Question

The \[..........\] consists of natural numbers, zero and negative of natural numbers. Zero is called the $ ........,........ $ and $...........$ is called the multiplicative identity.
 $ \left( a \right){\text{ Integers, additive identity, 1}} $
 $ \left( b \right){\text{ Integers, additive inverse, 1}} $
 $ \left( c \right){\text{ Whole number, additive identity, 0}} $
 $ \left( d \right){\text{ Rational numbers, additive inverse, 1}} $

Answer 1

Hint: So for solving this question, we should know the terms used in it. As we know that the numbers which when added to a number and when it returns the same number then that property is known to be an additive identity. Also, the same criteria are being followed for the multiplicative identity. So by using these we can now fill the blanks space.

Complete step-by-step answer:
 So, here in this question it is said that we have to fill the blank with the term which consists of natural numbers, zero and negative of natural numbers. As we know that the set of positive and negative natural numbers and also including the zero are known to be integers.
Therefore, the integers are the number that consists of natural numbers, zero, and negative of natural numbers.
Now we have to tell what zero is called and for this let us suppose an equation, $ 7 + x = 7 $ , from this we will get the $ x = 0 $ . So from this, we can see that the numbers which when added to a number and when it returns the same number then that property is known to be an additive identity.
Hence, zero is called the additive identity.
Now for the third blank, we have to tell what it will be called as a multiplicative identity. So for this, let us assume an equation as $ 4 \times y = 4 $ and from this we get $ y = 1 $ . Hence, from this example, we can see that the numbers which when multiplied to a number and when it returns the same number then that property is known to be a multiplicative identity.
So, $ 1 $ will be called the multiplicative identity.
So, the correct answer is “Option A”.

Note: As we have seen some of the terms above the rest terms are described here. Additive inverse is those inverse numbers which when added to the number return back the same number. And that number is also said to be an opposite sign change. Also zero is the only number having the additive inverse of itself.