Question

The standard form of $\dfrac{192}{-168}$ is
A. $\dfrac{-2}{3}$
B. $\dfrac{-8}{7}$
C. $\dfrac{-1}{7}$
D. $\dfrac{-6}{7}$

Answer 1

Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. 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 $\dfrac{192}{-168}$. We have $\dfrac{192}{-168}=-\dfrac{192}{168}$
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 give fraction $\dfrac{192}{168}$, the G.C.D of the denominator and the numerator is 24.
$\begin{align}
  & 2\left| \!{\underline {\,
  168,192 \,}} \right. \\
 & 2\left| \!{\underline {\,
  84,96 \,}} \right. \\
 & 2\left| \!{\underline {\,
  42,48 \,}} \right. \\
 & 3\left| \!{\underline {\,
  21,24 \,}} \right. \\
 & 1\left| \!{\underline {\,
  7,8 \,}} \right. \\
\end{align}$
Now we divide both the denominator and the numerator with 24 and get $\dfrac{{}^{192}/{}_{24}}{{}^{168}/{}_{24}}=\dfrac{8}{7}$.
Now we can write $\dfrac{192}{-168}=-\dfrac{192}{168}=-\dfrac{8}{7}=\dfrac{-8}{7}$. The correct option is B.

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.