分式相乘題目及答案

一、單項(xiàng)選擇題（總共10題，每題2分）1.分式\(\frac{a}\)與\(\frac{c}njxdpnz\)相乘的結(jié)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\(\frac{2}{5}\)，結(jié)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\(\frac{x+1}{x-1}\)與\(\frac{x-1}{x+1}\)相乘的結(jié)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\(\frac{2a}{3b}\)與\(\frac{3b}{4a}\)相乘的結(jié)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\(\frac{3y}{10x}\)，結(jié)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\(\frac{m+2}{m-2}\)與\(\frac{m-2}{m+2}\)相乘的結(jié)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\(\frac{4}{5}\)與\(\frac{5}{4}\)相乘的結(jié)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\(\frac{8}{7}\)，結(jié)果是多少？A.1B.\(\frac{56}{56}\)C.\(\frac{1}{56}\)D.\(\frac{56}{64}\)答案：A9.分式\(\frac{a}\)與\(\frac{a}\)相乘的結(jié)果是？A.1B.\(\frac{a^2}{b^2}\)C.\(\frac{1}{a^2}\)D.\(\frac{1}{b^2}\)答案：A10.分式\(\frac{3x}{4y}\)與\(\frac{4y}{3x}\)相乘的結(jié)果是？A.1B.\(\frac{12xy}{12xy}\)C.\(\frac{1}{12}\)D.\(\frac{xy}{12}\)答案：A二、多項(xiàng)選擇題（總共10題，每題2分）1.下列哪些是分式相乘的正確結(jié)果？A.\(\frac{a}\times\frac{c}dxvjntz=\frac{a+c}{b+d}\)B.\(\frac{a}\times\frac{c}nrpnbzl=\frac{ac}{bd}\)C.\(\frac{a}\times\frac{c}lzvtfbz=\frac{a}{b+c}\)D.\(\frac{a}\times\frac{c}brnzvnj=\frac{ad}{bc}\)答案：B2.下列哪些分式相乘的結(jié)果是1？A.\(\frac{a}\times\frac{a}\)B.\(\frac{c}xlzdjhd\times\fracnrtvhdr{c}\)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結(jié)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結(jié)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結(jié)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結(jié)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結(jié)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結(jié)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結(jié)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結(jié)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、判斷題（總共10題，每題2分）1.分式\(\frac{a}\)與\(\frac{c}lnbpvxf\)相乘的結(jié)果是\(\frac{a+c}{b+d}\)。答案：錯(cuò)誤2.分式\(\frac{2}{3}\)與\(\frac{3}{2}\)相乘的結(jié)果是1。答案：正確3.分式\(\frac{a}\)與\(\frac{a}\)相乘的結(jié)果是1。答案：正確4.分式\(\frac{4}{5}\)與\(\frac{5}{4}\)相乘的結(jié)果是1。答案：正確5.分式\(\frac{3}{4}\)與\(\frac{4}{3}\)相乘的結(jié)果是1。答案：正確6.分式\(\frac{2}{3}\)與\(\frac{3}{2}\)相乘的結(jié)果是1。答案：正確7.分式\(\frac{5}{6}\)與\(\frac{6}{5}\)相乘的結(jié)果是1。答案：正確8.分式\(\frac{7}{8}\)與\(\frac{8}{7}\)相乘的結(jié)果是1。答案：正確9.分式\(\frac{9}{10}\)與\(\frac{10}{9}\)相乘的結(jié)果是1。答案：正確10.分式\(\frac{11}{12}\)與\(\frac{12}{11}\)相乘的結(jié)果是1。答案：正確四、簡(jiǎn)答題（總共4題，每題5分）1.簡(jiǎn)述分式相乘的步驟。答案：分式相乘的步驟包括：首先，將兩個(gè)分式的分子相乘，得到新的分子；然后，將兩個(gè)分式的分母相乘，得到新的分母；最后，將新的分子和分母組合成一個(gè)新的分式，并化簡(jiǎn)結(jié)果。2.解釋為什么分式\(\frac{a}\)與\(\frac{c}ljfdhlr\)相乘的結(jié)果是\(\frac{ac}{bd}\)。答案：分式\(\frac{a}\)與\(\frac{c}lznznnb\)相乘時(shí)，根據(jù)分式的乘法規(guī)則，分子與分子相乘，分母與分母相乘，即\(\frac{a}\times\frac{c}rlrflpl=\frac{a\timesc}{b\timesd}=\frac{ac}{bd}\)。3.分式\(\frac{2x}{3y}\)與\(\frac{3y}{4x}\)相乘的結(jié)果是什么？請(qǐng)化簡(jiǎn)。答案：分式\(\frac{2x}{3y}\)與\(\frac{3y}{4x}\)相乘的結(jié)果是\(\frac{2x\times3y}{3y\times4x}=\frac{6xy}{12xy}=\frac{1}{2}\)。4.分式\(\frac{a+1}{a-1}\)與\(\frac{a-1}{a+1}\)相乘的結(jié)果是什么？請(qǐng)化簡(jiǎn)。答案：分式\(\frac{a+1}{a-1}\)與\(\frac{a-1}{a+1}\)相乘的結(jié)果是\(\frac{(a+1)\times(a-1)}{(a-1)\times(a+1)}=\frac{a^2-1}{a^2-1}=1\)。五、討論題（總共4題，每題5分）1.討論分式相乘在日常生活中的應(yīng)用。答案：分式相乘在日常生活中有許多應(yīng)用，例如在烹飪中調(diào)整食譜的分量，計(jì)算折扣和利率，以及解決工程問題等。通過分式相乘，可以方便地計(jì)算不同比例和比例的乘積，從而解決實(shí)際問題。2.討論分式相乘與整數(shù)乘法的區(qū)別。答案：分式相乘與整數(shù)乘法的區(qū)別在于，分式相乘需要考慮分母和分子的乘積，而整數(shù)乘法只需要考慮整數(shù)的乘積。此外，分式相乘后需要化簡(jiǎn)結(jié)果，而整數(shù)乘法的結(jié)果通常不需要化簡(jiǎn)。3.