Question

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

$\mathbf{0}\mathbf{.2}\mathbf{\cdot }\mathbf{4}\mathbf{.6}\mathbf{\cdot }\mathbf{5}$

Short answer

The value of the expression is: $\mathbf{0}\mathbf{.2}\mathbf{\cdot }\mathbf{4}\mathbf{.6}\mathbf{\cdot }\mathbf{5}\mathbf{=}\mathbf{4}\mathbf{.6}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$0.2\cdot 4.6\cdot 5$

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 property of multiplicative identity is:

$a\cdot 1=a=1\cdot a$

The Associative property is:

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

Step 3. Evaluate the expression.

The expression$0.2\cdot 4.6\cdot 5$ can be solved below:

$\begin{array}{l}0.2\cdot 4.6\cdot 5=\left(0.2\cdot 5\right)\cdot 4.6\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(1.0\right)\cdot 4.6\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =1\cdot 4.6\\ =4.6\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplicative\hspace{0.17em}\hspace{0.17em}identity}\right]\end{array}$