Question

Name the property indicated in the following:
 $ 5 + 0 = 0 + 5 = 5 $

Answer 1

Hint: In this question two numbers are added in two different configurations, one of the numbers is zero, and the answer for both the configurations of the numbers is the same. We have to determine the name of the property that is used in this problem.

Complete step-by-step answer:
Given:
Two numbers given are 0 and 5.
First by adding 5 and 0 we get,
 $ \Rightarrow 5 + 0 = 5 $
The sum of the numbers is 5 because when any number is added to the zero then the result of the sum is always that number itself.
Similarly, now adding 0 and 5 we get,
 $ \Rightarrow 0 + 5 = 5 $
The sum of the numbers in this configuration is also 5 because adding any number to the zero results in that number itself.
So, we can say that,
 $
\Rightarrow 5 + 0 = 0 + 5\\
 = 5
 $
This property in which the result of the addition of any number with the zero is the number itself, no matter what the configuration or order of the numbers is, known as the “Additive Identity Property of Zero”.
It means that the identity of the number remains unchanged if we add that number to the zero. This is the property of the addition with zero.
Therefore, the property indicated in the following question is the “Additive Identity Property of Zero”.

Note: If there is no zero in the addition of the numbers but the sum of the numbers remains unchanged in any configuration then this property of number addition is known as the “Additive Identity”. For example, the sum of the two numbers 2 and 3 is equal to the sum of the numbers 3 and 2.
 $
\Rightarrow 2 + 3 = 3 + 2\\
 = 5
 $