Question

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

$\mathbf{12}\mathbf{\cdot }\mathbf{2}\mathbf{\cdot }\mathbf{6}\mathbf{\cdot }\mathbf{5}$

Short answer

The value of the expression is: $\mathbf{12}\mathbf{\cdot }\mathbf{2}\mathbf{\cdot }\mathbf{6}\mathbf{\cdot }\mathbf{5}\mathbf{=}\mathbf{720}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$12\cdot 2\cdot 6\cdot 5$

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 commutative property is:

$a+b=b+a$

The Associative property is:

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

Step 3. Evaluate the expression.

The expression can be solved below:

$\begin{array}{l}12\cdot 2\cdot 6\cdot 5=\left(12\cdot 5\right)\cdot 2\cdot 6\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(60\right)\cdot 2\cdot 6\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(60\cdot 2\right)\cdot 6\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(120\right)\cdot 6\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =720\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$