Let x be the missing number.
We can write the proportion as:
\(\displaystyle\frac{{63}}{{27}}=\frac{{49}}{{x}}\)

The left side can be reduced to lowest terms since both numbers have 9 as their factor: \(\displaystyle\frac{{{9}\cdot{7}}}{{{9}\cdot{3}}}=\frac{{49}}{{x}}\)

\(\displaystyle\frac{{7}}{{3}}=\frac{{49}}{{x}}\)

Cross multiply: 7x=3(49)

7x=147

Divide both sides by 7: x=21

The left side can be reduced to lowest terms since both numbers have 9 as their factor: \(\displaystyle\frac{{{9}\cdot{7}}}{{{9}\cdot{3}}}=\frac{{49}}{{x}}\)

\(\displaystyle\frac{{7}}{{3}}=\frac{{49}}{{x}}\)

Cross multiply: 7x=3(49)

7x=147

Divide both sides by 7: x=21