Question

What will be the additive inverse of \[\dfrac{-3}{9}\] ?, \[\dfrac{-9}{11}\] ?, \[\dfrac{5}{7}\] ?

Answer 1

Hint: We must discover the additive inverse of the given number, as stated in the question. When the total of two numbers equals zero, the numbers are additive inversely. It's also known as the original number's negation. As a result, finding the additive inverse of a given number is simple.

Complete step-by-step answer:
The value of an additive inverse of a number is defined as the value that when added to the original number yields zero. It's the amount we add to a number to make it equal zero. If ‘a' is the original number, its additive inverse will be minus of ‘a’ that is \[-a\] such that;
 \[a+(-a)=0\]
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 find the additive inverse of \[\dfrac{-3}{9}\]
That means we have to find the value in such a way when this value, which is added with the original number, results in zero value. Consider the value which we add is x
So, we can write expression for this given by:
 \[\dfrac{-3}{9}+x=0\]
On simplification we get:
 \[x=\dfrac{3}{9}\]
That means the additive inverse of \[\dfrac{-3}{9}\] is \[\dfrac{3}{9}\]
Similarly, we can find the other two given number
Now, we have to find the additive inverse of \[\dfrac{-9}{11}\]
That means we have to find the value in such a way when this value, which is added with the original number, results in zero value. Consider the value which we add is y.
 \[\dfrac{-9}{11}+y=0\]
On simplification we get:
 \[y=\dfrac{-9}{11}\]
That means the additive inverse of \[\dfrac{-9}{11}\] is \[\dfrac{9}{11}\]
Last one that is we have to find the additive inverse of \[\dfrac{5}{7}\]
That means we have to find the value in such a way when this value, which is added with the original number, results in zero value. Consider the value which we add is z.
 \[\dfrac{5}{7}+z=0\]
On simplification we get:
 \[z=\dfrac{5}{7}\]
That means the additive inverse of \[\dfrac{5}{7}\] is \[\dfrac{-5}{7}\] .
Therefore, additive inverse of \[\dfrac{-3}{9}\] , \[\dfrac{-9}{11}\] and \[\dfrac{5}{7}\] is \[\dfrac{3}{9}\] , \[\dfrac{9}{11}\] and \[\dfrac{-5}{7}\]

Note: To produce an answer equal to 0, additive inverse simply entails changing the sign of the number and adding it to the original number. A natural number, integer, rational number, complex number, or other number can be used as the value of additive inverse.