Q8. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Which expression below illustrates the Associative property?

F $\mathit{a}\mathit{b}\mathit{c}\mathbf{=}\mathit{b}\mathit{a}\mathit{c}$

G $\mathbf{2}\left(x-3\right)\mathbf{=}\mathbf{2}\mathit{x}\mathbf{-}\mathbf{6}$

H $\left(p+3\right)\mathbf{-}\mathit{t}\mathbf{=}\mathit{p}\mathbf{+}\left(3-t\right)$

J $\mathbf{5}\mathbf{+}\left(-5\right)\mathbf{=}\mathbf{0}$

Step-by-Step Solution

Answer

The expression that illustrates the associative property is $\left(p+3\right)\mathbf{-}\mathit{t}\mathbf{=}\mathit{p}\mathbf{+}\left(3-t\right)$. Therefore, the option H is correct.

Step 1. Write the associative property.

The associative property states that:

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

Step 2. Determine which expression illustrates the Associative property.

It can be noticed that the expression $\left(p+3\right)-t=p+\left(3-t\right)$ resembles with the expression $a+\left(b+c\right)=\left(a+b\right)+c$.

 

Therefore, the expression that illustrates the associative property is $\left(p+3\right)-t=p+\left(3-t\right)$. Therefore, the option H is correct.