Additive Identity vs Multiplicative Identity

The arithmetic operations that we perform in our day to day life depends mainly on the identity that we applied on the numbers. The basic algebraic identities are additive identity and multiplicative identity. In this 0 is the additive identity and 1 is the multiplicative identity for all the whole numbers, natural numbers and so on. Additive identity is the number when it is added to another number it gives the original number and similarly multiplicative identity is the number when it is multiplied by another number it gives the original number.

For addition operations additive property is used and multiplicative identity is used for the multiplicative operations. There are many properties in mathematics that are used for various properties. These properties help to reduce the complexity of problems and to solve the problems easily. These properties are used in addition, subtraction, multiplication and division operations.

Additive Identity

Additive Identity is a property that states that when a zero is added to any number it results in the same number. Therefore, zero is known as additive identity. Hence this property is also known as “zero property”. Generally it is defined as when a number n is added to a zero then it gives the output as the same number n. Here n may be a real number, integer, rational number, complex number or imaginary number. It can be represented as follows.

0 + n = n

Where n can be any number.

Multiplicative Identity

Multiplicative Identity is a property which is applied when we are performing multiplication operations. It states that when a number is multiplied by 1 it results in the same number. Here 1 is known as the multiplicative identity. Hence this property is also known as “one property”. In general, it can be defined as when 1 is multiplied by any number n it gives the same number n. Here n may be a real number, integer, rational number, complex number or imaginary number. It can be represented as follows.

1 x n = n

Where n can be any number.

Differences between the Additive Identity and Multiplicative Identity

The main differences between additive identity and multiplicative identity are as follows.

• For any number additive identity is 0 and multiplicative identity is 1.

• Additive identity is an identity which can be used in addition operations and multiplicative identity is also an identity that can be used in multiplication operations.