Question

How do you simplify the fraction $\dfrac{14}{8}$?

Answer 1

Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. The common factors of both the numerators and the denominators need to be eliminated. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form when the G.C.D is 1.

Complete step by step solution:
We need to find the simplified form of the proper fraction $\dfrac{14}{8}$.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 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 $\dfrac{14}{8}$, the G.C.D of the denominator and the numerator is 2.
$\begin{align}
  & 2\left| \!{\underline {\,
  8,14 \,}} \right. \\
 & 1\left| \!{\underline {\,
  4,7 \,}} \right. \\
\end{align}$
Now we divide both the denominator and the numerator with 2 and get $\dfrac{{}^{14}/{}_{2}}{{}^{8}/{}_{2}}=\dfrac{7}{4}$.
Therefore, the simplified form of $\dfrac{14}{8}$ is $\dfrac{7}{4}$.

Note:
We need to remember that the denominator in both cases of improper fraction and the mixed fraction will be the same. The only change happens in the numerator. The relation being the equational representation of $a=bx+c$ for mixed fraction $x\dfrac{c}{b}$. In case of mixed fractions, we can convert it into an improper fraction and then apply the simplification.