Question

Which fraction is smaller \[\dfrac{8}{15}\] or \[\dfrac{4}{7}\] ?

Answer 1

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 \[\dfrac{4}{7}\] .