Question

How do you simplify $6\dfrac{1}{2}\div 2\dfrac{1}{3}$?

Answer 1

Hint: In this problem they have asked to simplify the given value. In the given equation, we can observe two mixed fractions are in division. So, we will first convert the given mixed fractions into normal fractional form. We know that the normal fractional form of the mixed fraction $a\dfrac{b}{c}$ is $\dfrac{ac+b}{c}$. So, we will consider each fraction individually and convert them as normal fractions. After that we will divide both the fractions to get the required result.

Complete step by step solution:
Given that, $6\dfrac{1}{2}\div 2\dfrac{1}{3}$.
Considering the fraction $6\dfrac{1}{2}$ individually and converting it into normal fraction, then we will get
$\begin{align}
  & \Rightarrow 6\dfrac{1}{2}=\dfrac{6\times 2+1}{2} \\
 & \Rightarrow 6\dfrac{1}{2}=\dfrac{12+1}{2} \\
 & \Rightarrow 6\dfrac{1}{2}=\dfrac{13}{2} \\
\end{align}$
Now considering the fraction $2\dfrac{1}{3}$ and converting this into normal fraction, then we will have
$\begin{align}
  & \Rightarrow 2\dfrac{1}{3}=\dfrac{2\times 3+1}{3} \\
 & \Rightarrow 2\dfrac{1}{3}=\dfrac{6+1}{3} \\
 & \Rightarrow 2\dfrac{1}{3}=\dfrac{7}{3} \\
\end{align}$
Now dividing the both the fractions, then we will get
$\Rightarrow 6\dfrac{1}{2}\div 2\dfrac{1}{3}=\dfrac{13}{2}\div \dfrac{7}{3}$
While dividing a fraction with another fraction, we will multiply the inverse of the second fraction, then we will have
$\begin{align}
  & \Rightarrow 6\dfrac{1}{2}\div 2\dfrac{1}{3}=\dfrac{13}{2}\times \dfrac{3}{7} \\
 & \Rightarrow 6\dfrac{1}{2}\div 2\dfrac{1}{3}=\dfrac{39}{14} \\
\end{align}$

Hence the simplified value of the given value $6\dfrac{1}{2}\div 2\dfrac{1}{3}$ is $\dfrac{39}{14}$.

Note: In the above solution we can also use the formula $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\times c}{b\times d}$ to divide the two fractions. We will compare the obtained fraction with the above formula and calculate the values of $ac$, $bd$. After getting those values we will substitute them in the formula and simplify to get the result. But it will be some lengthy process to do, so we have not followed this method.