关于分式乘法题目及答案

关于分式乘法题目及答案考试时间：120分钟 总分：100分 年级/班级：七年级（上学期）

关于分式乘法题目及答案

一、选择题

1.分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘，结果正确的是

A.\(\frac{a+c}{b+d}\)

B.\(\frac{ac}{bd}\)

C.\(\frac{a-d}{b-c}\)

D.\(\frac{ad}{bc}\)

2.若分式\(\frac{3x}{4y}\)与\(\frac{2y}{5x}\)相乘，结果为

A.\(\frac{6xy}{20xy}\)

B.\(\frac{6}{20}\)

C.\(\frac{1}{10}\)

D.\(\frac{3}{20}\)

3.下列分式相乘，结果为\(\frac{8}{15}\)的是

A.\(\frac{4}{5}\)与\(\frac{6}{8}\)

B.\(\frac{2}{3}\)与\(\frac{4}{5}\)

C.\(\frac{3}{4}\)与\(\frac{5}{6}\)

D.\(\frac{1}{2}\)与\(\frac{4}{3}\)

4.计算\(\frac{2x}{3y}\times\frac{3y}{4z}\)的结果，正确的是

A.\(\frac{6xy}{12yz}\)

B.\(\frac{1}{2}\)

C.\(\frac{x}{2z}\)

D.\(\frac{1}{6}\)

5.分式\(\frac{a+b}{a-b}\)与\(\frac{a-b}{a+b}\)相乘，结果为

A.1

B.-1

C.\(\frac{a^2-b^2}{a^2+b^2}\)

D.\(\frac{1}{a^2-b^2}\)

6.若分式\(\frac{5}{x}\)与\(\frac{x}{5}\)相乘，结果为

A.1

B.\(\frac{25}{x^2}\)

C.\(\frac{1}{x^2}\)

D.\(\frac{x^2}{25}\)

7.计算\(\frac{3m}{4n}\times\frac{2n}{5m}\)的结果，正确的是

A.\(\frac{6mn}{20mn}\)

B.\(\frac{3}{20}\)

C.\(\frac{1}{10}\)

D.\(\frac{6}{20}\)

8.分式\(\frac{2x}{3y}\)与\(\frac{3y}{2x}\)相乘，结果为

A.1

B.\(\frac{1}{6}\)

C.\(\frac{4x^2y^2}{9x^2y^2}\)

D.\(\frac{1}{9}\)

9.计算\(\frac{a}{b}\times\frac{b}{c}\times\frac{c}{a}\)的结果，正确的是

A.1

B.\(\frac{1}{abc}\)

C.\(\frac{a^3}{b^3}\)

D.\(\frac{b^3}{a^3}\)

10.分式\(\frac{x^2}{y^2}\)与\(\frac{y^2}{x^2}\)相乘，结果为

A.1

B.\(\frac{x^4}{y^4}\)

C.\(\frac{1}{x^2y^2}\)

D.\(\frac{y^4}{x^4}\)

二、填空题

1.分式\(\frac{2a}{3b}\)与\(\frac{4b}{5a}\)相乘的结果是

2.计算\(\frac{3x}{4y}\times\frac{2y}{5x}\)的结果是

3.分式\(\frac{5}{m}\)与\(\frac{m}{5}\)相乘的结果是

4.计算\(\frac{2m}{3n}\times\frac{3n}{4m}\)的结果是

5.分式\(\frac{a+b}{a-b}\)与\(\frac{a-b}{a+b}\)相乘的结果是

6.计算\(\frac{3x}{4y}\times\frac{4y}{5z}\)的结果是

7.分式\(\frac{2a}{3b}\)与\(\frac{3b}{2a}\)相乘的结果是

8.计算\(\frac{5x}{6y}\times\frac{6y}{5x}\)的结果是

9.分式\(\frac{a}{b}\)与\(\frac{b}{a}\)相乘的结果是

10.计算\(\frac{x^2}{y^2}\times\frac{y^2}{x^2}\)的结果是

三、多选题

1.下列分式相乘，结果为\(\frac{1}{1}\)的是

A.\(\frac{2}{3}\)与\(\frac{3}{2}\)

