Q18. - Algebra 1

Question

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

$11+7+5+13$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{11}\mathbf{+}\mathbf{7}\mathbf{+}\mathbf{5}\mathbf{+}\mathbf{13}\mathbf{=}\mathbf{36}$.

Step 1. Given information.

The given expression is:

$11+7+5+13$

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 $11+7+5+13$ can be solved below:

$\begin{array}{l}11+7+5+13=11+5+\left(7+13\right) \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right)\\ =11+5+20 \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right)\\ =11+\left(5+20\right) \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right)\\ =11+25 \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right)\\ =36 \text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right)\end{array}$