Question

What should be added to $\left( {\dfrac{2}{3} + \dfrac{3}{5}} \right)$ to get $ - \dfrac{2}{{15}}$?

Answer 1

Hint: To solve this question, we will first assume a variable whose value is to be determined. Let it be x, then we will apply the given condition in the question that x added by the number should give the result using the basic concept of addition of two numbers as $x + y = z$. As we know the values of y will be obtained from adding the numbers and z and so put the values in the above equation and hence the value of x can be calculated

Complete step-by-step answer:
Given: - As the given numbers are $\left( {\dfrac{2}{3} + \dfrac{3}{5}} \right)$ and $ - \dfrac{2}{{15}}$.
So, the addition of the given number is given by the equation $x + y = z$.
Let us assume the number as x. Then according to the given condition in the question, x is a rational number and x added with $\left( {\dfrac{2}{3} + \dfrac{3}{5}} \right)$ should give $ - \dfrac{2}{{15}}$. Now, let us write this mathematically, then we will have,
$ \Rightarrow x + \left( {\dfrac{2}{3} + \dfrac{3}{5}} \right) = - \dfrac{2}{{15}}$
Take LCM on the left side,
$ \Rightarrow x + \left( {\dfrac{{10 + 9}}{{15}}} \right) = - \dfrac{2}{{15}}$
Add the terms in the bracket,
$ \Rightarrow x + \dfrac{{19}}{{15}} = - \dfrac{2}{{15}}$
Move the constant term on the right side,
$ \Rightarrow x = - \dfrac{2}{{15}} - \dfrac{{19}}{{15}}$
As the denominator is the same, subtract the term on the right side,
$ \Rightarrow x = - \dfrac{{21}}{{15}}$
Cancel out the common terms,
$\therefore x = - \dfrac{7}{5}$

Hence, $ - \dfrac{7}{5}$ should be added to $\left( {\dfrac{2}{3} + \dfrac{3}{5}} \right)$ to get $ - \dfrac{2}{{15}}$.

Note: Addition is one of the four basic operations of arithmetic. “Addition” is one of the basic arithmetic operations in Mathematics. The addition is the process of adding things together. To add the numbers together, a sign “+” is used. The numbers which are going to add are called “addends” and the result which we are going to obtain is called “sum”.