Question

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

$0.25\cdot 7\cdot 4$

Short answer

The value of the expression is: $0.25\cdot 7\cdot 4=1$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$0.25\cdot 7\cdot 4$

Step 2. Write the concept.

The substitution property for multiplication, addition and subtraction is:

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

The associative property is:

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

And the property of multiplicative identity is:

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

Step 3. Evaluate the expression.

The expression $0.25\cdot 7\cdot 4$can be solved as in below:

role="math" localid="1642018487410" $\begin{array}{c}0.25\cdot 7\cdot 4=\left(0.25\cdot 4\right)\cdot 7\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Associativity}\right]\\ =\left(1.00\right)\cdot 7\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =7\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Multiplicative\hspace{0.17em}\hspace{0.17em}Indentity}\right]\end{array}$