Question

How do you find a fraction between $\dfrac{1}{5}$ and $\dfrac{1}{4}$?

Answer 1

Hint: $\dfrac{1}{5}$ and $\dfrac{1}{4}$ are the fractions given in the question. We need to find out the fraction in between them. To solve the question, we need to calculate both the fractions. As the numerators and the denominators in both the fractions are different, we need to add the fractions. as a result, we get the required fraction.

Complete step-by-step solution:
The given fractions are $\dfrac{1}{5}$ and $\dfrac{1}{4}$
In the fractions both the denominator and the numerator are different. To solve any fraction denominator must be equal. So, solving the numerator will be easy.
To make the denominator common we need to simplify both denominators with suitable numbers.
The denominators given in the question are five and four.
Now we can get the common denominator by multiplying both five and four in the denominator.
 The numerator can be solved by cross multiplying the numerator of $\dfrac{1}{5}$ with a denominator of $\dfrac{1}{4}$ and multiplying the numerator of $\dfrac{1}{4}$ with the denominator of $\dfrac{1}{5}$.
$\Rightarrow \dfrac{1}{5}+\dfrac{1}{4}$
Let’s write the terms which are needed to be multiplied in the brackets.
$\Rightarrow \dfrac{\left( 1\times 4 \right)+\left( 1\times 5 \right)}{\left( 5\times 4 \right)}$
The resultant is
$\Rightarrow \dfrac{4+5}{20}$
$\Rightarrow \dfrac{9}{20}$
Therefore the fraction between $\dfrac{1}{4}$ and $\dfrac{1}{5}$ is $\dfrac{9}{20}$.

Note: There are many types of fractions. In fractions, all the operations can be applied. Fractions have different properties based on operational signs. For fractions that have addition and multiplication operational signs there are two different properties, those fractions have a commutative property and associative property. Inverse property is applicable for the fractions which have the numerator and denominator which are not equal to zero and have multiplication operation.
Inverse property example: $\dfrac{x} {y}\times \dfrac{y}{x}=1$.