Question & Answer
QUESTION

The product of two rational numbers is $\dfrac{7}{9}$. If one of the numbers is $-\dfrac{14}{27}$. Find the other number?

ANSWER Verified Verified
Hint: Mathematics includes the study of topics which are related to quantity, structure, space and change. To solve this problem, consider the other number to be x. Then we formulate some equations by using the problem statement. Once equations are formed then we can obtain the answer.

Complete step-by-step answer:
In mathematics, the number system is the branch that deals with various types of numbers possible to form and easy to operate with different operators such as addition, multiplication and so on. Rational numbers are those numbers which can be represented in the form of $\dfrac{p}{q}$, where p is the numerator and q is the denominator. P and Q may belong to any of the three categories such as natural, whole or integers.
From the second part of the problem statement, one of the numbers is $-\dfrac{14}{27}$. Now, considering the first part of the statement and letting the other number be x:
$\begin{align}
  & -\dfrac{14}{27}x=\dfrac{7}{9} \\
 & x=\dfrac{7}{9}\times -\dfrac{27}{14} \\
 & x=-\dfrac{3}{2} \\
\end{align}$
So, the other number obtained is $-\dfrac{3}{2}$.

Note: The key step for solving this problem is the knowledge of the number system and particularly rational numbers. The basic idea of a rational number system is good enough to solve and formulate the parts into an equation. This knowledge is helpful in solving complex problems.