Question

What is \[\dfrac{5}{7} \div \dfrac{7}{{10}}\] ?

Answer 1

Hint: As we can clearly see that the expression given in the question here means that a rational number \[\dfrac{5}{7}\] is divided by another rational number \[\dfrac{7}{{10}}\]. Whenever we see a question like this, our approach should be to simplify it. Thus, we need to expand it and convert it into multiplication so that we can cancel the common factors in numerator and denominator and we will get our required answer.

Complete step by step solution:
So, we are given,
\[\dfrac{5}{7} \div \dfrac{7}{{10}}\]
Now, we know that $\left( {\dfrac{a}{b}} \right)$ means $a \div b$.
Now, as we know that dividing by a fraction is the same as multiplying by its reciprocal, so we get,
\[\dfrac{5}{7} \div \dfrac{7}{{10}} = \dfrac{5}{7} \times \dfrac{{10}}{7}\]
Since we know that the reciprocal of the fraction $\dfrac{7}{{10}}$ is $\dfrac{{10}}{7}$. So, we get,
\[ \Rightarrow \dfrac{5}{7} \div \dfrac{7}{{10}} = \dfrac{{50}}{{49}}\]
Therefore, we get the result of the expression as \[\left( {\dfrac{{50}}{{49}}} \right)\].
We can also report the final answer in mixed fraction form as \[1\dfrac{1}{{49}}\].
So, the correct answer is “\[1\dfrac{1}{{49}}\]”.

Note: Numerator and denominator never get cut through while division, they only get cut in multiplication. Also, here we see that we converted a division of two fractions into multiplication of two fractions so as to get the common factors cancelled in the numerator and denominator. The visible pattern here shows a general rule i.e. $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$. 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.