Question

Question 15

Find the missing number in the box in each of the proportions:

$\frac{16}{36}=\frac{\square }{63}=\frac{36}{\square }=\frac{\square }{117}$

Answer 1

We have, $\frac{16}{36}=\frac{?}{63}=\frac{36}{?}=\frac{?}{117}$

$\frac{4}{9}$ is the simplest form of all the three ratio.
For first two ratios, $\frac{16}{36}=\frac{4\times 4}{9\times 4}=\frac{4\times 7}{9\times 7}=\frac{28}{63}$
Hence, missing number = 28
For middle two ratios, $\frac{28}{63}=\frac{36}{?}\frac{28}{63}=\frac{4\times 7}{9\times 7}=\frac{4\times 9}{9\times 9}=\frac{36}{81}$
Hence, missing number = 81
For last two ratios $\frac{36}{81}=\frac{?}{117}\frac{36}{81}=\frac{4\times 9}{9\times 9}=\frac{4\times 13}{9\times 13}=\frac{52}{117}$
Hence, missing number = 52