The expression of the division \[\dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}}\] equals
A) \[\dfrac{4}{9}\]
B) \[\dfrac{4}{5}\]
C) \[\dfrac{1}{3}\]
D) \[\dfrac{1}{4}\]

Hint: In this question first we will write the given equation in \[\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}} = \dfrac{a}{b} \div \dfrac{c}{d}\] format. After that write \[\dfrac{a}{b} \div \dfrac{c}{d}\;as\;\dfrac{a}{b} \times \dfrac{d}{c}\] on simplifying this we will get the required result.

Complete step by step solution: We have given \[\dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}}\].
In order to simplify the above expression we will use the rule: \[\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}} = \dfrac{a}{b} \div \dfrac{c}{d}\]
So, we get
\[\dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}} = \dfrac{1}{3} \div \dfrac{3}{4}\]
And we know that \[\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}\]
Therefore, we can write \[\dfrac{1}{3} \div \dfrac{3}{4}\] as \[\dfrac{1}{3} \times \dfrac{4}{3}\]
\[ \Rightarrow \dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}} = \dfrac{1}{3} \times \dfrac{4}{3}\]
\[ \Rightarrow \dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}} = \dfrac{{4 \times 1}}{{3 \times 3}}\]
\[ \Rightarrow \dfrac{{\dfrac{1}{3}}}{{\dfrac{3}{4}}} = \dfrac{4}{9}\]

Hence, option A. \[\dfrac{4}{9}\]is the correct answer.

Note: There are 3 simple steps to divide fractions is given below:
It we have fraction as \[\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}}\] then
Step 1: Turn the second fraction i.e. \[\dfrac{c}{d}\] upside down which means reciprocal.
Step 2: Multiply the first fraction i.e. \[\dfrac{a}{b}\] by that reciprocal of \[\dfrac{c}{d}\].
Step 3: Simplify the fraction.