B.\(\frac{4}{5}\)与\(\frac{5}{4}\)

C.\(\frac{1}{2}\)与\(\frac{2}{1}\)

D.\(\frac{3}{4}\)与\(\frac{4}{3}\)

2.计算\(\frac{2x}{3y}\times\frac{3y}{4z}\)的结果，正确的有

A.\(\frac{6xy}{12yz}\)

B.\(\frac{x}{2z}\)

C.\(\frac{1}{2}\)

D.\(\frac{1}{6}\)

3.分式\(\frac{a+b}{a-b}\)与\(\frac{a-b}{a+b}\)相乘，结果正确的有

A.1

B.-1

C.\(\frac{a^2-b^2}{a^2+b^2}\)

D.\(\frac{1}{a^2-b^2}\)

4.下列分式相乘，结果为\(\frac{6}{15}\)的是

A.\(\frac{2}{5}\)与\(\frac{3}{4}\)

B.\(\frac{3}{4}\)与\(\frac{2}{5}\)

C.\(\frac{4}{5}\)与\(\frac{3}{2}\)

D.\(\frac{5}{4}\)与\(\frac{2}{3}\)

5.计算\(\frac{3m}{4n}\times\frac{2n}{5m}\)的结果，正确的有

A.\(\frac{6mn}{20mn}\)

B.\(\frac{3}{20}\)

C.\(\frac{1}{10}\)

D.\(\frac{6}{20}\)

6.分式\(\frac{x^2}{y^2}\)与\(\frac{y^2}{x^2}\)相乘，结果正确的有

A.1

B.\(\frac{x^4}{y^4}\)

C.\(\frac{1}{x^2y^2}\)

D.\(\frac{y^4}{x^4}\)

7.下列分式相乘，结果为\(\frac{1}{1}\)的是

A.\(\frac{1}{2}\)与\(\frac{2}{1}\)

B.\(\frac{3}{4}\)与\(\frac{4}{3}\)

C.\(\frac{5}{6}\)与\(\frac{6}{5}\)

D.\(\frac{7}{8}\)与\(\frac{8}{7}\)

8.计算\(\frac{2x}{3y}\times\frac{3y}{4z}\)的结果，正确的有

A.\(\frac{6xy}{12yz}\)

B.\(\frac{x}{2z}\)

C.\(\frac{1}{2}\)

D.\(\frac{1}{6}\)

9.分式\(\frac{a+b}{a-b}\)与\(\frac{a-b}{a+b}\)相乘，结果正确的有

A.1

B.-1

C.\(\frac{a^2-b^2}{a^2+b^2}\)

D.\(\frac{1}{a^2-b^2}\)

10.下列分式相乘，结果为\(\frac{8}{15}\)的是

A.\(\frac{4}{5}\)与\(\frac{6}{8}\)

B.\(\frac{2}{3}\)与\(\frac{4}{5}\)

C.\(\frac{3}{4}\)与\(\frac{5}{6}\)

D.\(\frac{1}{2}\)与\(\frac{4}{3}\)

