Question

Which is the smallest of the following fractions?
$\left( A \right)\dfrac{4}{9}$
$\left( B \right)\dfrac{2}{5}$
$\left( C \right)\dfrac{3}{7}$
$\left( D \right)\dfrac{1}{4}$

Answer 1

Hint: From the question we have been asked to find the smallest fraction among the given fractions. So, to solve this question we will use the basic operation that is division and using that we will divide all given fractions among them and check which fraction is smaller among them. So, we proceed with our solution as follows.

Complete step-by-step solution:
Firstly, we will assume that,
\[\Rightarrow \dfrac{4}{9}......\left( 1 \right)\]
\[\Rightarrow \dfrac{2}{5}......\left( 2 \right)\]
\[\Rightarrow \dfrac{3}{7}......\left( 3 \right)\]
\[\Rightarrow \dfrac{1}{4}......\left( 4 \right)\]
Now after assuming the given fractions as mentioned in above. We will proceed with our solution as follows.
We will divide the equation \[1\] and \[2\] and find the smaller fraction among those both.
So, when we divide those both we get,
\[\Rightarrow \dfrac{\dfrac{4}{9}}{\dfrac{2}{5}}\]
\[\Rightarrow \dfrac{4}{9}\times \dfrac{5}{2}\]
\[\Rightarrow \dfrac{10}{9}\]
Here, we got the resultant as greater than one. So, the numerator is greater than the denominator. Therefore among \[1\] and \[2\], \[2\] is a smaller fraction.
Next we will divide the equations \[3\] and \[4\]. After doing the division operation we will find the smaller fraction among those two.
So, after doing division we get,
\[\Rightarrow \dfrac{\dfrac{3}{7}}{\dfrac{1}{4}}\]
\[\Rightarrow \dfrac{3}{7}\times 4\]
\[\Rightarrow \dfrac{12}{7}\]
Here, we got the resultant after dividing these both as greater than one. So, we can say that the numerator fraction is greater than the denominator fraction. So, the fraction \[3\] is greater than fraction \[4\].
Now, to get the final answer to our given question we will divide among the smaller fractions we got in the above two cases.
So, after doing it we get,
\[\Rightarrow \dfrac{\dfrac{2}{5}}{\dfrac{1}{4}}\]
\[\Rightarrow \dfrac{2}{5}\times 4\]
\[\Rightarrow \dfrac{8}{5}\]
Here, we got the resultant as greater than one. So, the denominator is the smallest fraction among the both fractions.
So, we conclude that the fraction \[\Rightarrow \dfrac{1}{4}\] is the smallest among all the fractions.
Therefore, the solution will be \[\Rightarrow \dfrac{1}{4}\].

Note: Students must be very careful in doing the calculations. Students should not be confused that when two fractions are divided if the outcome is greater than one then the numerator is greater than the denominator fraction. We can also solve it by finding the result of division of the fractions and then decide the smallest one. We will get results as 0.44.., 0.4, 0.428 and 0.25 for options A, B, C and D respectively. Hence, we can conclude option D is the right answer.