Question

What should be added to $\dfrac{2}{9}$ to get $ - 1$ ?

Answer 1

Hint: We will suppose that $x$ be the number which needs to be added in $\dfrac{2}{9}$ in order to obtain $ - 1$. Then, we will form an equation $\dfrac{2}{9} + x = - 1$ as per the data given in the question. We will solve this equation for the value of $x$ and it will be the desired number.

Complete step-by-step answer:
We are required to find a number which should be added to $\dfrac{2}{9}$ in order to get $ - 1$.
Let us suppose that the number which should be added is $x$.
So, we can now form an equation that if we add $x$ to $\dfrac{2}{9}$, we will get $ - 1$.
$ \Rightarrow \dfrac{2}{9} + x = - 1$
Solving this equation for the value of x, we get
$
   \Rightarrow \dfrac{{2 + 9x}}{9} = - 1 \\
   \Rightarrow 2 + 9x = - 9 \\
   \Rightarrow 9x = - 9 - 2 \\
   \Rightarrow 9x = - 11 \\
   \Rightarrow x = - \dfrac{{11}}{9} \\
 $
So, we get the value of $x = - \dfrac{{11}}{9}$ .
Therefore, $ - \dfrac{{11}}{9}$ should be added to $\dfrac{2}{9}$ in order to get $ - 1$.

Note: We must take care of our steps while calculating the value of x from the equation obtained. Such numbers $\left( {\dfrac{2}{9}, - \dfrac{{11}}{9},etc.} \right)$ are called rational numbers and are defined as the numbers in mathematics, which can be expressed in the form of , where p and q are two integers or we can say that those numbers which can be expressed as a fraction or a quotient.$\dfrac{p}{q},q \ne 0$