Q22. - Algebra 1

Question

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

$\mathbf{3}\mathbf{.25}\mathbf{+}\mathbf{2}\mathbf{.2}\mathbf{+}\mathbf{5}\mathbf{.4}\mathbf{+}\mathbf{10}\mathbf{.75}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{3}\mathbf{.25}\mathbf{+}\mathbf{2}\mathbf{.2}\mathbf{+}\mathbf{5}\mathbf{.4}\mathbf{+}\mathbf{10}\mathbf{.75}\mathbf{=}\mathbf{21}\mathbf{.6}$.

Step 1. Given information.

The given expression is:

$3.25+2.2+5.4+10.75$

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 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:

$\begin{array}{l}3.25+2.2+5.4+10.75=\left(3.25+10.75\right)+2.2+5.4\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(14.00\right)+2.2+5.4\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(14+2.2\right)+5.4\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =16.2+5.4\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =21.6\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$