Question

How do you determine which fraction is greater $\dfrac{3}{7}$ or $\dfrac{4}{9}$?

Answer 1

Hint: From the question we are asked to find the greater fraction among the $\dfrac{3}{7}$ and $\dfrac{4}{9}$. Here for this question we will take $\dfrac{3}{7}$ as a and $\dfrac{4}{9}$ as b and by using the division operation we will divide these both and see if it is greater than 1 or less than 1. By doing the process we can find the greater fraction among the both.

Complete step-by-step solution:
Firstly, as we mentioned earlier we will assume that $\dfrac{3}{7}$ as \[a\] and $\dfrac{4}{9}$ as \[b\].
So, we get that,
\[\Rightarrow a=\dfrac{3}{7}\]
\[\Rightarrow b=\dfrac{4}{9}\]
Now, we know that if we divide two numbers and the result is greater than one then the numerator is greater than the denominator for a fraction or any numerical. In the same way if we divide two fractions or any numerical and the resultant is less than one we can say that numerator is less than the denominator and the denominator is greater than the numerator.
Here we use this principle and divide the fractions and check this principle.
So, we get,
\[\Rightarrow \dfrac{a}{b}=\dfrac{\dfrac{3}{7}}{\dfrac{4}{9}}\]
\[\Rightarrow \dfrac{a}{b}=\dfrac{3}{7}\times \dfrac{9}{4}\]
\[\Rightarrow \dfrac{a}{b}=\dfrac{27}{28}\]
Here we can clearly see that this resultant fraction is less than one. \[\left( \dfrac{27}{28}<1 \right)\].
Therefore, we can say that \[b>a\] which means \[\dfrac{4}{9}>\dfrac{3}{7}\].

Note: In this question students must be careful in doing the division of two fractions. Students must be careful in doing the calculations. We can also do this question in an easy method by changing the fractions into decimals.
\[\Rightarrow \dfrac{3}{7}=0.428..\]
\[\Rightarrow \dfrac{4}{9}=0.444..\]
From this we can say that \[\dfrac{4}{9}>\dfrac{3}{7}\]. In this way we solve these questions involving fractions.