What is the correct ordering of the three numbers (5/19) , (7/21), and (9/23), in increasing order?

hspace.05in(5/19)<(7/21)<(9/23)quad

hspace.05in(9/23)<(7/21)<(5/19)quad

hspace.05in(5/19)<(7/21)<(9/23)quad

hspace.05in(5/19)<(9/23)<(7/21)quad

AMC 8 2012 Problem 20

AMC8 2012 年第 20 题

比与比例★★★☆☆

What is the correct ordering of the three numbers

\displaystyle \frac{5}{19} , \frac{7}{21}

, and

\displaystyle \frac{9}{23}

, in increasing order?

把

\displaystyle \frac{5}{19}

、

\displaystyle \frac{7}{21}

、

\displaystyle \frac{9}{23}

这三个数从小到大排列，正确的顺序是什么？

A. $\displaystyle \hspace{.05in}\frac{9}{23}<\frac{7}{21}<\frac{5}{19}\quad$
B. $\displaystyle \hspace{.05in}\frac{5}{19}<\frac{7}{21}<\frac{9}{23}\quad$
C. $\displaystyle \hspace{.05in}\frac{9}{23}$
D. $\displaystyle \hspace{.05in}\frac{5}{19}<\frac{9}{23}<\frac{7}{21}\quad$
E. $\displaystyle \hspace{.05in}\frac{7}{21}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Using a common denominator, 5 19 = 105 399 19 5 = 399 105 and 7 21 = 133 399 21 7 = 399 133 , so 5 19 < 7 21 19 5 < 21 7 . Also 7 21 = 161 483 21 7 = 483 161 and 9 23 = 189 483 23 9 = 483 189 , so 7 21 < 9 23 21 7 < 23 9 . OR OR Comparing each fraction, 7 21 = 1 3, 5 19 < 5 15 = 1 3 21 7 = 3 1 , 19 5 < 15 5 = 3 1 , and 9 23 > 9 27 = 1 3 23 9 > 27 9 = 3 1 , so the correct increasing order is 5 19 < 7 21 < 9 23 19 5 < 21 7 < 23 9 . Answer: 𝐵 B .

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