Q64. - Algebra 2

Question

Name the property illustrated by the following equation.

 

$\left(5+9\right)+13=5+(9+13)$

Step-by-Step Solution

Answer

The property is associative property of addition.

Step 1- Define the associative property.

The associative property of addition states that changing the grouping of the numbers does not change the sum of the numbers.

Mathematically, the property is represented as 

$\left(a+b\right)+c=a+\left(b+c\right)$

Step 2- Step description.

Consider the equation $\left(5+9\right)+13=5+(9+13)$.

 

Simplify the equation as follows:

$\begin{array}{c}\left(5+9\right)+13=5+(9+13)\\ 14+13=5+22\\ 27=27\end{array}$

Step 3- Step description.

Since changing the grouping of the numbers does not change the sum of the numbers, thus the property is associative property of addition.

 

Therefore, the property is associative property of addition.