Introduction
The feature of numbers known as additive identity, as the name suggests, is used when performing addition operations. According to the property, adding a number to zero results in the same number. The identity element is zero, commonly referred to as additive identity. If we add any number to zero, the outcome will be that same number. This holds true for all types of real numbers, including imaginary and complex ones.
If ‘\( x\)’ is a real number of any kind, then,
\( x+ 0 = x = 0 + x\)
The identity property of addition is demonstrated with the example of 61 + 0 = 61, where 0 represents the additive identity.
Additive Identity of Whole numbers
Zero is the additive identity of all whole numbers. This means that the result of adding a whole number to zero is the number itself. The result will be the entire number, when ‘\( y \)’ is a whole number and is added to zero.
For every single whole number, ‘\( y \)’, subsequently,
\( y + 0 = 0 + y = y\).
Within the set of whole numbers, zero serves as the additive identity element. Checking this attribute with a whole number, such as 12, will yield the number itself, that is, 12+ 0 = 12.
Additive identity of Integers
If any integer is added to zero, according to the additive identity of integers, the outcome is the integer itself. We are aware that integers can be both positive and negative; for instance, the numbers 6, 0, -37, and so on are all integers. Let’s now use integers to apply the identity property of addition. For instance, if -17 and 0 need to be added, -17 + 0, the result is -17.
What distinguishes Multiplicative Identity from Additive Identity?
The following details highlight how the multiplicative identity of numbers differs from the additive identity of numbers.
- The addition operation uses the additive identity of integers, but the multiplication operation uses the multiplicative identity.
- While referring to the additive identity, \(x + 0 = x,\) the identity element is ‘0’. However, the multiplicative identity, represented by the equation, \(x \times~ 1 = x\) the identity element is ‘1’.
- Examples of the additive and multiplicative identity properties are 11 + 0 = 11 and 11 × 1 = 11 respectively.
Solved Examples
Example 1: Fill in the blanks in the following addition equations using the identity property.
(a) 4 + 0 =_ ?
(b) 0 + 12 =_ ?
(c) 1 + 0 =_?
(d) 0 + 15 =_ ?
(e) 7 + 0 =_ ?
(f) 13 + 0 =_ ?
Solution:
Note: The identity property of addition states that the result of adding any number to 0 is the number itself.
Therefore,
(a) By adding 4 and 0, will get ‘4’ as answer, 4 + 0 = 4. So, the missing number is 4.
(b) By adding 0 and 12, will get‘12’ as answer, 0 + 12 = 12. So, the missing number is 12.
(c) By adding 1 and 0, will get‘1’ as answer, 1 + 0 = 1. So, the missing number is 1.
(d) By adding 0 and 15, will get‘15’ as answer, 0 + 15 = 15. So, the missing number is 15.
(e) By adding 7 and 0, will get‘7’ as answer, 7 + 0 = 7. So, the missing number is 7.
(f) By adding 13 and 0, will get‘13’ as answer, 13 + 0 = 13. So, the missing number is 13.
Example 2: Compute the missing numbers.
(a) 11 + ? = 11
(b) ? + 0 = 2
(c) 0 + 6 = ?
(d) 17 + ? = 17
(e) 0 + ? = 3
Solution:
Note: We can find the missing numbers using the additive identity characteristic.
Therefore,
(a) By adding 11 and 0, will get ‘11’ as answer 11 + 0 = 11. So, the missing number is 0.
(b) By adding 2 and 0, will give ‘2’ as answer 2 + 0 = 2. So, the missing number is 2.
(c) By adding 0 and 6, will give ‘6’ as answer 0 + 6 = 6. So, the missing number is 6.
(d) By adding 17 and 0, will give ‘17’ as answer 17 + 0 = 17. So, the missing number is 0.
(e) By adding 0 and 3, will give ‘3’ as answer 0 + 3 = 3. So, the missing number is 3.
Example 3: Find the correct answer from the below given pictures.
Solution:
By applying the concept of additive identity, adding 0 to a number causes it to retain its original value.
Therefore, the answer for the first question is 15 + 0 = 15.
The answer for the second question is 0 + 2 = 2.
The answer for the third question is 13 + 0 = 13.
The property of zero that ensures a whole number’s value doesn’t change when added to zero is known as the additive identity of whole numbers. Accordingly, the outcome of adding zero to any whole number, such as 0, 5, or 12, is the number itself.
A number that, when added to another, produces the same result as the original is said to be an additive identity element. One such number that satisfies this particular requirement is zero. As a result, 0 is an identity element.
It states that the outcome of adding a number to zero is the number itself. For instance, the result of adding 5 to 0 is the number 5 itself. 5 + 0 = 5. The identity element in this case is zero, which maintains the identity of the number.