Question

What fraction is between $\dfrac{1}{8}$ and $\dfrac{1}{4}$ ?

Answer 1

Hint: We need to find the fraction between $\dfrac{1}{8}$ and $\dfrac{1}{4}$ . We start to solve the given question by equalizing the denominators of the fractions $\dfrac{1}{8}$ and $\dfrac{1}{4}$ . Then, we find out the fraction between the like fractions to get the desired result.

Complete step by step solution:
A fraction, in mathematics, represents a part of a whole thing. It consists of two parts namely,
numerator, denominator.
The number on the top is called the numerator.
The number on the bottom is called the denominator.
Let us understand the concept of the fraction with an example as follows,
Example:
$\Rightarrow \dfrac{a}{b}$
In the above fraction,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction.
According to the question,
We need to equalize the denominators of the fractions $\dfrac{1}{8}$ and $\dfrac{1}{4}$ . From factors and multiples, we know that one of the common multiples of the numbers 8 and 4 is 16.
$\Rightarrow 8\times 2=16$
$\Rightarrow 4\times 4=16$
Following the same,
We can equalize the denominators of the fraction by multiplying the numerator and denominator fraction $\dfrac{1}{8}$ by 2 and the fraction $\dfrac{1}{4}$ by 4
Following the same, we get,
$\Rightarrow \dfrac{1}{8}$
Multiplying the numerator and denominator of the fraction by 2, we get,
$\Rightarrow \dfrac{1}{8}\times \dfrac{2}{2}$
Simplifying the above expression, we get,
$\Rightarrow \dfrac{2}{16}$
Now,
$\Rightarrow \dfrac{1}{4}$
Multiplying the numerator and denominator of the fraction by 4, we get,
$\Rightarrow \dfrac{1}{4}\times \dfrac{4}{4}$
Simplifying the above expression, we get,
$\Rightarrow \dfrac{4}{16}$
The fraction between $\dfrac{2}{16}$ and $\dfrac{4}{16}$ is the average of the two fractions.
The average of the numbers $a$ and $b$ is given by $\dfrac{\left( a+b \right)}{2}$
Following the same, we get,
$\Rightarrow \dfrac{\left( \dfrac{2}{16}+\dfrac{4}{16} \right)}{2}$
Simplifying the above equation, we get,
$\Rightarrow \dfrac{\left( \dfrac{6}{16} \right)}{2}$
The fraction $\dfrac{\left( \dfrac{a}{b} \right)}{c}$ can be written as $\dfrac{a}{b\times c}$
Writing the same, we get,
$\Rightarrow \dfrac{6}{16\times 2}$
Canceling the common factors, we get,
$\Rightarrow \dfrac{3}{16}$
The fraction between $\dfrac{2}{16}$ and $\dfrac{4}{16}$ is $\dfrac{3}{16}$

$\therefore$ The fraction between $\dfrac{1}{8}$ and $\dfrac{1}{4}$ is $\dfrac{3}{16}$

Note: The fractions $\dfrac{2}{16}$ and $\dfrac{4}{16}$ are said to be equivalent fractions of $\dfrac{1}{8}$ and $\dfrac{1}{4}$ . Equivalent fractions have the same value but are represented in a different form. If $\dfrac{p}{q}$ is a fraction and $r$ is any non-zero integer. The equivalent rational number to $\dfrac{p}{q}$ can be found out as follows,
$\Rightarrow \dfrac{p\times r}{q\times r}$