Question

What is the quotient when $\dfrac{6}{7}$ is divided by $\dfrac{3}{7}$ ?

Answer 1

Hint: As we can clearly see that the question given requires us to divide $\dfrac{6}{7}$ by $\dfrac{3}{7}$ and find the quotient. Whenever we see a question like this, our approach should be to simplify it. Thus, we need to write it in division format as a complex fraction and then expand and work on it. Then, we write the fraction in the simplest form after cancelling the common factor between numerator and denominator.

Complete step by step answer:
In the given problem, we are required to find the quotient when $\dfrac{6}{7}$ is divided by $\dfrac{3}{7}$.
 So, we first write it in division of rational number format as: $\dfrac{{\left( {\dfrac{6}{7}} \right)}}{{\left( {\dfrac{3}{7}} \right)}}$ .
So, we know that the division of a number by a rational number is as good as multiplying the number by the multiplicative inverse of the same rational number.
Multiplicative inverse of $\dfrac{3}{7}$ is $\dfrac{7}{3}$.
Hence, we multiply the first rational number $\dfrac{6}{7}$ by the multiplicative inverse of the second rational number $\dfrac{3}{7}$, that is $\dfrac{7}{3}$ to get the desired answer of the given problem.
So, $\dfrac{{\left( {\dfrac{6}{7}} \right)}}{{\left( {\dfrac{3}{7}} \right)}} = \left( {\dfrac{6}{7}} \right) \times \left( {\dfrac{7}{3}} \right)$
Cancelling the common factor $7$ between the numerator and denominator, we get,
$ = \left( {\dfrac{{6 \times 7}}{{7 \times 3}}} \right)$
$ = \left( {\dfrac{6}{3}} \right)$
Now, dividing the numerator and denominator by three, we get,
$ = 2$
Hence, the quotient obtained on division of $\dfrac{6}{7}$ by $\dfrac{3}{7}$ is $2$.

Note:
Numerator and denominator never get cut through while division, they only get cut in multiplication. Also, division of a number by a rational number is as good as multiplying the number by the multiplicative inverse of the same rational number. Lastly, it is good to convert your answer from improper fraction to mixed fraction even if it is not mentioned in the question otherwise.