In the world of Numbers which we deal with on daily basis, many of the properties of real numbers are used in operations such as addition, subtraction, multiplication, division etc. One such property which involves a specific operation on numbers resulting in obtaining the same number!! This property of numbers is called IDENTITY property. This article looks at this identity property and its characteristics.

ADDITIVE IDENTITY OF NUMBERS

Additive identity of numbers, as the name suggests, is a property of numbers which is applied when carrying out addition operations. The property states that when a number is added to zero it will give the same number. “Zero” is called the identity element, (also known as additive identity) If we add any number with zero, the resulting number will be the same number. This is true for any real numbers, complex numbers and even for imaginary numbers.

Suppose, \(a\)* *is any real number, then

\(a ~+~ 0\)

For example, \(120 ~+~ 0\)

MULTIPLICATIVE IDENTITY OF NUMBERS

Multiplicative identity of numbers, as the name suggests, is a property of numbers which is applied when carrying out multiplication operations Multiplicative identity property says that whenever a number is multiplied by the number \(1\)

\(a ~\times~ 1\)

Some examples:

\(-1 ~+~ 0\)

\(0 ~+ ~259\)

\(-1\)

Note*: \(- 1\) \(\times\) \(-1\) = \(1\) (proves that \(-1\) is not a multiplicative identity)*

Solve: Which of the following illustrates the multiplicative identity and additive identity?

- \(45~ +~ 1\)
= \(46\) - \(50~ ×~ 2\)
= \(100\) - \(14~ × ~1\)
= \(14\) - \(-54 ~+~ 0\)
= \(-54\)

*Solution: *

According to identity property of multiplication, the product of any number multiplied by \(1\)

Here, only \(14\)

Therefore, \(14\)

According to identity property of addition, the sum of any number added to 0 is the number itself.

Here, only \(-54~ +~ 0\)

Therefore, \(-54~ +~ 0\)

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