Question

下列哪种运算对一个数的作用，与先乘以 $\dfrac34$ 再除以 $\dfrac35$ 相同？

Which of the following operations has the same effect on a number as multiplying by $\dfrac34$ and then dividing by $\dfrac35?$

除以 $\dfrac43$

dividing by $\dfrac43$

除以 $\dfrac{9}{20}$

dividing by $\dfrac{9}{20}$

乘以 $\dfrac{9}{20}$

multiplying by $\dfrac{9}{20}$

除以 $\dfrac54$

dividing by $\dfrac54$

乘以 $\dfrac54$

multiplying by $\dfrac54$

知识点：分数

除以 $\dfrac35$ 等于乘以 $\dfrac53$ ，所以两个运算合起来相当于乘以

$\dfrac34 \times \dfrac53 = \dfrac54.$

因此总效果是乘以 $\dfrac54$ 。

所以正确答案是 E。

Dividing by $\dfrac35$ is the same as multiplying by $\dfrac53,$ so the two operations together multiply by

$\dfrac34 \times \dfrac53 = \dfrac54.$

So the combined effect is multiplying by $\dfrac54$ .

Thus, the correct answer is E .