Answer

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**Hint**: We first convert the improper fraction to proper fraction. The other number can be simply found by dividing the number 9 by $3\dfrac{3}{7}$ in proper form.

**:**

__Complete step-by-step answer__The product of two numbers is 9. If one of them is $3\dfrac{3}{7}$. Changing from improper fraction to proper fraction for $3\dfrac{3}{7}$, we get $3\dfrac{3}{7}=\dfrac{24}{7}$.

The other number will be the division of 9 by $\dfrac{24}{7}$. The quotient is $\dfrac{9}{\dfrac{24}{7}}=\dfrac{63}{24}$.

We need to find the simplified form of the proper fraction $\dfrac{63}{24}$.

Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.

This means we can’t eliminate any more common root from them other than 1.

For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.

For our given fraction $\dfrac{63}{24}$, the G.C.D of the denominator and the numerator is 3.

$\begin{align}

& 3\left| \!{\underline {\,

24,63 \,}} \right. \\

& 1\left| \!{\underline {\,

8,21 \,}} \right. \\

\end{align}$

Now we divide both the denominator and the numerator with 3 and get $\dfrac{{}^{63}/{}_{3}}{{}^{24}/{}_{3}}=\dfrac{21}{8}$.

Therefore, the other number is $\dfrac{21}{8}$.

**So, the correct answer is “$\dfrac{21}{8}$”.**

**Note**: The process is similar for both proper and improper fractions. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case like we did in the above problem. If the given form is improper itself, then we just have to complete the division.

For conversion we follow the equational condition of $\dfrac{a}{b}=x+\dfrac{c}{b}$. The representation of the mixed fraction will be $x\dfrac{c}{b}$.

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