分式相乘题目及答案

分式相乘题目及答案

一、单项选择题（总共10题，每题2分）1.分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘的结果是？A.\(\frac{a+c}{b+d}\)B.\(\frac{a}{b+c}\)C.\(\frac{ac}{bd}\)D.\(\frac{ad}{bc}\)答案：C2.如果\(\frac{3}{4}\)乘以\(\frac{2}{5}\)，结果是多少？A.\(\frac{5}{8}\)B.\(\frac{6}{20}\)C.\(\frac{6}{10}\)D.\(\frac{8}{10}\)答案：A3.分式\(\frac{x+1}{x-1}\)与\(\frac{x-1}{x+1}\)相乘的结果是？A.1B.\(\frac{x^2-1}{x^2+1}\)C.\(\frac{1}{x^2-1}\)D.\(\frac{1}{x^2+1}\)答案：A4.分式\(\frac{2a}{3b}\)与\(\frac{3b}{4a}\)相乘的结果是？A.\(\frac{6ab}{12ab}\)B.\(\frac{1}{2}\)C.\(\frac{1}{6}\)D.\(\frac{ab}{6}\)答案：B5.如果\(\frac{5x}{6y}\)乘以\(\frac{3y}{10x}\)，结果是多少？A.\(\frac{15xy}{60xy}\)B.\(\frac{1}{4}\)C.\(\frac{1}{2}\)D.\(\frac{3}{4}\)答案：B6.分式\(\frac{m+2}{m-2}\)与\(\frac{m-2}{m+2}\)相乘的结果是？A.1B.\(\frac{m^2-4}{m^2+4}\)C.\(\frac{1}{m^2-4}\)D.\(\frac{1}{m^2+4}\)答案：A7.分式\(\frac{4}{5}\)与\(\frac{5}{4}\)相乘的结果是？A.1B.\(\frac{20}{25}\)C.\(\frac{1}{5}\)D.\(\frac{1}{4}\)答案：A8.如果\(\frac{7}{8}\)乘以\(\frac{8}{7}\)，结果是多少？A.1B.\(\frac{56}{56}\)C.\(\frac{1}{56}\)D.\(\frac{56}{64}\)答案：A9.分式\(\frac{a}{b}\)与\(\frac{b}{a}\)相乘的结果是？A.1B.\(\frac{a^2}{b^2}\)C.\(\frac{1}{a^2}\)D.\(\frac{1}{b^2}\)答案：A10.分式\(\frac{3x}{4y}\)与\(\frac{4y}{3x}\)相乘的结果是？A.1B.\(\frac{12xy}{12xy}\)C.\(\frac{1}{12}\)D.\(\frac{xy}{12}\)答案：A二、多项选择题（总共10题，每题2分）1.下列哪些是分式相乘的正确结果？A.\(\frac{a}{b}\times\frac{c}{d}=\frac{a+c}{b+d}\)B.\(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\)C.\(\frac{a}{b}\times\frac{c}{d}=\frac{a}{b+c}\)D.\(\frac{a}{b}\times\frac{c}{d}=\frac{ad}{bc}\)答案：B2.下列哪些分式相乘的结果是1？A.\(\frac{a}{b}\times\frac{b}{a}\)B.\(\frac{c}{d}\times\frac{d}{c}\)C.\(\frac{e}{f}\times\frac{f}{e}\)D.\(\frac{g}{h}\times\frac{h}{g}\)答案：A,B,C,D3.下列哪些分式相乘的结果是\(\frac{1}{4}\)？A.\(\frac{2}{3}\times\frac{3}{2}\)B.\(\frac{5}{6}\times\frac{6}{5}\)C.\(\frac{7}{8}\times\frac{8}{7}\)D.\(\frac{1}{2}\times\frac{2}{1}\)答案：A,B,C,D4.下列哪些分式相乘的结果是\(\frac{6}{10}\)？A.\(\frac{3}{5}\times\frac{2}{3}\)B.\(\frac{2}{3}\times\frac{3}{5}\)C.\(\frac{5}{3}\times\frac{3}{2}\)D.\(\frac{3}{2}\times\frac{5}{3}\)答案：A,B,C,D5.下列哪些分式相乘的结果是\(\frac{1}{2}\)？A.\(\frac{4}{6}\times\frac{3}{2}\)B.\(\frac{6}{4}\times\frac{2}{3}\)C.\(\frac{2}{3}\times\frac{3}{4}\)D.\(\frac{3}{4}\times\frac{4}{3}\)答案：A,B,C,D6.下列哪些分式相乘的结果是\(\frac{1}{3}\)？A.\(\frac{2}{3}\times\frac{3}{2}\)B.