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 $n = 14$ .

$3 (p + n)$

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

$3 (p + n) = 3 ((- 4) + 14)$

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

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

$= 3 (10)$

Now, multiply $3$ and $10$ .

$3 (10) = 30$

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 $y = 3$ .

$\frac{x y}{3} + 2$

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

$\frac{x y}{3} + 2 = \frac{7 \cdot 3}{3} + 2$

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 $9$ .