The sum 2frac17+3frac12+5(1/19) is between

AMC 8 1987 Problem 11

AMC8 1987 年第 11 题

表达式与运算★★★☆☆

The sum

\displaystyle 2\frac17+3\frac12+5\frac{1}{19}

is between

和

\displaystyle 2\frac17+3\frac12+5\frac{1}{19}

在以下哪两个数之间？

正确答案 · Correct Answer

Solution 1

Since

\displaystyle \frac{1}{7} < \frac14

and

\displaystyle \frac{1}{19} < \frac14

, it follows that

\displaystyle 2\frac17+3\frac12+5\frac{1}{19} < 2\frac14+3\frac12+5\frac14 = 11

. Also,

\displaystyle 2\frac17+3\frac12+5\frac{1}{19} > 2+3\frac12+5 = 10\frac12

. Therefore, the sum is between

\displaystyle 10\frac{1}{2} \text{ and } 11

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