Question

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

$\frac{-7}{8}\square \frac{-7}{9}$

Answer 1

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

Given rational numbers are $\frac{-7}{8}$ and $\frac{-7}{9}$.

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.

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

Consider $\frac{-7}{8}$

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

$\frac{-7\times 9}{8\times 9}=\frac{-63}{72}............\left(1\right)$

Consider $\frac{-7}{9}$

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

$\frac{-7\times 8}{9\times 8}=\frac{-56}{72}.........\left(2\right)$

Step $2$ : Comparing the numerator :

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

$-63<-56$

$\frac{-63}{72}<\frac{-56}{72}$

Therefore, $\frac{-7}{8}<\frac{-7}{9}$