\(\frac{3}{2}\times\frac{2}{3}\)C.\(\frac{4}{6}\times\frac{3}{2}\)D.\(\frac{6}{4}\times\frac{2}{3}\)答案：A,B,C,D7.下列哪些分式相乘的结果是\(\frac{1}{5}\)？A.\(\frac{2}{5}\times\frac{5}{2}\)B.\(\frac{5}{2}\times\frac{2}{5}\)C.\(\frac{3}{5}\times\frac{5}{3}\)D.\(\frac{5}{3}\times\frac{3}{5}\)答案：A,B,C,D8.下列哪些分式相乘的结果是\(\frac{1}{6}\)？A.\(\frac{2}{3}\times\frac{3}{2}\)B.\(\frac{3}{2}\times\frac{2}{3}\)C.\(\frac{4}{6}\times\frac{3}{2}\)D.\(\frac{6}{4}\times\frac{2}{3}\)答案：A,B,C,D9.下列哪些分式相乘的结果是\(\frac{1}{8}\)？A.\(\frac{2}{3}\times\frac{3}{2}\)B.\(\frac{3}{2}\times\frac{2}{3}\)C.\(\frac{4}{6}\times\frac{3}{2}\)D.\(\frac{6}{4}\times\frac{2}{3}\)答案：A,B,C,D10.下列哪些分式相乘的结果是\(\frac{1}{9}\)？A.\(\frac{3}{4}\times\frac{4}{3}\)B.\(\frac{4}{3}\times\frac{3}{4}\)C.\(\frac{5}{6}\times\frac{6}{5}\)D.\(\frac{6}{5}\times\frac{5}{6}\)答案：A,B,C,D三、判断题（总共10题，每题2分）1.分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘的结果是\(\frac{a+c}{b+d}\)。答案：错误2.分式\(\frac{2}{3}\)与\(\frac{3}{2}\)相乘的结果是1。答案：正确3.分式\(\frac{a}{b}\)与\(\frac{b}{a}\)相乘的结果是1。答案：正确4.分式\(\frac{4}{5}\)与\(\frac{5}{4}\)相乘的结果是1。答案：正确5.分式\(\frac{3}{4}\)与\(\frac{4}{3}\)相乘的结果是1。答案：正确6.分式\(\frac{2}{3}\)与\(\frac{3}{2}\)相乘的结果是1。答案：正确7.分式\(\frac{5}{6}\)与\(\frac{6}{5}\)相乘的结果是1。答案：正确8.分式\(\frac{7}{8}\)与\(\frac{8}{7}\)相乘的结果是1。答案：正确9.分式\(\frac{9}{10}\)与\(\frac{10}{9}\)相乘的结果是1。答案：正确10.分式\(\frac{11}{12}\)与\(\frac{12}{11}\)相乘的结果是1。答案：正确四、简答题（总共4题，每题5分）1.简述分式相乘的步骤。答案：分式相乘的步骤包括：首先，将两个分式的分子相乘，得到新的分子；然后，将两个分式的分母相乘，得到新的分母；最后，将新的分子和分母组合成一个新的分式，并化简结果。2.解释为什么分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘的结果是\(\frac{ac}{bd}\)。答案：分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘时，根据分式的乘法规则，分子与分子相乘，分母与分母相乘，即\(\frac{a}{b}\times\frac{c}{d}=\frac{a\timesc}{b\timesd}=\frac{ac}{bd}\)。3.分式\(\frac{2x}{3y}\)与\(\frac{3y}{4x}\)相乘的结果是什么？请化简。答案：分式\(\frac{2x}{3y}\)与\(\frac{3y}{4x}\)相乘的结果是\(\frac{2x\times3y}{3y\times4x}=\frac{6xy}{12xy}=\frac{1}{2}\)。4.分式\(\frac{a+1}{a-1}\)与\(\frac{a-1}{a+1}\)相乘的结果是什么？请化简。答案：分式\(\frac{a+1}{a-1}\)与\(\frac{a-1}{a+1}\)相乘的结果是\(\frac{(a+1)\times(a-1)}{(a-1)\times(a+1)}=\frac{a^2-1}{a^2-1}=1\)。五、讨论题（总共4题，每题5分）1.讨论分式相乘在日常生活中的应用。答案：分式相乘在日常生活中有许多应用，例如在烹饪中调整食谱的分量，计算折扣和利率，以及解决工程问题等。通过分式相乘，可以方便地计算不同比例和比例的乘积，从而解决实际问题。2.讨论分式相乘与整数乘法的区别。答案：分式相乘与整数乘法的区别在于，分式相乘需要考虑分母和分子的乘积，而整数乘法只需要考虑整数的乘积。此外，分式相乘后需要化简结果，而整数乘法的结果通常不需要化简。3.