四、判断题

1.分式\(\frac{a}{b}\)与\(\frac{c}{d}\)相乘，结果为\(\frac{ac}{bd}\)是正确的

2.计算\(\frac{2x}{3y}\times\frac{3y}{4z}\)的结果为\(\frac{x}{2z}\)是正确的

3.分式\(\frac{a+b}{a-b}\)与\(\frac{a-b}{a+b}\)相乘的结果为-1是正确的

4.分式\(\frac{5}{m}\)与\(\frac{m}{5}\)相乘的结果为1是正确的

5.计算\(\frac{3m}{4n}\times\frac{2n}{5m}\)的结果为\(\frac{3}{10}\)是正确的

6.分式\(\frac{2a}{3b}\)与\(\frac{3b}{2a}\)相乘的结果为1是正确的

7.计算\(\frac{5x}{6y}\times\frac{6y}{5x}\)的结果为1是正确的

8.分式\(\frac{a}{b}\)与\(\frac{b}{a}\)相乘的结果为1是正确的

9.计算\(\frac{x^2}{y^2}\times\frac{y^2}{x^2}\)的结果为1是正确的

10.分式\(\frac{2}{3}\)与\(\frac{3}{2}\)相乘的结果为1是正确的

五、问答题

1.解释如何进行分式的乘法运算

2.请举例说明分式乘法的应用

3.如果分式中包含多项式，如何进行分式的乘法运算

试卷答案

一、选择题答案及解析

1.B.\(\frac{ac}{bd}\)

解析：分式乘法法则，将分子相乘，分母相乘。

2.C.\(\frac{1}{10}\)

解析：\(\frac{3x}{4y}\times\frac{2y}{5x}=\frac{3\times2\timesx\timesy}{4\times5\timesy\timesx}=\frac{6xy}{20xy}=\frac{3}{10}\)。

3.B.\(\frac{2}{3}\)与\(\frac{4}{5}\)

解析：\(\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}\)。

4.C.\(\frac{x}{2z}\)

解析：\(\frac{2x}{3y}\times\frac{3y}{4z}=\frac{2x\times3y}{3y\times4z}=\frac{6xy}{12yz}=\frac{x}{2z}\)。

5.B.-1

解析：\(\frac{a+b}{a-b}\times\frac{a-b}{a+b}=\frac{(a+b)(a-b)}{(a-b)(a+b)}=-1\)。

6.A.1

解析：\(\frac{5}{x}\times\frac{x}{5}=\frac{5x}{5x}=1\)。

7.B.\(\frac{3}{20}\)

解析：\(\frac{3m}{4n}\times\frac{2n}{5m}=\frac{3m\times2n}{4n\times5m}=\frac{6mn}{20mn}=\frac{3}{20}\)。

8.A.1

解析：\(\frac{2x}{3y}\times\frac{3y}{2x}=\frac{2x\times3y}{3y\times2x}=1\)。

9.A.1

解析：\(\frac{a}{b}\times\frac{b}{c}\times\frac{c}{a}=\frac{a\timesb\timesc}{b\timesc\timesa}=1\)。

10.A.1

解析：\(\frac{x^2}{y^2}\times\frac{y^2}{x^2}=\frac{x^2\timesy^2}{y^2\timesx^2}=1\)。

二、填空题答案及解析

1.\(\frac{8ab}{15b^2}\)

解析：\(\frac{2a}{3b}\times\frac{4b}{5a}=\frac{2a\times4b}{3b\times5a}=\frac{8ab}{15ab}=\frac{8ab}{15b^2}\)。

2.\(\frac{3}{10}\)

解析：\(\frac{3x}{4y}\times\frac{2y}{5x}=\frac{3x\times2y}{4y\times5x}=\frac{6xy}{20xy}=\frac{3}{10}\)。

3.1

解析：\(\frac{5}{m}\times\frac{m}{5}=\frac{5m}{5m}=1\)。

4.\(\frac{1}{10}\)

解析：\(\frac{2m}{3n}\times\frac{3n}{4m}=\frac{2m\times3n}{3n\times4m}=\frac{6mn}{12mn}=\frac{1}{10}\)。

5.-1

解析：\(\frac{a+b}{a-b}\times\frac{a-b}{a+b}=\frac{(a+b)(a-b)}{(a-b)(a+b)}=-1\)。

6.\(\frac{x}{z}\)

解析：\(\frac{3x}{4y}\times\frac{4y}{5z}=\frac{3x\times4y}{4y\times5z}=\frac{12xy}{20yz}=\frac{x}{z}\)。

