What should be subtracted from $\dfrac{{ - 3}}{4}$ to get $\dfrac{{ - 5}}{6}$ ?

Hint: In this question we will first assume any number that has to be subtracted from the given number i.e. $\dfrac{{ - 3}}{4}$. We will assume the required number to be $x$. After this we will apply them according to the data given in the question and then we solve them by taking the LCM of the denominators.

Complete step by step answer:
Let us assume that the number has to be subtracted by $x$. Now we can write them according to the data given in the given:
$\dfrac{{ - 3}}{4} - x = \dfrac{{ - 5}}{6}$
We will now take the LCM in the LHS and the solve them:
$\dfrac{{ - 3 - 4x}}{4} = \dfrac{{ - 5}}{6}$
Now we will apply the cross multiplication,
$6( - 3 - 4x) = - 5 \times 4$
On multiplying the numbers we have:
$6 \times ( - 3) - 6 \times ( - 4x) = - 20 \\
\Rightarrow - 18 - 24x = - 20$
We can group the similar terms together by transferring to the RHS;
$ - 24x = - 20 + 18 \Rightarrow - 24x = - 2$
By isolating the term $x$, we have:
$x = \dfrac{{ - 2}}{{ - 24}} = \dfrac{1}{{12}}$ .

Hence the required number is $\dfrac{1}{{12}}$.

Note:We should note that we should always cross check our answers by putting them in the question. Since our required number is $\dfrac{1}{{12}}$.
So according to the question, we can write:
$\dfrac{{ - 3}}{4} - \dfrac{1}{{12}}$
We can now subtract this by taking the LCM of the denominator:
$\dfrac{{ - 9 - 1}}{{12}} = \dfrac{{ - 10}}{{12}}$
We can write the fraction in the simpler form as:
$\dfrac{{ - 5}}{6}$
Hence we can see that the LHS is equal to RHS, so our above solution is correct.