Question

Find the equivalent fraction of $\dfrac{36}{48}$ with a) numerator $9$ b) denominator $4$

Answer 1

Hint: To solve the question we need to know the concept of equivalent fraction. Equivalent fraction is a fraction that has a different numerator and denominator but are equal to the same value which means a fraction when turned into the lowest form gives the same form of the fraction. The first step will be to equate the given fraction with the numbers asked in the question. The value which we need to find should be taken as an unknown variable $x$.

Complete step-by-step solution:
The question asks us to convert the fraction $\dfrac{36}{48}$ into the form where the numerator is $9$ and also in the form when the denominator given is $4$.
a) So first we will change the fraction $\dfrac{36}{48}$ into the fraction having the numerator as $9$. To solve this we will consider the fraction $\dfrac{9}{x}$, where $x$is the denominator. On equating the two we get:
$\Rightarrow \dfrac{36}{48}=\dfrac{9}{x}$
We will find the value of $x$, further finding the fraction equivalent to $\dfrac{36}{48}$. On cross multiplying the above fraction we get:
$\Rightarrow x=\dfrac{9\times 48}{36}$
On multiplying the numerator and the denominator together we get:
$\Rightarrow x=\dfrac{432}{36}$
On calculating the above expression we get:
$\Rightarrow x=12$
$\therefore $ The equivalent fraction of $\dfrac{36}{48}$ is $\dfrac{9}{12}$ .
b) So the second part of the question is to convert the fraction $\dfrac{36}{48}$ into the fraction having the denominator as $4$. To solve this we will consider the fraction $\dfrac{y}{4}$, where $y$is the numerator. On equating the two we get:
$\Rightarrow \dfrac{36}{48}=\dfrac{y}{4}$
We will find the value of $y$, further finding the fraction equivalent to $\dfrac{36}{48}$. On cross multiplying the above fraction we get:
\[\Rightarrow y=\dfrac{4\times 36}{48}\]
On multiplying the numerator and the denominator together we get:
$\Rightarrow x=\dfrac{144}{48}$
On calculating the above expression we get:
$\Rightarrow x=3$
$\therefore $ The equivalent fraction of $\dfrac{36}{48}$ is $\dfrac{3}{4}$ .

Note: We can check whether the answers are correct or not. For this we will convert the fraction into its lowest form. If the fraction in the lowest form are the equal then the fractions are equivalent.
Starting by converting the fraction, $\dfrac{36}{48}$. To convert we will divide the numerator and the denominator by $12$. On doing this we get $\dfrac{3}{4}$. Similarly on converting the fraction $\dfrac{9}{12}$ in lowest term we get $\dfrac{3}{4}$.
Since each fraction in its lowest form is equal, the fraction is equivalent.