which is the greatest ratio of following 3:4 , 5:7 ,9:11 ,1:8

Which can be rewritten as $\frac{3}{4};\frac{5}{7};\frac{9}{11}\mathrm{and}\frac{1}{8}$.

To find the greatest number, we have to first find the L.C.M. of their denominators as;

$2\times 2\times 1\times 7\times 11\times 2=616$

Now we make the denominators of all given rational numbers same as;

$\frac{3}{4}\times \frac{154}{154}=\frac{462}{616}\phantom{\rule{0ex}{0ex}}\frac{5}{7}\times \frac{88}{88}=\frac{440}{616}\phantom{\rule{0ex}{0ex}}\frac{9}{11}\times \frac{56}{56}=\frac{504}{616}\frac{1}{8}\times \frac{77}{77}=\frac{77}{616}$

So the greatest rational number is $\frac{504}{616}$ i.e. $\frac{9}{11}$.

Therefore the greatest ratio is 9 : 11.

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