Q7. - Algebra 1

Question

Evaluate the following expression. Name the property used in each step:

$\mathbf{3}\mathbf{\cdot }\mathbf{7}\mathbf{\cdot }\mathbf{10}\mathbf{\cdot }\mathbf{2}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{3}\mathbf{\cdot }\mathbf{7}\mathbf{\cdot }\mathbf{10}\mathbf{\cdot }\mathbf{2}\mathbf{=}\mathbf{420}$.

Step 1 – Given information.

Given expression is:

$3\cdot 7\cdot 10\cdot 2$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

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

The commutative property of multiplication is:

$a\cdot b=b\cdot a$

Step 3 – Evaluate the expression.

The expression $3\cdot 7\cdot 10\cdot 2$ can be solved in below:

$\begin{array}{c}3\cdot 7\cdot 10\cdot 2=\left(3\cdot 10\right)\cdot \left(7\cdot 2\right)\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =30\cdot 14\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =420\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$