AMC 8 2022 Problem 8

AMC8 2022 年第 8 题

表达式与运算★★☆☆☆

What is the value of the expression shown below?

下面算式的值是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Note that common factors (from 3 to 20, inclusive) of the numerator and the denominator cancel. Therefore, the original expression becomes

\displaystyle \frac{1}{\cancel{3}}\cdot \frac{2}{\cancel{4}}\cdot\frac{\cancel{3}}{\cancel{5}}\cdots\frac{\cancel{18}}{\cancel{20}}\cdot\frac{\cancel{19}}{21}\cdot\frac{\cancel{20}}{22}= \frac{1\cdot2}{21\cdot22}= \frac{1}{21\cdot11}=\frac{1}{231}.

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