What is \[ - \dfrac{1}{4}\] divided by \[ - \dfrac{5}{6}\]?

Hint: We will use the concepts of fractions and their properties to solve this problem. When we divide a fraction with another fraction, then the division changes to multiplication and the second fraction is inverted. Using this concept we will get a solution.

Complete step by step answer:
Suppose that, there are two fractions \[\dfrac{a}{b}\] and \[\dfrac{c}{d}\], then product of these fractions is \[\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{{ac}}{{bd}}\]
When you divide a fraction with another fraction, then the division changes to multiplication and the second fraction is inverted.
\[ \Rightarrow \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{{ad}}{{bc}}\]
So, as per question, \[ - \dfrac{1}{4}\] is divided by \[ - \dfrac{5}{6}\].
So, \[ - \dfrac{1}{4} \div - \dfrac{5}{6}\]
And it will be changed as \[ - \dfrac{1}{4} \times - \dfrac{6}{5}\]
So, that will be equal to \[\dfrac{6}{{20}}\]
(As \[( - ) \times ( - ) = ( + )\], that means, product of two negative numbers is a positive number)
On simplification, we finally get, \[ - \dfrac{1}{4} \div - \dfrac{5}{6} = \dfrac{3}{{10}}\]

Note:
Whenever you get a fraction, try to simplify it to its lowest value. Here we got \[\dfrac{6}{{20}}\]. Here, both numerator and denominator are divisible by 2, so we simplified it to \[\dfrac{3}{{10}}\]. Also make a note that, like fractions can be added directly, whereas unlike fractions should be added by changing them into like fractions by taking LCM.