Which ratio is greater: $2 ˸ 15$ and $7 ˸ 12$

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Solution

Given:
$2 ˸ 15$ and $7 ˸ 12$
$2 ˸ 15 = \frac{2}{15} 7 ˸ 12 = \frac{7}{12}$
Make the denominator of each fraction equal by taking LCM
LCM $(15, 12) = 36$
$\frac{2}{15} = \frac{2}{15} \times \frac{4}{4} = \frac{8}{60} \frac{7}{12} = \frac{7}{12} \times \frac{5}{5} = \frac{35}{60} ∵ \frac{8}{60} < \frac{35}{60} \Rightarrow \frac{2}{15} < \frac{7}{12} \Rightarrow 2 ˸ 15 < 7 ˸ 12$
Hence, $2 ˸ 15 < 7 ˸ 12$

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