Question

What is equivalent to $\dfrac{5}{9}$ when the denominator is 108?

Answer 1

Hint: We have given the denominator of fraction as 108 so we will assume the numerator to be x. Then we will equate the obtained fraction to $\dfrac{5}{9}$. Then by simplifying the obtained equation we will get the desired answer.

Complete step by step answer:
We have been given a fraction $\dfrac{5}{9}$ and the denominator of another fraction 108.
We have to find the equivalent fraction to $\dfrac{5}{9}$ when the denominator is 108.
Now, as we have given the denominator of a fraction as 108, let us assume the numerator to be x. Then the fraction will be
$\Rightarrow \dfrac{x}{108}$
Now, both the fractions are equivalent then we can write as
$\Rightarrow \dfrac{x}{108}=\dfrac{5}{9}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow x=\dfrac{5\times 108}{9} \\
 & \Rightarrow x=5\times 12 \\
 & \Rightarrow x=60 \\
\end{align}$
So the fraction becomes $ \dfrac{60}{108}$

Hence the equivalent fraction of$\dfrac{5}{9}$ is $\dfrac{60}{108}$.

Note: The key concept to solve this question is that we have to consider the denominator of the fraction and make it equal to 108. Alternatively we can solve the question by converting the denominator of the given fraction to 108 by multiplying the suitable number. For this we will multiply the numerator and denominator of the fraction by 12. Then we will get
$\begin{align}
  & \Rightarrow \dfrac{5}{9}\times \dfrac{12}{12} \\
 & \Rightarrow \dfrac{60}{108} \\
\end{align}$
Hence we get the equivalent fraction as $\dfrac{60}{108}$. Also point to be remembered is that we have to multiply both numerator as well as denominator.