Write the ratios in ascending order:
$2 : 3, 3 : 7, 5 : 6, 11 : 14 .$

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Solution

Change the ratio into rational numbers
$\frac{2}{3}' \frac{3}{7}, \frac{5}{6}, \frac{11}{14} F i n d t h e L . C . M . f o r t h e d e n o m i n a t o r L . C . M . o f 3, 7, 6, 14 i s 42 M u l t i p l y t h e c o r r e c t f a c t o r w i t h d e n o m i n a t o r t o g e t a 42 s i m i l a r l y m u l i p l y t h e s a m e n u m b e r w i t h n u m e r a t o r \frac{2 \times 14}{3 \times 14} = \frac{28}{42} [i f m u l t i p l y t h e 14 w i t h d e n o m i n a t o r w e g o t 42] \frac{3 \times 6}{7 \times 6} = \frac{18}{42} [7 \times 6 = 42] \frac{5 \times 7}{6 \times 7} = \frac{35}{42} [6 \times 7 = 42] \frac{11 \times 3}{14 \times 3} = \frac{33}{42} \frac{18}{42} < \frac{28}{42} < \frac{33}{42} < \frac{35}{42} \frac{3}{7} < \frac{2}{3} < \frac{11}{14} < \frac{5}{6} 3 : 7, 2 : 3, 11 : 14, 5 : 6$
Hence, the ascending order for the given ratio is $3 : 7, 2 : 3, 11 : 14, 5 : 6 .$

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