Commutative Properties of Real Numbers

posted on: 14 Feb, 2012 | updated on: 22 Oct, 2012

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 operations which are addition and multiplication.

1.Commutative property of addition:

a + b = b + a

In the above given equation, it shows the commutative property of real numbers by addition. 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.. In the general sense, in any an additive equation you can change the arrangement of real numbers anywhere but final result does not get affected through this shift of numbers. Here are some examples through which we can easily describe the Commutative property of addition.

e.g, 4 + 5 = 5 + 4 = 9

2.Commutative property of multiplication:

a * b = b * a

In the above given equation, it shows the commutative property of real numbers by multiplication. The commutative property of multiplication states that altering the arrangement of two numbers that are added does not make any modification in the final result i.e, we can multiply numbers in any arrangement it wont affect the concluding result. In the general sense, in any an multiplicative equation you can change the arrangement of real numbers anywhere but final result does not get affected through this shift of numbers. Here are some examples through which we can easily describe the Commutative property of multiplication.

e.g, 4 * 5 = 5 * 4 = 20

Add the following given number with the help of commutative property, 4+5?

Before solving this question we need to know what Commutative Property is? According to this property, if we have two Numbers a and b and we asked to add the given number then the order of adding is not important. If we add a+b or b+a, the result for both the variables remains the same. For the above question we can see that 4 is the first real number and 5 is the second real number. So we can take the value of a as 4 and value of 5 as b. Now according to commutative property:

a+b = b+a

First take left hand side values:

= 4+5.

=9,

Now, take right hand side value:

= 5+4,

=9.

In this way we can add two Real Numbers.

Add the following given number with the help of commutative property, 4x+5x where x=1?

We know Commutative Property of real number, but here we are having x as a variable but as the value of x is a real number so we can add them quit easily. Now we will solve both the real Numbers separately then we will apply commutative law.

We will put the value of x=1 in 4x and 5x

4*(1)=4 and 5*(1)=5

On applying commutative property,

a+b = b+a,

Here 4 is the given value for a and 5 is the given value for b.

We will take left hand side:

4+5,

=9,

We will take right hand side,

5+4,

=9.

This is a simple way to solve problems using commutative property.

Add the following given number with the help of commutative property, 12x+13y where x=2 and y =3?

In this problem we are having different variable with both the given Numbers but we don't need to worry as we are having both the variables as Real Numbers. Now we will solve both the real numbers separately then we will apply commutative law.

12*(2)=24 and 13*(3)=39,

Now we can rewrite our question as:

24+39,

We will apply Commutative Property,

a+b = b+a,

Here 24 is the given value for a and 39 is the given value for b.

We will take left hand side:

24+39,

=63,

We will take right hand side,

39+24,

=63.