Question

By what rational number should $ - 3$ be divided to get $\dfrac{{ - 9}}{{13}}$? Write the result in mixed fraction.

Answer 1

Hint: Rational numbers can be defined as the numbers which can be written in the form of a fraction where numerator and denominator are integers or the numbers which can be written in the form of $\dfrac{p}{q}$ where $q \ne 0$. Here, we have to find a rational number which should divide $ - 3$ to get $\dfrac{{ - 9}}{{13}}$ as a result.

Complete step by step answer:
Here, we have to find a rational number which should divide $ - 3$ to get $\dfrac{{ - 9}}{{13}}$ as a result.
Rational numbers can be defined as the numbers which can be written in the form of a fraction where numerator and denominator are integers or the numbers which can be written in the form of $\dfrac{p}{q}$ where $q \ne 0$. In rational numbers, numerator and denominator should be coprime, that means the numbers whose common factor is only $1$.

Let the rational number be $x$. We can write the given question as,
$\dfrac{{ - 3}}{x} = \dfrac{{ - 9}}{{13}}$
Rearranging the above equation to get the value of $x$. We get,
$ \Rightarrow x = \dfrac{{ - 3 \times 13}}{{ - 9}}$
Solving the above equation. We get
$ \Rightarrow x = \dfrac{{13}}{3}$
On dividing $13$ by $3$. We get $4$ as a quotient and $1$ as a remainder.
So, we can write $\dfrac{{13}}{3}$ as a mixed fraction. Therefore,
$\therefore \dfrac{{13}}{3} = 4\dfrac{1}{3}$

Hence, the rational which should divide $ - 3$ to get $\dfrac{{ - 9}}{{13}}$ as a result is $4\dfrac{1}{3}$.

Note: Here, we wrote the result in mixed fraction. A mixed fraction is a combination of a proper fraction and a whole number. It represents a number between any two. In our result $4$ is a whole number and $\dfrac{1}{3}$ is a proper fraction. In proper fraction numerator is smaller than its denominator and if numerator is greater or equal than its denominator then it is an improper fraction.