Which Equation Illustrates the Identity Property of Multiplication

August 3, 2022 admin 199 Views

Identity Holding of Multiplication

The
identity property of multiplication
is also known as the Multiplicative Identity Property, which states that multiplying ane with whatever 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 unproblematic words, we can say that the identity property of multiplication states that a number that when multiplied by i gives the original number equally the product.

In this article, we will discuss the concept of the identity belongings of multiplication and its formula. We will talk over the awarding of the multiplicative identity property for integers and rational numbers with the help of solved examples for a better understanding of the concept.

i.	What is the Multiplicative Identity Belongings?
2.	Identity Property of Multiplication Definition
iii.	Multiplicative Identity Belongings Formula
4.	Multiplicative Identity Holding for Integers
5.	Multiplicative Identity Holding of Rational Numbers
6.	FAQs on Multiplicative Identity Holding

What is the Identity Property of Multiplication?

The multiplicative identity holding is applied to numbers in the performance 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, ane is known as the multiplicative identity element because when we multiply any number with ane, the obtained result will exist 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 equally
a × ane = a,
where ‘a’ is whatsoever real number.

Instance:

44 × i = 44, where 44 is the number on which nosotros applied the multiplicative identity.

Note:
The multiplicative identity is not applied when whatever number is multiplied by -1 because the effect will non be the aforementioned number.

For example, 23 × -1 = -23

Identity Holding of Multiplication Definition

The Identity Belongings of Multiplication is divers as the property of multiplication which states that the product of a number and 1 is always equal to the given number. Information technology tin can be mathematically written equally, a × 1 = a, where ‘a’ tin can be whatever number.

Multiplicative Identity Property Formula

The multiplicative identity formula is expressed equally a × 1 = a, where ‘a’ is any real number. This shows that when whatever number is multiplied by one, the product is the number itself. For example, if we multiply 65 with 1 nosotros become 65 as the product. 65 × 1 = 65.

Identity Holding of Multiplication for Integers

The multiplicative identity for integers is 1. We know that the Identity Belongings of Multiplication states that whenever we multiply any number by ane, the production 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 past the number 1, the production is the aforementioned integer. For case, when an integer p = -8 so, -viii × i = -8. Therefore, the multiplicative identity for integers is ane.

Multiplicative Identity Belongings of Rational Numbers

The multiplicative identity of rational numbers is i. Every bit discussed in the above section, if whatever number is multiplied by i the production volition exist the number itself. Similarly, for any non-naught rational number p/q, if we multiply it by one the event will exist the same, that is, p/q.

For example -4/5 × 1 = -iv/5

Important Notes on Identity Property of Multiplication

Identity Property of Multiplication states that multiplying 1 with whatsoever number results in the number itself.
This property can be practical to all real numbers including natural numbers, integers, rational numbers, and even complex numbers.

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Identity Holding of Multiplication Examples

Example 1:
Using the Identity Property of Multiplication, detect the value of S if Southward × 1 = 56

Solution:
Co-ordinate to the multiplicative identity holding when we multiply whatsoever number by 1 the event volition be the aforementioned number.

Thus, S = 56

56 × one = 56
Example 2:
Place the equation that shows the multiplicative identity property.

a) -79 × one = -79

b) -59 × -1 = 59

Solution:
Co-ordinate to the Identity Belongings of Multiplication, when nosotros multiply any number by ane the result is the number itself.

a) -79 × 1 = -79, this equation satisfies the identity as the production is the aforementioned number that is -79 and the multiplicative identity chemical element is i in this case.

b) -59 × -1 = 59, this equation does non satisfy the multiplicative identity property as the product is not the same number -59. The event 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 × one = 1/9

b) 2/3 × 0 = 0

Solution:
According to the multiplicative identity belongings when nosotros 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 one/9 and the multiplicative identity chemical element is ane in this example.

b) 2/three × 0 = 0, this equation does not satisfy the holding as the upshot is non the same number 2/3. The result is 0 and the multiplicative identity element is not 1 in this case.

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Practice Questions on Identity Holding of Multiplication

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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 production is the number itself (9 × i = ix). Here, one is known as the identity element which keeps the identity of the number.

What is an Example of the Identity Holding of Multiplication?

An example of the identity property of multiplication is 45 × 1 = 45. This shows that when 1 is multiplied past 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 existent number. For instance, 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 six is 1, because if nosotros multiply six by 1 the reply will be 6. (half dozen × one = 6). Thus, 1 is the multiplicative identity element of whatever real number.

Is 0 a Multiplicative Identity Element?

No, 0 is not a multiplicative identity chemical element considering if 0 is multiplied by whatever number the result will always be 0. The multiplicative identity element is 1 because when the number 1 multiplies with whatever number, it does not change the value of the number or nosotros can say the value remains unchanged. For example, 99 × 1 = 99, while 99 × 0 = 0. Still, 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 = iii.

What is the Dominion for Identity Property of Multiplication?

The rule for the Identity Property of Multiplication says that the issue of multiplying any real number by one is the number itself. This ways that if a number is multiplied by 1, information technology does not alter its value, information technology allows the number to maintain its identity.

Why is i Called the Multiplicative Identity Element?

The identity property of ane tells that when any number is multiplied past one the number remains unchanged. In other words, when 1 is multiplied by a number, information technology maintains the identity of the number, that is the reason 1 is called the multiplicative identity chemical element. For example, xiii × 1 = 13

What is the Multiplicative Identity of Whole Numbers?

The multiplicative identity of whole numbers is 1 because when whatsoever whole number is multiplied by one the event will be equal to that aforementioned whole number. For example, 78 × 1 = 78.

Is -one a Multiplicative Identity Property Element?

No, -1 cannot be a multiplicative identity belongings element because if we multiply whatsoever number by -one the sign of that number gets changed. For instance, nine × -1 = -ix and -9 × -1 = 9, we can see that the sign of the product changes.

How is Identity Belongings of Multiplication Dissimilar From Zero Property of Multiplication?

The Identity belongings of multiplication states that when we multiply one by any number, the product is the number itself. For example, 8 × ane = 8. On the other hand, the zero property of multiplication states that when nosotros multiply a number by zero, the production is e’er zippo. For example, 8 × 0 = 0.