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# Which fraction is smaller $\dfrac{8}{15}$ or $\dfrac{4}{7}$ ?

Answer
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Hint: In this question, we need to know which fraction is smaller among $\dfrac{8}{15}$ or $\dfrac{4}{7}$ . The symbol used for greater than is $>$ and less than is $<$ . First let us get the common denominator for both the given fractions. That is let us multiply the fraction $\dfrac{8}{15}$ by $7$ and then the fraction $\dfrac{4}{7}$ by $15$ , in order to get a common denominator. Then we can compare both the fractions easily.

Complete step-by-step answer:
Given, $\dfrac{8}{15}$ and $\dfrac{4}{7}$
First we need to make the common denominator for both the given fractions.
Now on multiplying both the numerator and denominator of $\dfrac{8}{15}$ by $7$ ,
We get,
$= \dfrac{8}{15} \times \dfrac{7}{7}$
On simplifying,
We get,
$= \dfrac{56}{105}$ ••• (1)
Then on multiplying both the numerator and denominator of $\dfrac{4}{7}$ by $15$ ,
We get,
$= \dfrac{4}{7} \times \dfrac{15}{15}$
On simplifying,
We get,
$= \dfrac{60}{105}$ ••• (2)
Now on comparing equation (1) and (2) ,
We can conclude that $\dfrac{56}{105}$ is the smaller one, as its numerator is smaller.
$= \dfrac{8}{15} < \dfrac{4}{7}$
Thus $\dfrac{8}{15}$ is smaller than $\dfrac{4}{7}$
Final answer :
$\dfrac{8}{15}$ is smaller than $\dfrac{4}{7}$

Note: In order to solve these types of questions, we should have a strong grip over fractions as a part of the whole. We can also convert the given fractions into decimals in order to find the smallest fraction. That is $\dfrac{8}{15}$ can be converted into decimals and it’s value is $0.533$ whereas $\dfrac{4}{7}$ is $0.57$ . Now on comparing both , we can easily tell that $0.533$ is lesser than $0.57$ . Hence $\dfrac{8}{15}$ is smaller than $\dfrac{4}{7}$ .