Question

How do you simplify $\dfrac{2}{{\dfrac{3}{{11}}}}$ ?

Answer 1

As we can clearly see that the expression given in the question here means $2$ divided by
$\dfrac{3}{{11}}$. Whenever we see a question like this, our approach should be to simplify it. Thus, we need to expand it and then multiply $2$ with the reciprocal of $\dfrac{3}{{11}}$ so that if there are digits which can be cut through the numerator and the denominator, they will get cut and the rest will be multiplied straight cross to obtain the answer.

Complete step by step solution:
(i)
We are given,
$\dfrac{2}{{\dfrac{3}{{11}}}}$
As we know that $\dfrac{a}{b}$ means $a \div b$, the expression given in the question means the same as:
$2 \div \dfrac{3}{{11}}$
Or, we could also write it as:
$\dfrac{2}{1} \div \dfrac{3}{{11}}$ [to have both as fractions]
(ii)
Now, as we know that dividing by a fraction is the same as multiplying by its reciprocal i.e.,
$x \div y = x \times \dfrac{1}{y}$
Therefore, we can write our expression as:
$\dfrac{2}{1} \div \dfrac{3}{{11}} = \dfrac{2}{1} \times \dfrac{{11}}{3}$
(iii)
As we multiply it straight cross, we will get:
$\dfrac{{2 \times 11}}{{1 \times 3}}$
That will be,
$\dfrac{{22}}{3}$
(iv)
Converting our answer from improper fraction to mixed fraction, we will get:
$\dfrac{{22}}{3} = 7\dfrac{1}{3}$
Hence, $\dfrac{2}{{\dfrac{3}{{11}}}} = 7\dfrac{1}{3}$

Note: Numerator and denominator never get cut through while division, they only get cut in multiplication. Also, here we see that $\dfrac{{\dfrac{2}{1}}}{{\dfrac{3}{{11}}}} = \dfrac{{(2 \times11)}}{{(1 \times 3)}}$, the visible pattern here shows a general rule i.e.,
$\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}} = \dfrac{{a \times d}}{{b \times c}}$. This rule could also be directly used to solve questions like this.
The answer obtained would have remained the same. Lastly, it is good to convert your answer from improper fraction to mixed fraction even if it is not mentioned in the question.