Which ratio is greater: $2 ˸ 3$ and $11 ˸ 15$

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Solution

Given:
$2 ˸ 3$ and $11 ˸ 15$
$2 ˸ 3 = \frac{2}{3} 11 ˸ 15 = \frac{11}{15}$
Make the denominator of each fraction equal by taking LCM
LCM $(3, 15) = 45$
$\frac{2}{3} = \frac{2}{3} \times \frac{15}{15} = \frac{30}{45} \frac{11}{15} = \frac{11}{15} \times \frac{3}{3} = \frac{33}{45} ∵ \frac{30}{45} < \frac{33}{45} \Rightarrow \frac{2}{3} < \frac{11}{15} \Rightarrow 2 ˸ 3 < 11 ˸ 15$
Hence, $2 ˸ 3 < 11 ˸ 15$

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