Question

Which of the two rational numbers is greater in each of the following pairs ?

$\frac{-1}{2},\frac{4}{-5}$

Answer 1

First of all we will convert the given fractions in their standard form

$\frac{4}{-5}=\frac{3\times -1}{-5\times -1}=\frac{-4}{5}$

and

$\frac{-1}{2}=\frac{-1}{2}$

Now , we will make their denominators equal by taking their LCM

LCM $\left(2,5\right)=10.$

Now , we will make their denominators equal

$\frac{-4}{5}=\frac{-4\times 2}{5\times 2}=\frac{-8}{10}$

$\frac{-1}{2}=\frac{-1\times 5}{2\times 5}=\frac{-5}{10}$

Now ,Since , denominators of both the fractions are same , we will directly compare their numerators.

$-5>-8$

So , $\frac{-5}{10}>\frac{-8}{10}$

Hence , $\frac{-1}{2}>\frac{4}{-5}$.