Question

How to find $\dfrac{3}{4}\div \dfrac{2}{3}$?

Answer 1

Hint: To solve the fraction expression given in the above problem we are going to replace division sign by multiplication sign and then take the reciprocal of $\dfrac{2}{3}$. When the sign is multiplication then we can easily solve it by multiplying the numerators of the two fractions and the respective denominators of the two fractions.

Complete step by step solution:
The fraction expression given in the above problem is as follows:
$\dfrac{3}{4}\div \dfrac{2}{3}$
We know that when we can solve the above fraction expression by eliminating the division sign and substitute multiplication sign in place of division sign. When we substitute multiplication sign in place of division sign then we have to take the reciprocal of the term written after the division sign. Hence, the above expression will look like: $ \dfrac{3}{4}\times \dfrac{3}{2}$
As you can see that we have taken the reciprocal of the term written after the division sign (i.e. $\dfrac{2}{3}$). We know that the reciprocal of any fraction is interchanging the places of the denominator and the numerator of that fraction.
Solving the above mathematical expression by multiplying the numerators and denominators of the two fractions we get,
$=\dfrac{9}{8}$
Hence, we have simplified the expression given in the above problem and the result of simplification is $\dfrac{9}{8}$.

Note: In the below, we are going to show how the two fractions will look like when we divide them:
$\dfrac{3}{4}\div \dfrac{2}{3}$
$=\dfrac{\dfrac{3}{4}}{\dfrac{2}{3}}$
The above expression is simplified by multiplying 3 by 3 and 4 by 2 then the above expression will resolve to:
$\begin{align}
  & =\dfrac{3}{4}\times \dfrac{3}{2} \\
 & =\dfrac{9}{8} \\
\end{align}$
In the above solution, this is how we have substituted the division sign by the multiplication sign and then took the reciprocal of the term written after the division sign.