Question

Equalise the denominators to determine which number is bigger and which smaller.

(1) $\frac{3}{7},\frac{4}{9}$

Answer 1

$\frac{3}{7},\frac{4}{9}$
L.C.M of 7 and 9 is 63.
$$\begin{gathered} \therefore \frac{3}{7}=\frac{3\times 9}{7\times 9}=\frac{27}{63} \\ \mathrm{and}\frac{4}{9}=\frac{4\times 7}{9\times 7}=\frac{28}{63} \end{gathered}$$

Denominators of both the numbers are same; therefore, the rational number with the greater numerator will be greater.
$$\begin{gathered} \therefore \frac{28}{63}>\frac{27}{63} \\ \therefore \frac{4}{9}>\frac{3}{7} \end{gathered}$$