Question

Write the additive inverse of the following:
1. \[-\dfrac{7}{19}\]
2. $\dfrac{21}{112}$

Answer 1

Hint: We here need to find the additive inverse of two numbers. To find the additive inverse of a number, we should first know what it means. The additive inverse of a number ‘$a$’ is the number which when added to a gives $0$. To find the additive inverse here, we will first assume the additive inverse of the given number to be a variable like $x$ or $y$ and then we will keep the sum of the variable and the given number equal to 0. Then we will solve that equation for the value of the unknown variable and obtain the value of the required additive inverse. We will do it for the parts and hence obtain the required answer.

Complete step by step answer:
Now, we know that the additive inverse of a number ‘$a$’ is the number which when added to $a$, gives zero as the result. Now, we will calculate the additive inverse of both the parts.
1. The number given to us is $-\dfrac{7}{19}$. Now, let us assume its additive inverse to be ‘$x$’. Thus, we can say that $x$ is the additive inverse of $-\dfrac{7}{19}$. We know that there sum will be $0$, thus we can say that:
$-\dfrac{7}{19}+x=0$
Now, solving this for ‘$x$’, we get:
$ -\dfrac{7}{19}+x=0 $
$  \Rightarrow x=0-\left( -\dfrac{7}{19} \right) $
$\therefore x=\dfrac{7}{19} $
Hence, the additive inverse of $-\dfrac{7}{19}$ is $\dfrac{7}{19}$.

2. The number given to us is $\dfrac{21}{112}$. Now, let us assume its additive inverse to be ‘$y$’. Thus, we can say that the additive inverse of $\dfrac{21}{112}$ is y. We know that there sum will be $0$, hence we can say that:
$\dfrac{21}{112}+y=0$
Now, solving this equation for ‘$y$’ we get:
$ \dfrac{21}{112}+y=0 $
$ \Rightarrow y=0-\dfrac{21}{112} $
$ \therefore y=-\dfrac{21}{112} $
Hence, the additive inverse of $\dfrac{21}{112}$ is $-\dfrac{21}{112}$.

Note: Here, we can notice that both the additive inverses are the numbers with opposite signs of their respective inverses. This is true for all real numbers. Thus, we can say that the additive inverse of each real number is equal to the negation of that number. We can use this in all kinds of examinations and we need not to follow this whole procedure and it will save us a lot of time.