7.1

解析：\(\frac{2a}{3b}\times\frac{3b}{2a}=\frac{2a\times3b}{3b\times2a}=1\)。

8.1

解析：\(\frac{5x}{6y}\times\frac{6y}{5x}=\frac{5x\times6y}{6y\times5x}=1\)。

9.1

解析：\(\frac{a}{b}\times\frac{b}{a}=\frac{a\timesb}{b\timesa}=1\)。

10.1

解析：\(\frac{x^2}{y^2}\times\frac{y^2}{x^2}=\frac{x^2\timesy^2}{y^2\timesx^2}=1\)。

三、多选题答案及解析

1.A.\(\frac{2}{3}\)与\(\frac{3}{2}\),B.\(\frac{4}{5}\)与\(\frac{5}{4}\),C.\(\frac{1}{2}\)与\(\frac{2}{1}\),D.\(\frac{3}{4}\)与\(\frac{4}{3}\)

解析：这些分式相乘结果均为1。

2.A.\(\frac{6xy}{12yz}\),B.\(\frac{x}{2z}\)

解析：\(\frac{2x}{3y}\times\frac{3y}{4z}=\frac{6xy}{12yz}=\frac{x}{2z}\)。

3.B.-1

解析：\(\frac{a+b}{a-b}\times\frac{a-b}{a+b}=-1\)。

4.A.\(\frac{2}{5}\)与\(\frac{3}{4}\),B.\(\frac{3}{4}\)与\(\frac{2}{5}\)

解析：\(\frac{2}{5}\times\frac{3}{4}=\frac{6}{20}=\frac{3}{10}\)，\(\frac{3}{4}\times\(\frac{2}{5}\)=\(\frac{6}{20}=\frac{3}{10}\)。

5.A.\(\frac{6mn}{20mn}\),B.\(\frac{3}{20}\)

解析：\(\frac{3m}{4n}\times\frac{2n}{5m}=\frac{6mn}{20mn}=\frac{3}{20}\)。

6.A.1

解析：\(\frac{x^2}{y^2}\times\frac{y^2}{x^2}=1\)。

7.A.\(\frac{1}{2}\)与\(\frac{2}{1}\),B.\(\frac{3}{4}\)与\(\frac{4}{3}\),C.\(\frac{5}{6}\)与\(\frac{6}{5}\),D.\(\frac{7}{8}\)与\(\frac{8}{7}\)

解析：这些分式相乘结果均为1。

8.A.\(\frac{6xy}{12yz}\),B.\(\frac{x}{2z}\)

解析：\(\frac{2x}{3y}\times\frac{3y}{4z}=\frac{6xy}{12yz}=\frac{x}{2z}\)。

9.B.-1

解析：\(\frac{a+b}{a-b}\times\frac{a-b}{a+b}=-1\)。

10.A.\(\frac{4}{5}\)与\(\frac{6}{8}\),B.\(\frac{2}{3}\)与\(\frac{4}{5}\)

解析：\(\frac{4}{5}\times\frac{6}{8}=\frac{24}{40}=\frac{3}{5}\)，\(\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}\)。

四、判断题答案及解析

1.正确

解析：分式乘法法则，将分子相乘，分母相乘。

2.正确

解析：\(\frac{2x}{3y}\times\frac{3y}{4z}=\frac{2x\times3y}{3y\times4z}=\frac{6xy}{12yz}=\frac{x}{2z}\)。

3.正确

解析：\(\frac{a+b}{a-b}\times\frac{a-b}{a+b}=\frac{(a+b)(a-b)}{(a-b)(a+b)}=-1\)。

4.正确

解析：\(\frac{5}{m}\times\frac{m}{5}=\frac{5m}{5m}=1\)。

5.正确

解析：\(\frac{3m}{4n}\times\frac{2n}{5m}=\frac{3m\times2n}{4n\times5m}=\frac{6mn}{20mn}=\frac{3}{10}\