Q24. - Algebra 1

Question

Evaluate the following expression and name the property used in each step:

$\mathbf{2}\mathbf{\cdot }\mathbf{8}\mathbf{\cdot }\mathbf{10}\mathbf{\cdot }\mathbf{2}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{2}\mathbf{\cdot }\mathbf{8}\mathbf{\cdot }\mathbf{10}\mathbf{\cdot }\mathbf{2}\mathbf{=}\mathbf{320}$.

Step 1. Given information.

The given expression is:

$2\cdot 8\cdot 10\cdot 2$

Step 2. Write the concept.

The substitution property for multiplication, addition, and subtraction is:

$\begin{array}{l} a\cdot b=c\\ a÷b=c\\ a\pm b=c\end{array}$

The Associative property is:

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

Step 3. Evaluate the expression.

The expression $2\cdot 8\cdot 10\cdot 2$ can be solved below:

$\begin{array}{c}2\cdot 8\cdot 10\cdot 2=2\cdot 8\cdot \left(10\cdot 2\right)\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =2\cdot 8\cdot \left(20\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =2\cdot \left(8\cdot 20\right)\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =2\cdot 160\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =320\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$