# Identity Property of Real Numbers

Real numbers are those numbers that are not imaginary numbers. The Real Numbers did not have a name before Imaginary numbers, that‘s why they were known as a real numbers. Identity properties holds true under two operations which are addition and multiplication.

1. Identity Property of Addition:

a + 0 = a

The above equation shows the Identity Property of Addition. The identity property of addition for real numbers states that,  there exist a real number  0 such that  if we add any real number to that number, the number remains unchanged.

e.g, 4 + 0  = 4

Here we observe that when 0 is added to a real number 4 the result remains unchanged, so we say that 0 is additive identity.

2. Identity Property of Multiplication:

a * 1 = a

The above equation shows the Identity Property of Multiplication. The identity property of multiplication for real numbers states that,  there exist a real number  0 such that  if we multiply any real number to that number, the number remains unchanged.

e.g, 4 * 1  = 4

Here we observe that when 0 is multiplied to a real number 4 the result remains unchanged, so we say that 0 is multiplicative identity.

## Find the additive identity for a real number 6/5. Is the Additive identity same for all real numbers?

Here we see that if zero ( 0) is added to 6/5, then ( 6 / 5) + 0 = 6 / 5 More over we can also check that if the additive inverse of any real number is added to the given number, the result we get is additive identity of the number. Let us check the same: We see that the additive inverse of 6 / 5 is -6 / 5. So, (6/ 5) + (-6/5) = (6/ 5) - (6/5) = 0. So it is the additive identity of 6/5 or we conclude that 0 is the additive identity for any real number.

## Find the multiplicative identity of a real number 3.4 ? Is the multiplicative identity same for all the real numbers?

We observe that if we multiply 1 with the given number i.e. 3.4, then the product is the original real number. So, we get 3.4 * 1 = 3.4 Moreover we also know that if the multiplicative inverse of any real number is multiplied by the original number, then we get the multiplicative identity as the result. Let us try it for the given real number 3.4 First we write 3.4 as 34/10 We observe that its multiplicative inverse is 10 / 34 Now multiplying both real Numbers we get: ( 34/10) * (10/34) = 1 So we conclude that 1 is the multiplicative identity for 3.4 If we try it for any other real number , we get the same answer. So 1 is the multiplicative identity for all the Real Numbers.

## Show that 0 is the additive identity for a real number 2.

We first find the additive inverse of a real number 2 is -2. Now to get the additive identity of any real number, we add 2 and its additive inverse. We get, = 2 + ( -2 ) = 0 So we find that additive identity of 2 is 0.

## Show that 1 is the multiplicative identity for a real number 7?

We first find the multiplicative inverse of a real number Now to get the multiplicative identity of any real number, we multiply 7 and its multiplicative inverse i.e. 1/7. We get, = 7 * (1/7), = 1. So we find that multiplicative identity of 7 is 1.