Question

What is the additive identity of any rational number?
(a). 0
(b). 1
(c). – 1
(d). 2

Answer 1

Hint: An identity is a number which when operated on another number does not change the number. Additive identity is the number which when added to any number will give the same number as the result.

Complete step-by-step answer:
For any operation, we have many properties such as commutative property, associative property, distributive property, and so on. The identity property is one of the properties.
In addition, the additive identity property for rational numbers is that when you add a rational number to the additive identity, then you get back the same rational number.
Let the additive identity for rational numbers be x.
Let a is any rational number.
The definition states that when a is added to x, we get back a itself. Hence, we have the following:
a + x = a
We now, take the a in the left-hand side of the equation to the right-hand side to get as follows:
x = a – a
Now, when two same numbers are subtracted, we know that the result is zero. Hence, we have:
x = 0
Hence, the additive identity for all rational numbers is the number 0.
Hence, the correct answer is option (a).

Note: You may get confused with the multiplicative identity which is the number 1. Additive identity is the number which when added to another number gives the same number. Only 0 is used as an additive identity because if we add o with any number the result we get as the same number.