Question

State whether the following statement is true or false?
\[ - \dfrac{5}{7}\] is the additive inverse of \[\dfrac{5}{7}\].

Answer 1

Hint: Here in this question, we have to check whether the given number is additive inverse of each other. If the sum of two numbers is zero, then the two numbers are called additive inverse of each other then we can say the given statement is true otherwise the statement is false.

Complete step by step solution:
An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, ‘a’ is the original number, then its additive inverse will be minus of a i.e., ‘-a’, such that;
\[a + \left( { - a} \right) = a - a = 0\]
Additive inverse is also called the opposite of the number, negation of number or changed sign of original number.
Consider the given question:
We have to check whether the given statement is true or false:
\[ - \dfrac{5}{7}\] is the additive inverse of \[\dfrac{5}{7}\].
Now find the sum of these two numbers
\[ \Rightarrow \,\, - \dfrac{5}{7} + \dfrac{5}{7}\]
On simplification, we get
\[ \Rightarrow \,\,0\]
If the sum of two numbers yield zero, then the statement is true.
Therefore, \[ - \dfrac{5}{7}\] is the additive inverse of \[\dfrac{5}{7}\].
So, the correct answer is “True”.

Note: Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0. The value of additive inverse can be a natural number, integer, rational number, irrational number, complex number, etc.