AMC 8 2019 Problem 3 | Ordering Problem

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

• $\frac{15}{11}<\frac{17}{13}<\frac{19}{15}$
• $\frac{15}{11}<\frac{19}{15}<\frac{17}{13}$
• $\frac{17}{13}<\frac{19}{15}<\frac{15}{11}$
• $\frac{19}{15}<\frac{15}{11}<\frac{17}{13}$
• $\frac{19}{15}<\frac{17}{13}<\frac{15}{11}$

AMC 8 2019 Problem 3

$\frac{19}{15}<\frac{17}{13}<\frac{15}{11}$

First try to make all the denominators equal

$\frac{15}{11}, \frac{19}{15}, \frac{17}{13}$

=$\frac{15 \cdot 15 \cdot 13}{11 \cdot 15 \cdot 13}, \frac{19 \cdot 11 \cdot 13}{15 \cdot 11 \cdot 13}, \frac{17 \cdot 11 \cdot 15}{13 \cdot 11 \cdot 15}$

=$\frac{2925}{2145}, \frac{2717}{2145}, \frac{2805}{2145}$

Now, Try compare numerator

We have, $2717<2805<2925$

so , $\frac{19}{15}<\frac{17}{13}<\frac{15}{11}$ is the right order

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