Try this beautiful Problem based on Ordering of fraction from AMC 8 2019.
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?
Fraction
Greatest Common Divisor
Ordering in Fraction
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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