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Additive and Multiplicative Identity

 

Multiplicative Identity vs Additive Identity: Many of the characteristics of real numbers are employed in operations like addition, subtraction, multiplication, and division in the world of numbers that we interact with daily. One such characteristic entails a certain operation on integers that yields the same result!! Thus, the Identity feature of numbers is what it's called. This article examines the features of this identity attribute.

What is Additive Identity, and how does it work?

As the name implies, the additive identity of numbers is the characteristics of numbers that are used while performing addition operations. The additive identity property says that the result is the same when a number is multiplied by zero. This is because the identity element is zero. Thus, if we add any integer by zero, the outcome will be the original number. This is true for any real, complex, or imaginary number. Assume that 'x' is any real number. x + 0 = x = 0 + x For example, the identity characteristic of addition is shown as 15 + 0 = 15, where 0 represents the additive identity.

What is Multiplicative Identity, and how does it work?

As the name implies, the multiplicative identity is a characteristic of numbers that are used when performing multiplication operations. The property of multiplicative identity states that when a number is multiplied by 1 (one), the result is the product. A number's multiplicative identity is "1." If the integer being multiplied is 1 itself, this is true. The multiplicative identity attribute is denoted by the following: x × 1 = x = 1 × x (x is any real number)

Example of a Solved Problem:

Which of the following best exemplifies the multiplicative and additive identities? 32 + 1 = 33 25 × 2 = 50 56 × 1 = 56 −76 + 0 = −76 The product of any number multiplied by 1 is the number itself, according to the identity principle of multiplication. Only 10×1 = 10 validates the property in this case. As a result, 10×1= 10 exemplifies the Multiplicative identity. According to the identity principle of addition, the total of any number added to 0 equals the number itself. Only -89 + 0 = -89 satisfies the condition in this case. As a result, the additive identity is illustrated as -89 + 0 = -89.

FAQs – Frequently Asked Questions

What is the definition of additive identity?
When a value is added to a number, the outcome is the same as the original number. We obtain the same real number when we add 0 to any real number. For instance, 7 + 0 is 7. As a result, the additive identity of every real number is 0.

Is it 0 or 1 that is the multiplicative identity?
A real number's multiplicative identity is 1. We obtain the same number when we multiply 1 by any real integer. 8 x 1 = 8, -79 x 1 = -79, and 29 x 1 = 29 are some examples.

Is -1 a multiplicative identity as well?
Because multiplying -1 to any real number changes the sign of that number, it is not a multiplicative identity. 8 x -1 = -8 -23 x -1 = 23

What is the multiplicative identity for the number eight?
Since 8 x 1 = 8, the multiplication identity of 8 is merely 1.

What does a's additive identity look like?
Because a+0 = a, the additive identity of a is 0.

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