Which ratio is greater: $3 ˸ 7$ and $2 ˸ 5$

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Solution

Given:
$3 ˸ 7$ and $2 ˸ 5$
$3 ˸ 7 = \frac{3}{7} 2 ˸ 5 = \frac{2}{5}$
Make the denominator of each fraction equal by taking LCM
LCM $(7, 5) = 35$
$\frac{3}{7} = \frac{3}{7} \times \frac{5}{5} = \frac{15}{35} \frac{2}{5} = \frac{2}{5} \times \frac{7}{7} = \frac{14}{35} ∵ \frac{15}{35} > \frac{14}{35} \Rightarrow \frac{3}{7} > \frac{2}{5} \Rightarrow 3 ˸ 7 > 2 ˸ 5$
Hence, $3 ˸ 7 > 2 ˸ 5$

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