Question

Fill in the box with the correct symbol $>$, $<$ or $=$.

$\frac{5}{9}\square \frac{9}{8}$

Answer 1

Step $1$: Making the denominators equal by taking LCM

In order to compare two rational numbers with different denominators, we have to take the LCM of the denominators of the given rational numbers and then convert them into like rational numbers.

Given rational numbers are $\frac{5}{9}$ and $\frac{9}{8}$.

Here, LCM of $9$ and $8$ is $72$.

Considering $\frac{5}{9}$,

To make a denominator $72$, multiply both numerator and denominator by $8$. We get,

$\frac{5\times 8}{9\times 8}=\frac{40}{72}............\left(1\right)$

Considering $\frac{9}{8}$,

To make a denominator $72$, multiply both numerator and denominator by $9$. We get,

$\frac{9\times 9}{8\times 9}=\frac{81}{72}.........\left(2\right)$

Step $2$ : Comparing the numerator

Since the denominator is equal in equation $\left(1\right)$ and $\left(2\right)$. Therefore compare the numerator,

$40<81$

$\frac{40}{72}<\frac{81}{72}$

Therefore, $\frac{5}{9}<\frac{9}{8}$