1839 LearnersLast updated on June 18th, 2025
Multiplicative Identity Property
The multiplicative identity property states that any number multiplied by 1 remains unchanged. In this topic, we are going to talk about the multiplicative identity property and how it is used in different number systems.
What is the identity property of multiplication?
When using the operation of multiplication, we apply the multiplicative identity property. This property indicates that when a number is multiplied by it result in the number itself. We can apply this property to real numbers, rational numbers, complex numbers, etc. Note that the multiplicative identity property does not apply when a number is multiplied by -1. This is because any number multiplied by -1 will not result in the same number.
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Difference between Additive and Multiplicative Identity
When a number is added to another number, and the sum is the number itself, we call it the additive idenity. In additive identity, the number is 0. Here are some differences between additive identity and multiplicative identity:
| Additive Identity | Multiplicative Identity |
| An additive identity is a number that, when added to another number, and the sum is of the number itself. | Multiplicative identity is when the number 1 is multiplied by the product, it gives the number itself. |
| The additive identity is 0. | Here, the multiplicative identity is 1. |
| It is used with an additional operation. | The multiplication operation is used. |
| We express the additive identity formula as: a + 0 = a 0 + a = a |
The multiplicative identity formula is expressed as: a × 1 = a 1 × a = a |
Multiplicative Identity Property Formula
When a number is multiplied by 1, the product is always the number itself. This is known as the multiplicative identity property. Mathematically, we write it as a × 1 = a, where ‘a’ is any real number. For example, if we multiply 112 by 1, we get 112 as the product. 112 × 1 = 112.
The formula is expressed as:
a × 1 = a
1 × a = a
Identity Property of Multiplication for Integers
The multiplicative identity property for integers is 1. Whenever a number is multiplied by 1, the product is the number itself. This same rule applies to integers as well. When an integer is multiplied by 1, the product will result in the same integer. For example, an integer r = -9 then, -9 × 1 = -9.
Multiplicative Identity Property of Rational Numbers
For rational numbers, the multiplicative identity is 1. If any number is multiplied by 1, then the product of the number will be the number itself. Rational numbers include fractions, decimals, and integers. The number 1 is called the multiplicative identity property because it does not change the value of the number it is multiplied with.
For example, 3/5 is a rational number; when multiplied by 1, we will get ⅗. As you can see, the value of the number does not change.
Real-life applications on Multiplicative Identity Property
The Multiplicative Identity Property is widely used in various fields. Here are a few real-world applications of fields that use multiplicative identity property:
- Banking and transactions: Account balances remain unchanged when multiplied by 1, as the value stays the same, which ensures accuracy in financial transactions.
- Retail: Product prices will remain the same when it is multiplied by 1. This indicates no discount or markup.
- Physics: In most formulas and equations, multiplying by 1 preserves quantities, ensuring no change in units or values.
Common Mistakes and How to Avoid Them in Multiplicative Identity Property
When learning about the multiplicative identity property, students often make small mistakes. Here are some common mistakes that students make and ways to avoid them:
Mistake 1
Incorrectly assuming the identity property for the zero property
Students might think that multiplying 1 gives 0 instead of the same number. Remember that when a number is multiplied by 1, it gives the same number. Whereas multiplying a number by 0 will always give 0.
Mistake 2
Getting additive identity confused with multiplicative identity
Some students might think 1 is the additive identity instead of 0. The additive identity is 0 because x + 0 = x, while the multiplicative identity is 1 because x ×1 = x.
Mistake 3
Assuming that multiplicative identity works only for whole numbers.
When students see fractions or decimals in the question, they assume that the multiplicative identity will not work. Multiplicative identity property works for all numbers, and not just whole numbers. For example, 1.5 × 1 = 1.5.
Mistake 4
Thinking that the multiplicative identity property does not work for variables
Students should not assume that the multiplicative identity property works only for numbers. When applying the property to variables, the values won't change, similar to when multiplying 1 by numbers.
Mistake 5
Forgetting this rule when solving word problems
When solving real-life word problems, students should recognize that if a quantity remains unchanged after multiplication, it was multiplied by 1.
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Solved examples on Multiplicative Identity Property
Problem 1
Using the identity property of multiplication, find the missing number in the equation: X × 1 = -34.
X = -34
Explanation
The identity property states that multiplying any number by 1 results in the same number. Thus, X = -34, and checking: -34 × 1 = -34.
Problem 2
If A × 1 = A, what is the value of A when A = 1023?
A = 1023
Explanation
Since A × 1 = A holds true for all values of A. Substituting A = 1023 gives:
1023 × 1 = 1023.
Problem 3
A rectangle has a length of L. Using the identity property of multiplication, what is the new length after multiplying it by 1?
L
Explanation
Multiplying any quantity by 1 keeps it the same, so the new length remains L. Therefore, L × 1 = L.
Problem 4
Find the missing number in the equation using the Multiplicative Identity Property: 1 × Z = ¾
Z = ¾
Explanation
Multiplying ¾ by 1 does not change its value. Thus, Z = ¾, and checking: 1 × ¾ = ¾.
Problem 5
Using the multiplicative Identity Property, find the value of N if: (25) × 1 = N.
N = 5.
Explanation
First, simplify 25 =5. Then, apply the identity property: 5 × 1 = 5, so N = 5.
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FAQs on Multiplicative Identity Property
1.Which do we consider 1 as the multiplicative identity property?
2.Can we apply multiplicative identity properties to algebraic expressions?
3.Does the multiplicative identity property apply in every number system?
4.Does the multiplicative identity property have any exceptions?
5.How do we recognize the multiplicative identity property in a problem?
6.How can children in Australia use numbers in everyday life to understand Multiplicative Identity Property?
7.What are some fun ways kids in Australia can practice Multiplicative Identity Property with numbers?
8.What role do numbers and Multiplicative Identity Property play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Multiplicative Identity Property skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
