Q60. - Algebra 2

Question

Name the property illustrated by each equation.

 

60. $7+\left(w+5\right)=\left(7+w\right)+5$

Step-by-Step Solution

Answer

The property illustrated by the equation $7+\left(w+5\right)=\left(7+w\right)+5$ is associative property of addition.

Step 1 - Define associative property of addition

The associative property of addition is if $a+\left(b+c\right)=\left(a+b\right)=c$, that is the order in which the numbers are added does not change the sum.

Step 2 - State an example

Give an example to illustrate the inverse property of multiplication. Let $a=5$, $b=8$ and $c=2$, then

$\begin{array}{c}5+\left(8+2\right)=5+\left(10\right)\\ =15\\ \left(5+8\right)+2=13+2\\ =15\\ 5+\left(8+2\right)=\left(5+8\right)+2\end{array}$

Step 3 - State the conclusion

Since it is given that $7+\left(w+5\right)=\left(7+w\right)+5$, therefore, as per the definition of associative property of addition, the order in which we add doesn’t change the sum, therefore they illustrate associative property of addition.