Q21. - Algebra 1

Question

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

$\mathbf{4}\mathbf{.3}\mathbf{+}\mathbf{2}\mathbf{.4}\mathbf{+}\mathbf{3}\mathbf{.6}\mathbf{+}\mathbf{9}\mathbf{.7}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{4}\mathbf{.3}\mathbf{+}\mathbf{2}\mathbf{.4}\mathbf{+}\mathbf{3}\mathbf{.6}\mathbf{+}\mathbf{9}\mathbf{.7}\mathbf{=}\mathbf{20}$.

Step 1. Given information.

The given expression is:

$4.3+2.4+3.6+9.7$

Step 2. Write the concept.

The substitution property for multiplication, addition, and subtraction is:

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

Step 3. Evaluate the expression.

The expression can be solved below:

$\begin{array}{l}4.3+2.4+3.6+9.7=\left(4.3+2.4\right)+3.6+9.7\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(6.7\right)+3.6+9.7\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(6.7+3.6\right)+9.7\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =10.3+9.7\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =20.0\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$