Question

What is the commutative property of addition?

Answer 1

Hint: For solving this problem you should know about the commutative properties of addition. In this question first we will define the commutative property and then we will take some examples for determining the addition and proving this property. Thus, the question will be solved.

Complete step-by-step solution:
According to our question we have to ask to describe the commutative property of addition.
So, if we add any numbers in any sequence then they will give us a result and this result will be the same always if the sequence of that numbers will be changed, it means if we change the position of numbers in that addition then the result of that addition will remain always the same. And this is also the same rule for the variable terms addition also, that if we change the position of variables in any addition, then too the result of that addition of variables remains the same. And if we add any variable numbers with the normal integers or numbers or we can say that if we add expressions to each other then too the number remains the same as a total of that expression. The result does not affect it. And this can be said that,
\[A+B=B+A\]
This is a commutative rule or property.
And if we see examples for this then:
Eq: (1) Solve 2 + 32 + 16 + 8
\[\begin{align}
  & =34+16+8 \\
 & =58 \\
\end{align}\]
If we change the place of some numbers then,
\[\begin{align}
  & =32+16+2+8 \\
 & =32+26 \\
 & =58 \\
\end{align}\]
So, both are the same.
Eg: (2) Solve \[3{{x}^{2}}+4x+9{{x}^{2}}+12x\]
\[=12{{x}^{2}}+16x\]
And if we change position of any variable then,
\[\begin{align}
  & 9{{x}^{2}}+12x+3{{x}^{2}}+4x \\
 & =12{{x}^{2}}+16x \\
\end{align}\]
So, both results are the same and this is the commutative property of addition.

Note: The commutative property of addition can be used to solve various problems and mainly are use it to make whole square of any expression or terms and if we have given to proof any big expression then we set all same variables near to each other with the help of this property.