Which ratio is greater: $7 ˸ 9$ and $2 ˸ 11$

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Solution

Given:
$7 ˸ 9$ and $2 ˸ 11$
$7 ˸ 9 = \frac{7}{9} 2 ˸ 11 = \frac{2}{11}$
Make the denominator of each fraction equal by taking LCM
LCM $(9, 11) = 99$
$\frac{7}{9} = \frac{7}{9} \times \frac{11}{11} = \frac{77}{99} \frac{2}{11} = \frac{2}{11} \times \frac{9}{9} = \frac{18}{99} ∵ \frac{77}{99} > \frac{18}{99} \Rightarrow \frac{7}{9} > \frac{2}{11} \Rightarrow 7 ˸ 9 > 2 ˸ 11$
Hence, $7 ˸ 9 > 2 ˸ 11$

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