Write the following ratio in ascending order.
$13 : 36, 8 : 9, 15 : 18, & 9 : 24$

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Solution

$13 : 36 = \frac{13}{36}; 8 : 9 = \frac{8}{9}; 15 : 18 = \frac{15}{18}; 9 : 24 = \frac{9}{24}$
Now, the LCM of $(36, 9, 18, 24) = 144$
$∴ \frac{13}{36} = \frac{13 \times 4}{36 \times 4} = \frac{52}{144}; \frac{8}{9} = \frac{8 \times 16}{9 \times 16} = \frac{128}{144}; \frac{15}{18} = \frac{15 \times 8}{18 \times 8} = \frac{120}{144}; \frac{9}{24} = \frac{9 \times 6}{24 \times 6} = \frac{54}{144};$
So, by comparing its numerator we get, $128 > 120 > 54 > 52 .$
Ascending order $= \frac{39}{144}, \frac{54}{144}, \frac{120}{144}, \frac{128}{144}$
$= \frac{13}{36}, \frac{9}{24}, \frac{15}{18}, \frac{8}{9}$
Hence, the required ascending order of the given ratio is $13 : 36, 9 : 24, 15 : 18, & 8 : 9 .$

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