Evaluate expressions
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Substitute values for variables in algebraic expressions and evaluate the expressions.

This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you with substituting values for variables in algebraic expressions and evaluating the expressions.   
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Algematics software. Click here for instructions.


Algebraic expressions contain 'variables', which are letters that can have many different values.

For example, this algebraic expression:

contains the variable: v

If we substitute a value for ‘v’ and write the expression using that value instead of ‘v’, it is then possible to calculate the value of the expression because then it contains only numbers.

For example, substituting 2 for v in the example expression we have:

2² + 6´2 - 16

Calculating the value of an expression is called ‘evaluating’ the expression. Thus evaluating the example expression for v = 2 we have:

4 + 12 - 16 = 0

To use Algematics to evaluate an expression, you enter the expression, enter the value of the variable(s) to substitute, substitute for the variable(s), then simplify step by step until you have a single number. These steps are explained below. We will use the example from the ‘theory’ section above to demonstrate...

Download the free support file... We have created an Algematics document containing the completed example from this topic. It also includes practice exercises to improve your skills.

File name:  'Evaluate expressions.alg'   File size: 4kb
Click here
to download the file.

If you choose 'Open this file from its current location', then Algematics should open the document immediately. If not, try the other option: 'Save this file to disk', then run Algematics and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Algematics installed on your computer, click here for instructions.


IMPORTANT: This topic assumes that you know how to enter mathematical formulas into Algematics. Find out how by completing the three simple tutorials in the 'Getting Started' section of the Algematics program 'Help'.

Step 1  Enter the data

Click  (or press F3) and type your expression into the maths box in the data entry dialog box.

If the ‘EMPTY’ message is not displayed between the blue buttons, click the  button until the message: ‘INSERT’ appears. If necessary, use the ' * ' symbol for multiply and the ' / ' symbol for divide.


   v[2] + 6v - 16



 Click the  button to enter more data, or click  to close this dialog box and then click


Step 2  Substitute for the variable(s)

Click on the input box and type the values to substitute:


 v = 2

Click  (substitute) to substitute these values into the formula.

This will substitute 2 for v in the example expression.

The example expression will now look like this:

2² + 6´2 - 16

Step 3  Evaluate

Click the  (simplify) button until a single answer is obtained.

The example expression evaluates to zero, like this:


4 + 6´2 - 16


4 + 12 - 16



To substitute many variables into an expression at the same time, type them into the input box with commas between them, like this:




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