Question

Fill in the blanks with $>,<$ or $=$ in the following:

$\frac{-3}{4}\_\_\_\frac{-5}{3}$

Answer 1

Step 1: Convert the given fractions into equivalent rational numbers.

Given : $\frac{-3}{4}\_\_\_\frac{-5}{3}$

First, convert them in equivalent fraction.

We have to take the LCM of the denominators.

So, LCM of $4$ and $3$ is $12$.

Now convert the given rational numbers in equivalent fraction with denominator $56$.

$\Rightarrow \frac{-3\times 3}{4\times 3}=\frac{-9}{12}$ and $\frac{-5\times 4}{3\times 4}=\frac{-20}{12}$

Step 2: Compare the fractions.

As we know that fraction with smaller numerator is smaller.

And, $-20<-9$

So, $\frac{-20}{12}<\frac{-9}{12}$

Therefore, $\frac{-9}{12}$ is greater then $\frac{-20}{12}$

Hence, $\frac{-3}{4}>\frac{-5}{3}$.