What is $\dfrac{5}{6}$ divided by $\dfrac{2}{7}$?

Hint: We are asked to divide two fractions, for which we need to be very careful while writing what should come in the numerator and what should come in the denominator. We first write the fractions into proper inverse format so that this division problem gets converted into a multiplication problem. After that by simple multiplication of fractions, we obtain the result.

Complete step by step solution:
We are given $\dfrac{5}{6}$ and $\dfrac{2}{7}$. We need to divide $\dfrac{5}{6}$ by $\dfrac{2}{7}$.
If we write it in fraction form, we need to perform the following:
$\dfrac{\left(\dfrac{5}{6}\right)}{\left(\dfrac{2}{7}\right)}$
In the denominator we have $\dfrac{2}{7}$. If we need to bring it to the numerator, we need to perform inverse operation on it, i.e. we need to do the following:
$\left(\dfrac{2}{7}\right)^{-1}=\dfrac{7}{2}$
So, now we need to multiply $\dfrac{7}{2}$ and $\dfrac{5}{6}$, which is quite easy. We do the multiplication as follows:
$\dfrac{5}{6}\times\dfrac{7}{2}=\dfrac{7\times 5}{6\times 2}=\dfrac{35}{12}$
So we see that
$\dfrac{\dfrac{5}{6}}{\dfrac{2}{7}}=\dfrac{35}{12}$
Hence, the result is obtained.

Note: If you see the operation to be performed as: $\dfrac{\left(\dfrac{5}{6}\right)}{\left(\dfrac{2}{7}\right)}$
Then you can simply take the denominator of the denominator and bring it in the numerator of the new expression. Also, we take the numerator of the denominator and make it the denominator of the new expression. In this way, the result would be obtained faster than usual, but this trick can lead to many calculation mistakes so make sure that you use it only when you have pure confidence that you won’t confuse the terms in the resultant numerator and the denominator which might lead to a wrong result.