Question

下列哪一项把分数 $\dfrac{15}{11},\dfrac{19}{15}$ 和 $\dfrac{17}{13}$ ，按从小到大排列正确？

Which of the following is the correct order of the fractions $\dfrac{15}{11},\dfrac{19}{15},$ and $\dfrac{17}{13},$ from least to greatest?

$\dfrac{15}{11} \lt \dfrac{17}{13} \lt \dfrac{19}{15}$

$\dfrac{15}{11} \lt \dfrac{19}{15} \lt \dfrac{17}{13}$

$\dfrac{17}{13} \lt \dfrac{19}{15} \lt \dfrac{15}{11}$

$\dfrac{19}{15} \lt \dfrac{15}{11} \lt \dfrac{17}{13}$

$\dfrac{19}{15} \lt \dfrac{17}{13} \lt \dfrac{15}{11}$

答案：E

知识点：分数

难度评级：770

视频讲解：

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文字解答：

先把三个分数改写为同整数部分加一个分数： $\begin{align*} \dfrac{15}{11} &= 1 + \dfrac{4}{11} \\ \dfrac{17}{13} &= 1 + \dfrac{4}{13} \\ \dfrac{19}{15} &= 1 + \dfrac{4}{15}. \end{align*}$

分子相同的正分数，分母越大，分数越小。

因此正确顺序是 $\dfrac{19}{15} \lt \dfrac{17}{13} \lt \dfrac{15}{11}.$

正确答案是 E。

We can rewrite the fraction as follows: $\begin{align*} \dfrac{15}{11} &= 1 + \dfrac{4}{11} \\ \dfrac{17}{13} &= 1 + \dfrac{4}{13} \\ \dfrac{19}{15} &= 1 + \dfrac{4}{15}. \end{align*}$

Recall that if two fractions have the same numerator, then the fraction with the larger denominator is smaller.

Using this fact, we can see that the correct ordering is $\dfrac{19}{15} \lt \dfrac{17}{13} \lt \dfrac{15}{11}.$

Thus, the correct answer is E.

2019 AMC 8 第 3 题

答案：E

难度评级：770

视频讲解：

文字解答：

其他年份的第 3 题