Question

How do you find the fraction between two fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ ?

Answer 1

Hint: We start solving the problem by assuming the variable for the fraction present between the first two terms. We then recall the fact that the mean of any two numbers lies between them. We then make use of the fact that the mean of any two numbers a and b is defined as $ \dfrac{a+b}{2} $ to proceed through the problem. We then make the necessary calculations to get the required value of the fraction.

Complete step by step answer:
According to the problem, we are asked to find the fraction that is present between two fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ .
We have given the fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ ---(1).
Let us assume the fraction between $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ be f.
We know that the mean of any two numbers lies between them. We know that the mean of any two numbers a and b is defined as $ \dfrac{a+b}{2} $. Let us use this result for the two fractions present in equation (1).
So, the mean of the given fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ is $ f=\dfrac{\dfrac{1}{4}+\dfrac{3}{5}}{2} $ .
 $ \Rightarrow f=\dfrac{\dfrac{5+12}{20}}{2} $ .
 $ \Rightarrow f=\dfrac{\dfrac{17}{20}}{2} $ .
 $ \Rightarrow f=\dfrac{17}{40} $ .
So, we have found the value of the fraction that is present in between the two fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ as $ \dfrac{17}{40} $ .
$ \therefore $ The value of the fraction that is present in between the two fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ is $ \dfrac{17}{40} $ .

Note:
We can also solve the given problem as shown below:
We have given the fractions $ \dfrac{1}{4} $ and $ \dfrac{3}{5} $ .
Let us convert the given fractions by changing denominator $ \dfrac{1}{4}\times \dfrac{5}{5}=\dfrac{5}{20} $ and $ \dfrac{3}{5}\times \dfrac{4}{4}=\dfrac{12}{20} $ .
Now, we can find the fractions between $ \dfrac{5}{20} $ and $ \dfrac{12}{20} $ as $ \dfrac{6}{20} $ , $ \dfrac{7}{20} $ , $ \dfrac{8}{20} $ , $ \dfrac{9}{20} $ , $ \dfrac{10}{20} $ , $ \dfrac{11}{20} $ .
Similarly, we can expect problems to find the fractions present between $ \dfrac{1}{2} $ and $ \dfrac{3}{4} $ .