Identity Property of Multiplication
The identity property of multiplication is also known as the Multiplicative Identity Property, which states that multiplying 1 with any number results in the number itself. This is due to the reason that when 1 is multiplied by any number, it does not change the number, it keeps its identity. So, we can say that 1 is the multiplicative identity. In simple words, we can say that the identity property of multiplication states that a number that when multiplied by 1 gives the original number as the product.
In this article, we will discuss the concept of the identity property of multiplication and its formula. We will discuss the application of the multiplicative identity property for integers and rational numbers with the help of solved examples for a better understanding of the concept.
What is the Identity Property of Multiplication?
The multiplicative identity property is applied to numbers in the operation of multiplication. The property states that when a number is multiplied by the number 1 (one), the product will be the number itself. This property is applied when numbers are multiplied by 1. Here, 1 is known as the multiplicative identity element because when we multiply any number with 1, the obtained result will be the same number. This Identity Property of Multiplication can be applied to real numbers, complex numbers, integers, rational numbers, and so on. The multiplicative identity property is expressed as a × 1 = a, where 'a' is any real number.
Example:
44 × 1 = 44, where 44 is the number on which we applied the multiplicative identity.
Note: The multiplicative identity is not applied when any number is multiplied by 1 because the result will not be the same number.
For example, 23 × 1 = 23
Identity Property of Multiplication Definition
The Identity Property of Multiplication is defined as the property of multiplication which states that the product of a number and 1 is always equal to the given number. It can be mathematically written as, a × 1 = a, where 'a' can be any number.
Multiplicative Identity Property Formula
The multiplicative identity formula is expressed as a × 1 = a, where 'a' is any real number. This shows that when any number is multiplied by 1, the product is the number itself. For example, if we multiply 65 with 1 we get 65 as the product. 65 × 1 = 65.
Identity Property of Multiplication for Integers
The multiplicative identity for integers is 1. We know that the Identity Property of Multiplication states that whenever we multiply any number by 1, the product is the same number. The same rule applies to integers as well. The multiplicative identity property for integers is that whenever we multiply an integer by the number 1, the product is the same integer. For example, when an integer p = 8 then, 8 × 1 = 8. Therefore, the multiplicative identity for integers is 1.
Multiplicative Identity Property of Rational Numbers
The multiplicative identity of rational numbers is 1. As discussed in the above section, if any number is multiplied by 1 the product will be the number itself. Similarly, for any nonzero rational number p/q, if we multiply it by 1 the result will be the same, that is, p/q.
For example 4/5 × 1 = 4/5
Important Notes on Identity Property of Multiplication
 Identity Property of Multiplication states that multiplying 1 with any number results in the number itself.
 This property can be applied to all real numbers including natural numbers, integers, rational numbers, and even complex numbers.
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Identity Property of Multiplication Examples

Example 1: Using the Identity Property of Multiplication, find the value of S if S × 1 = 56
Solution: According to the multiplicative identity property when we multiply any number by 1 the result will be the same number.
Thus, S = 56
56 × 1 = 56

Example 2: Identify the equation that shows the multiplicative identity property.
a) 79 × 1 = 79
b) 59 × 1 = 59
Solution: According to the Identity Property of Multiplication, when we multiply any number by 1 the result is the number itself.
a) 79 × 1 = 79, this equation satisfies the identity as the product is the same number that is 79 and the multiplicative identity element is 1 in this case.
b) 59 × 1 = 59, this equation does not satisfy the multiplicative identity property as the product is not the same number 59. The result is 59 and the multiplicative identity element is not 1 here.

Example 3: Select the equation that satisfies the Identity Property of Multiplication.
a) 1/9 × 1 = 1/9
b) 2/3 × 0 = 0
Solution: According to the multiplicative identity property when we multiply any rational number by 1 the result will be the same rational number.
a) 1/9 × 1 = 1/9, this equation satisfies the property because the result is the same number that is 1/9 and the multiplicative identity element is 1 in this case.
b) 2/3 × 0 = 0, this equation does not satisfy the property as the result is not the same number 2/3. The result is 0 and the multiplicative identity element is not 1 in this case.
FAQs on Identity Property of Multiplication
What is the Identity Property of Multiplication in Math?
According to the Identity Property of Multiplication, if a number is multiplied by 1, it results in the number itself. For example, if 9 is multiplied by 1, the product is the number itself (9 × 1 = 9). Here, one is known as the identity element which keeps the identity of the number.
What is an Example of the Identity Property of Multiplication?
An example of the identity property of multiplication is 45 × 1 = 45. This shows that when 1 is multiplied by 45, the product is 45 itself.
What is the Identity Property of Multiplication Formula?
The formula that describes the Identity Property of Multiplication is: a × 1 = a, where 'a' is any real number. For example, if we substitute the value of 77 in the formula we get, 77 × 1 = 77
What is the Multiplicative Identity of 6?
According to the multiplicative identity property, the multiplicative identity of 6 is 1, because if we multiply 6 by 1 the answer will be 6. (6 × 1 = 6). Thus, 1 is the multiplicative identity element of any real number.
Is 0 a Multiplicative Identity Element?
No, 0 is not a multiplicative identity element because if 0 is multiplied by any number the result will always be 0. The multiplicative identity element is 1 because when the number 1 multiplies with any number, it does not change the value of the number or we can say the value remains unchanged. For example, 99 × 1 = 99, while 99 × 0 = 0. However, 0 is an additive identity element, that is, when 0 is added to a number, the result is the number itself. For example, 3 + 0 = 3.
What is the Rule for Identity Property of Multiplication?
The rule for the Identity Property of Multiplication says that the result of multiplying any real number by 1 is the number itself. This means that if a number is multiplied by 1, it does not change its value, it allows the number to maintain its identity.
Why is 1 Called the Multiplicative Identity Element?
The identity property of 1 tells that when any number is multiplied by 1 the number remains unchanged. In other words, when 1 is multiplied by a number, it maintains the identity of the number, that is the reason 1 is called the multiplicative identity element. For example, 13 × 1 = 13
What is the Multiplicative Identity of Whole Numbers?
The multiplicative identity of whole numbers is 1 because when any whole number is multiplied by 1 the result will be equal to that same whole number. For example, 78 × 1 = 78.
Is 1 a Multiplicative Identity Property Element?
No, 1 cannot be a multiplicative identity property element because if we multiply any number by 1 the sign of that number gets changed. For example, 9 × 1 = 9 and 9 × 1 = 9, we can see that the sign of the product changes.
How is Identity Property of Multiplication Different From Zero Property of Multiplication?
The Identity property of multiplication states that when we multiply 1 by any number, the product is the number itself. For example, 8 × 1 = 8. On the other hand, the zero property of multiplication states that when we multiply a number by zero, the product is always zero. For example, 8 × 0 = 0.
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