Question

How do you simplify $\dfrac{{ - \dfrac{1}{4}}}{{\dfrac{3}{{10}}}}$?

Answer 1

Hint: Given a complex fraction which includes another fraction in numerator as well as in the denominator. In order to simplify the given fraction we have to multiply the numerator fraction of the fraction with the inverse of the denominator of the fraction. So now we have to simplify this complex fraction into a simpler form of fraction.

Complete step-by-step solution:
First consider the given complex fraction and then split it or by simplification of that fraction to simpler form of fractions.
The given fraction is considered below as shown below:
$ \Rightarrow \dfrac{{ - \dfrac{1}{4}}}{{\dfrac{3}{{10}}}}$
Now here first considering the numerator fraction of the complex fraction, which is $\dfrac{{ - 1}}{4}$.
Here the numerator of the numerator is -1, whereas the denominator of the numerator is 4.
Now considering the denominator fraction of the complex fraction, which is $\dfrac{3}{{10}}$.
Here the numerator of the denominator is 3, whereas the denominator of the denominator is 10.
On simplification of the complex fraction the numerator of the numerator and the denominator of the denominator are multiplied to form the new numerator of the fraction, whereas the denominator of the numerator and the numerator of the denominator are multiplied to form the new denominator of the fraction.
$ \Rightarrow \dfrac{{ - \dfrac{1}{4}}}{{\dfrac{3}{{10}}}} = \dfrac{{ - 1}}{4} \times \dfrac{{10}}{3}$
$ \Rightarrow \dfrac{{ - \dfrac{1}{4}}}{{\dfrac{3}{{10}}}} = \dfrac{{ - 5}}{6}$
The simplification of $\dfrac{{ - \dfrac{1}{4}}}{{\dfrac{3}{{10}}}}$ is equal to $\dfrac{{ - 5}}{6}$.

Note: Please note that this can also be simplified with one other method, that is instead of multiplying the numerator of the complex fraction with the inverse of the denominator of the complex fraction, we can just directly divide the numerators with numerators and the denominators with denominators if possible, still the result would be the same.