AMC 8 1995 Problem 3

AMC8 1995 年第 3 题

比与比例★★☆☆☆

Which of the following operations has the same effect on a number as multiplying by

\dfrac{3}{4}

and then dividing by

\dfrac{3}{5}

以下哪种运算对一个数的效果与先乘以

\dfrac{3}{4}

再除以

\dfrac{3}{5}

相同？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Dividing by

\displaystyle \frac{3}{5}

is the same as multiplying by its reciprocal,

\displaystyle \frac{5}{3}

Multiplying a number by two numbers is the same as multiplying the number by the product of those two numbers. Thus, multiplying by

\displaystyle \frac{3}{4}

and then

\displaystyle \frac{5}{3}

is the same as multiplying by

\displaystyle \frac{3\cdot 5}{4\cdot 3}

\displaystyle \frac{5}{4}

, and the answer is

E

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