# Properties Of Real Numbers

Real Numbers are used to measure the continuous values. A real number can be rational number or irrational number or it may be positive, negative or zero. It may also be algebraic or transcendental. Properties of Real Numbers that are used in various expressions and equations as follows:

1. The real numbers are dense in nature. Within two real numbers lies an infinite other real numbers.

2. The real numbers holds true for Commutative Property under addition and multiplication:
a + b = b + a
a * b = b * a

3. The real numbers holds true for Associative Property under addition and multiplication:
a + ( b + c ) = ( a + b ) + c
a * ( b * c ) = ( a * b ) * c

4. Distributive property holds true on real numbers:
a * (b + c) = (a * b) + (a * c)
a + (b * c) = (a + b) * (a + c)

5. The additive and multiplicative identity property for real number is:
a + 0 = a
a * 1 = a

6. Inverse property of real number is:
a + (- a ) = 0
a * ($\frac{1}{a}$) = 1

7. Zero property of real number is:
a * 0 = 0

## Commutative Properties of Real Numbers

Commutative property is an important part of mathematics, which is used to solve the problems of Algebra. In a proper definition, 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. Commutative properties holds true under two o...Read More

The Commutative property of addition states that altering the arrangement of two Numbers that are added does not make any modification in the final result i.e, we can sum up numbers in any order but it does not affect the final result.

a + b = b + a

The Commutative Property of addition can be explained by some real life applications:...Read More

## Commutative Property of Multiplication

The Commutative property of multiplication states that altering the arrangement of two Numbers that are multiplied does not make any modification in the final result i.e, we can multiply numbers in any order but it does not affect the final result.

a * b = b * a

The Commutative Property of multiplication can be explained by some ...Read More

## Associative Property of Real Numbers

Associative property is an important part of mathematics, which is used to solve the problems of Algebra. In a proper definition, 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. Associative properties holds true under two ope...Read More

The Associative property of addition states that altering the arrangement of brackets between the operators does not make any modification in the final result i.e, we can sum up Numbers in any order but it does not affect the final result.

a + (b + c) = (a + b) + c

The Associative Property of addition can be explained by some real life applica...Read More

## Associative Property of Multiplication

The Associative property of multiplication states that altering the arrangement of brackets between the operators does not make any modification in the final result i.e, we can multiply Numbers in any order but it does not affect the final result.
a * (b * c) = (a * b) * c
The Associative Property of multiplication can be explained by ex...Read More

## Distribution Property of Real Numbers

Real numbers are used to measure the continuous values. A real number can be rational number or irrational number or it may be positive, negative or zero. It may also be algebraic or transcendental.

The Distributive property is a property for binary operations with at least two operands. This property comes in case when any expression has bo...Read More

## Density Property of Real Numbers

Real numbers are used to measure the continuous values. A real number can be rational number or irrational number or it may be positive, negative or zero. It may also be algebraic or transcendental.

According to the density property, the Real Numbers are infinite. Between two real numbers lies an infinite other real numbers. For examples between 3...Read More

## 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.

a + 0 = a

The above equation shows the ...Read More

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.

a + 0 = a

The identity property of addition can be explained by the following examples:
1. 4 + 0 = 4
2. 2.7 + 0 = 2.7
3. 11 + 0 = 11
4. $\frac{3}{4}$ + 0 = $\frac{3}{4}$
Another thing to be remembered is that when a real number is added to its additive inverse we obtain the additive identity.

## Identity Property of Multiplication

The Identity property of multiplication for real Numbers states that, there exist a real number 1 such that if we multiply any real number to that number, the number remains unchanged.

a * 1 = a

The identity property of multiplication can be explained by the following examples:
1. 4 * 1 = 4
2. 2.7 * 1 = 2.7
3. 11 * 1 = 11