## How to evaluate an expression with one variable

Let's say we want to evaluate the expression $a + 4$. Well, first we need to know the value of the variable $a$. For example, to evaluate the expression when $\blueD {a = 1}$, we just replace $\blueD a$ with $\blueD 1$:

So, the expression $a + 4$ equals $5$ when $a = 1$.

We can just as easily evaluate $a + 4$ when $\blueD {a = 5}$:

So, the expression $a + 4$ equals $9$ when $a = 5$.

## Evaluating an expression with multiplication

You might be asked to "

**Evaluate $3x$ when $x = 5$.**"Notice how the number $3$ is right next to the variable $x$ in the expression $3x$. This means "$3$ times $x$". The reason we do this is because the old way of showing multiplication with the symbol $\times$ looks confusingly similar to the variable $x$.

Okay, so now let's solve the problem:

So, the expression $3x$ equals $15$ when $x = 5$.

### New ways to show multiplication

Hold on a second! Did you notice that we wrote "$3$ times $\blueD 5$" as $3 \cdot \blueD 5$ instead of as $3 \times \blueD 5$? Using a dot instead of the symbol $\times$ is another new way of showing multiplication:

Parentheses can also be used to show multiplication:

Let's summarize the new ways of showing multiplication that we learned.

Old way | New way | |
---|---|---|

With a variable | $3 \times x$ | $3x$ |

Without variable | $3 \times 5$ | $3\cdot 5$ or $3(5)$ |

## Evaluating expressions where order of operations matter

For more complex expressions, we'll have to be sure to pay close attention to order of operations. Let's take a look at an example:

**Evaluate $5 + 3e$ when $\blueD{e=4}$.**

So, the expression $5 + 3e$ equals $17$ when $e = 4$.

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is $\redD{32}$, which comes from first adding $5$ and $3$ to get $8$ then multiplying $8$ by $4$ to get $\redD{32}$.