Question

By what number should $\left( { - \dfrac{{44}}{9}} \right)$ be divided to get $\left( { - \dfrac{{11}}{3}} \right)$ ?

Answer 1

Hint: If you need to answer these types of questions, then you need to be clear with the language. Unless and until you understand the question clearly, you cannot answer. Consider the number as a variable and let the number be x. Then, write the equation with the help of the language and hints, which is given in the question. We must know the method to find the product of two fractions to solve the question.

Complete step-by-step solution:
If you find these types of questions, you must know to pick up the numbers which are given in the question. The numbers which are given in the question are $\left( { - \dfrac{{44}}{9}} \right)$, a variable and $\left( { - \dfrac{{11}}{3}} \right)$.
Now, we have to use the phrases given in the language of the question to arrange all these numbers in an equation. We have to divide the sentence into two comparatively smaller phrases.
Firstly, let us assume the unknown number to be x.
Then, we are given that if $\left( { - \dfrac{{44}}{9}} \right)$ is divided by the number x, we get the resultant as $\left( { - \dfrac{{11}}{3}} \right)$.So, we first divide the number $\left( { - \dfrac{{44}}{9}} \right)$ by x.
So, we have, $\dfrac{{\left( { - \dfrac{{44}}{9}} \right)}}{x}$.
Now, we are given that the result is equal to $\left( { - \dfrac{{11}}{3}} \right)$. So, we get,
$ \Rightarrow \dfrac{{\left( { - \dfrac{{44}}{9}} \right)}}{x} = \left( { - \dfrac{{11}}{3}} \right)$
Shifting the terms in the equation and isolating the variable, we get,
$ \Rightarrow \dfrac{{\left( { - \dfrac{{44}}{9}} \right)}}{{\left( { - \dfrac{{11}}{3}} \right)}} = x$
Now, we know that division by a fraction is equivalent to product by the reciprocal of the same fraction. So, we get,
$ \Rightarrow x = \left( { - \dfrac{{44}}{9}} \right) \times \left( { - \dfrac{3}{{11}}} \right)$
Now, simplifying the equation and cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow x = \left( { - \dfrac{4}{3}} \right) \times \left( { - \dfrac{1}{1}} \right)$
Now, we know that multiplication of two negative signs results in a positive sign. So, we get,
$ \Rightarrow x = \dfrac{4}{3}$
Hence, the number by which $\left( { - \dfrac{{44}}{9}} \right)$ should be divided to get $\left( { - \dfrac{{11}}{3}} \right)$ is $\dfrac{4}{3}$.

Note: The above-mentioned method can be remembered as a complete process for solving these types of questions. Be careful with the language while attending these types of questions, because there are many questions which may confuse you with the tricky and typical language. We must report the final answer in lowest terms as there should be no common factor in numerator and denominator.