Question

What are two equivalent fractions for $\dfrac{3}{6}$?

Answer 1

Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. We use the multiplication by any integer with both the denominator and the numerator of the simplified form to find the equivalent fractions.

Complete step by step solution:
We need to find the equivalent fractions of the proper fraction $\dfrac{3}{6}$.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.
For our given fraction $\dfrac{3}{6}$, the G.C.D of the denominator and the numerator is 3.
$\begin{align}
  & 3\left| \!{\underline {\,
  3,6 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,2 \,}} \right. \\
\end{align}$
Now we divide both the denominator and the numerator with 3 and get $\dfrac{{}^{3}/{}_{3}}{{}^{6}/{}_{3}}=\dfrac{1}{2}$.
Now we multiply an integer 2 with both the denominator and the numerator of the simplified fraction $\dfrac{1}{2}$ to find the other equivalent fraction which is $\dfrac{1\times 2}{2\times 2}=\dfrac{2}{4}$.

Therefore, the equivalent fractions of $\dfrac{3}{6}$ are $\dfrac{1}{2},\dfrac{2}{4}$.

Note: The process is similar for both proper and improper fractions. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case. Also, we can only apply the process on the proper fraction part of a mixed fraction.