### Algebra: Variables

### Variables

Max earns #4# euro per hour.

The number of hours that Max works varies.

If he works #\blue 3# hours a day, he earns #4 \times \blue3 =12# euro.

On another day he works #\blue 5# hours and earns #4 \times \blue 5=20# euro.

In math a varying quantity is represented by a letter, such as #\blue x#.

Now assume Max works #\blue x# hours.

Max earns #4# euro per hour, hence he earns #4\times \blue x# euro in total.

If Max works #\blue 7# hours, then #\blue x = \blue 7# and he will earn #4 \times \blue 7 =28# euro in total.

**With #\blue 3,\blue5# or #\blue 7# hours of work, Max earns:**

\[\begin{array}{rcl}

4 \times \blue3 &=& 12 \\

4 \times \blue 5 &=& 20 \\

4 \times \blue 7 &=& 28

\end{array}\]**With #\blue x# hours of work, Max earns:**

\[\begin{array}{c}

4 \times \blue x

\end{array}\]

In the example above, we use mathematical symbols to express a situation algebraically. Here #4 \times \blue x# is called an **algebraic expression **and the letter #\blue x# is called a **variable**.

Algebra is about calculating with variables. On the right hand side you can see more examples of algebraic expressions. In those examples, #\blue x#, #\green y# and #\purple z# are variables. In algebraic expressions, we can replace the variables with numbers. Calculating with variables is done in the same way as calculating with numbers.

**Examples**

\[\begin{array}{c}

\blue x+5 \\ \\

\sqrt{\green y-3} \\ \\

\purple z^2 + \purple z

\end{array}\]

**Pass Your Math**independent of your university. See pricing and more.

Or visit omptest.org if jou are taking an OMPT exam.