AMC8 1995

AMC8 1995 · Q3

AMC8 1995 · Q3. It mainly tests Fractions.

Which of the following operations has the same effect on a number as multiplying by $\frac{3}{4}$ and then dividing by $\frac{3}{5}$?

下列哪个运算与先乘以 $\frac{3}{4}$ 再除以 $\frac{3}{5}$ 对一个数的效果相同？

(A) dividing by $\frac{4}{5}$ 除以 $\frac{4}{5}$

(B) dividing by $\frac{9}{20}$ 除以 $\frac{9}{20}$

(D) dividing by $\frac{5}{4}$ 除以 $\frac{5}{4}$

(E) multiplying by $\frac{5}{4}$ 乘以 $\frac{5}{4}$

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since $\frac{3}{4} \div \frac{3}{5} = \frac{3}{4} \times \frac{5}{3} = \frac{5}{4}$, multiplying by $\frac{5}{4}$ has the same effect.

因为 $\frac{3}{4} \div \frac{3}{5} = \frac{3}{4} \times \frac{5}{3} = \frac{5}{4}$，所以乘以 $\frac{5}{4}$ 有相同效果。

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