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Additive Identity and Multiplicative Identity are two different identity properties of numbers. When we add a number, or say, additive identity to another number, we get the original number as the result of the addition. The multiplicative identity is the number that, when multiplied with another number, returns the original number. Additive identity and multiplicative identity can be applied to all real numbers.
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Key Terms: Additive Property, Multiplicative Property, Multiplication, Addition
Additive Identity
The additive identity of numbers is a property of numbers that is applied to addition operations. When a number is added to zero, it will result in the same number. This is called "additive identity." Zero is known as the identity element or additive identity. Zero is added to any number, such that the result is the same number. It applies to any real number, complex number, or even an imaginary number.
Let us understand additive identity with the help of an example.
We can take any real number, let's say x.
When we add 0 to x, we will get the original number x.
0 + x = x
Hence, 0 is an additive identity.
Let us see some examples of additive identity, given below.
- 0 + 4 = 4
- 0 + (-9) = -9
- 0 + 86 = 86
- 0 + 1781 = 1781
- 0 + (-3241) = -3241
In all the above examples, when 0 is added to numbers, the result of the addition is the number itself.
Multiplicative Identity
The multiplicative identity of numbers is a property of numbers that is applied to multiplication operations. When a number is multiplied by 1, it will result in the same number. This is called "multiplicative identity." One is known as the identity element or multiplicative identity. One multiplied by any number so that the product is the same number. The multiplicative identity applies to any real number, complex number, or even imaginary number.
Let us understand the multiplicative identity with the help of an example.
We can take any real number, let's say x.
When we multiply 1 by any real number x, we will get the original number x as the product.
1 * x = x
Hence, 1 is a multiplicative identity.
Let us see some examples of multiplicative identity given below.
- 1 * 6 = 6
- 1 * (-11) = -11
- 1 * 86 = 86
- 1 * 1341 = 1341
- 1 * (-2741) = -2741
In all the above examples, when 1 is multiplied by a number, the result of the multiplication is the number itself.
Difference Between Additive And Multiplicative Identity
Check out the differences between the additive and multiplicative identity in the table given below:
| Additive Identity | Multiplicative Identity |
|---|---|
| It is used in the addition operations. | It is used in the multiplicative operations. |
| For any real number, the additive identity is 0. | For any real number, the multiplicative identity is 1. |
| Additive identity is defined as x + 0 = x, where x is a real number. | Multiplicative identity is defined as x * 1 = x, where x is a real number. |
Things to remember
- There are two types of identity for numbers: additive and multiplicative identity.
- The additive identity of numbers is a property of numbers that is applied to addition operations. When a number is added to zero, it will result in the same number.
- 0 is known as the identity element or additive identity.
- The multiplicative identity of numbers is a property of numbers that is applied to multiplication operations. When a number is multiplied by one, it will result in the same number.
- (1) It is known as the identity element or multiplicative identity.
- Additive and multiplicative identities apply to any real number, complex number, or even imaginary number.
Sample Questions
Ques. Is additive identity applicable to negative integers? ( 2 Marks)
Ans. Yes, the additive identity is applicable to negative integers also. When we add 0 to any negative integer, the result of the addition will be the original number.
Example: 0 + (-93) = -93
Ques. Which of the following options shows an additive identity? ( 1 Mark)
(i) 2 + 4 = 6
(ii) 1 + 6 = 7
(iii) 0 + 17 = 17
(iv) 12 + 41 = 53
Ans. (iii) 0 + 17 = 17
Explanation: Only in option (iii) 0 + 17 = 17, the result of the addition is the number itself. Hence, it is an additive identity.
Ques. Solve x * 27 = 27. What is the value of x? ( 1 Mark)
Ans.1
Explanation: The result of the product is the original number. So it must be multiplied by the multiplicative identity 1.
Ques. What is the additive identity of 7? ( 1 Mark)
Ans. The additive identity of 7 is 0. Because when 7 is added to 0, we get 7 as the result of the addition.
Ques. Can we use -1 as a multiplicative identity? Use examples to explain your point. ( 2 Marks)
Ans. No, We cannot use -1 as a multiplicative identity because when we multiply -1 to any real number, it will give the negative of that number as the result.
Example:
-1 * 5 = -5
-1 * 23 = 23
Ques. Solve a+ 6 * 1 = 6. What is the value of a?( 1 Mark)
Ans. 0
Explanation: The result is 6, (a+6) when multiplied with 1, this gives 6. So, a + 6 = 6 and the value of a is 0.
Ques. Solve x + 8 = 8 . What is the value of x? ( 1 Mark)
Ans.0
Explanation: The result of the product is the original number. So it must be added to the additive identity 0.
Ques. 8. Which of the following options shows a multiplicative identity? ( 1 Mark)
(i) 2 * 4 = 8
(ii) 1 * 6 = 6
(iii) 0 * 17 = 0
(iv) 12 * 4 = 48
Ans.(ii) 1 * 6 = 6
Explanation: Only in option (ii) 1 * 6 = 6, the result of the multiplication is the number itself. Hence, it is a multiplicative identity.
Ques. 9. Solve 0+ 17 * x = 17. What is the value of x? ( 1 Mark)
Ans. 1
Explanation: The result is 17, (0 + 17) = 17 as 0 is the additive identity. So, 17 * 1 = 17 and the value of x = 1.
Ques. 10. Solve a * (-100) = -100. What is the value of a? ( 1 Mark)
Ans. 1
Explanation: The result is -100. So, the number must be multiplied with the multiplicative identity, 1 to get the original number as the product.
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