Question

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

$\frac{2}{10}\square \frac{10}{13}$

Answer 1

Given rational numbers are $\frac{2}{10}$ and $\frac{10}{13}$.

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.

Here LCM of $10$ and $13$ is $130$.

Consider $\frac{2}{10}$

To make a denominator $130$, multiply both numerator and denominator by $13$. We get,

$\frac{2\times 13}{10\times 13}=\frac{26}{130}............\left(1\right)$

Consider $\frac{10}{13}$

To make a denominator $130$, multiply both numerator and denominator by $10$. We get,

$\frac{10\times 10}{13\times 10}=\frac{100}{130}.........\left(2\right)$

Step $2$ : Comparing the numerator :

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

$26<100$

$\frac{26}{130}<\frac{100}{130}$

Therefore, $\frac{2}{10}<\frac{10}{13}$