Which ratio is greater: 3 : 7 or $6 : 13$ ?

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Solution

$3 : 7 = \frac{3}{7} 6 : 13 = \frac{6}{13}$
LCM of $7, 13 = 91$
$3 : 7 = \frac{3}{7} \times \frac{13}{13} = \frac{39}{91}$
$6 : 13 = \frac{6}{13} \times \frac{7}{7} = \frac{42}{91}$
$∵ \frac{42}{91} > \frac{39}{91}$
$∴ \frac{6}{13} > \frac{3}{7}$
$\Rightarrow 6 : 13 > 3 : 7$

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