# Evaluating Expressions

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

To evaluate an algebraic expression, replace the variable or variables with known values and then use the order of operations .

For your convenience, you can use parenthesis when you plug in negative values to the variables.

Example 1:

Evaluate the expression. Use the values $p=-4$ , and $n=14$ .

$3\left(p+n\right)$

To evaluate the expression, first substitute $-4$ for $p$ and $14$ for $n$ in the expression.

$3\left(p+n\right)=3\left(\left(-4\right)+14\right)$

Use the order of operations to simplify. First do the operation inside the parenthesis.

Add the numbers $-4$ and $14$ .

$=3\left(10\right)$

Now, multiply $3$ and $10$ .

$3\left(10\right)=30$

So, when $p$ is $-4$ and $n$ is $14$ , the value of the given expression is $30$ .

Example 2:

Evaluate each expression if $x=7$ , and $y=3$ .

$\frac{xy}{3}+2$

To evaluate the expression, replace $x$ with $7$ and $y$ with $3$ .

$\frac{xy}{3}+2=\frac{7\cdot 3}{3}+2$

Use the order of operations and simplify the expression.

Perform multiplication and division from left to right.

$\begin{array}{l}=\frac{21}{3}+2\\ =7+2\end{array}$

Add $7$ and $2$ .

$=9$

Therefore, for the given values of $x$ and $y$ , the value of the expression is $9$ .