6}frac{1}{3}=frac{5}{6}frac{2}{6}=frac{1}{2})C.(frac{1}{4}+frac{1}{5}=frac{5}{20}+frac{4}{20}=frac{9}{20})D.(frac{3}{4}frac{1}{2}=frac{3}{4}frac{2}{4}=frac{1}{4})2.C(frac{1}{2}frac{1}{3}+frac{1}{4}frac{1}{5}=frac{6}{12}frac{4}{12}+frac{3}{12}frac{2}{10}=frac{5}{12}frac{1}{5}=frac{25}{60}frac{12}{60}=frac{13}{60}approxfrac{1}{6})3.A(a=frac{1}{2}+frac{1}{3}frac{1}{4}=frac{6}{12}+frac{4}{12}frac{3}{12}=frac{7}{12})(b=frac{1}{3}+frac{1}{4}frac{1}{5}=frac{4}{12}+frac{3}{12}frac{2}{10}=frac{7}{12}frac{1}{5}=frac{35}{60}frac{12}{60}=frac{23}{60})(frac{7}{12}>frac{23}{60})4.A(frac{1}{1times2}+frac{1}{2times3}+frac{1}{3times4}+frac{1}{4times5}=left(1frac{1}{2}right)+left(frac{1}{2}frac{1}{3}right)+left(frac{1}{3}frac{1}{4}right)+left(frac{1}{4}frac{1}{5}right)=1frac{1}{5}=frac{4}{5})5.B(frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+frac{1}{42}=left(1frac{1}{2}right)+left(frac{1}{2}frac{1}{3}right)+left(frac{1}{3}frac{1}{4}right)+left(frac{1}{4}frac{1}{5}right)+left(frac{1}{5}frac{1}{6}right)+left(frac{1}{6}frac{1}{7}right)=1frac{1}{7}=frac{6}{7})三、解答题1.(frac{1}{2}+frac{2}{3}frac{3}{4}+frac{4}{5}frac{5}{6}=frac{6}{12}+frac{8}{12}frac{9}{12}+frac{12}{15}frac{10}{12}=frac{5}{12}+frac{4}{5}frac{5}{12}=frac{4}{5})2.原式(=left(1frac{1}{2}right)+left(frac{1}{2}frac{1}{3}right)+left(frac{1}{3}frac{1}{4}right)+cdots+left(frac{1}{99}frac{1}{100}right)=1frac{1}{100}=frac{99}{100})3.原式(=left(1frac{1}{2}right)+left(frac{1}{2}frac{1}{3}right)+left(frac{1}{3}frac{1}{4}right)+cdots+left(frac{1}{10}frac{1}{11}right)=1frac{1}{11}=frac{10}{11})4.设这个分数为(frac{abc}{def})，其中(abc)和(def)都是三位数，且(defabc=49)。化简后为(frac{5}{7})，所以(abc=5k)，(def=7k)，且(7k5k=49)，解得(k=7)，所以(abc=35)，(def=49)，这个分数为(frac{35}{49}=frac{5}{7})。5.设A、B两地