Åk 6–9

4.1 Addition and Subtraction
Adding variables isn’t difficult. Here below you see a quadrangle with different length for each side.

Example А: The expression for the quadrangles perimeter is written as:
Perimeter: 5f + 4f + 3f + 2f = 14f

Example B: If we are to express the perimeter for the figure above then it will look like this:

Perimeter = 3g + 2j + 2g + 3 = 5g + 2j + 3

We add the similar terms with each other. So, we cannot add 5g with 2j, because these have different variables which can have different variables.  Example C:

In three match boxes there are an equal amount of matches, and we write the number of matches in a match box with t.  Besides this there are a number of loose matches.     t t 3 t 2

We write the expression for the total number of matches as:

Number of matches : t + t + 3 + t + 2 = 3t + 5  We can show that 3a + 5 + a = 4a + 5 by looking at an example with distances. Check it for yourself if it is correct.

3a + 5 + a 3a
5
a
4a + 5 4a 5
4a + 5 4a 5

When subtracting, the same thing applies.

Example: 4m + 7 – m

4m + 7 - m 4m - m 7
3m + 7 3m 7

Can you add the following terms with variables: a + a2 + a3 ?

We can test this with the following figures:
• a can be illustrated by a line.
• а2 can be illustrated by a square with the side a.
• а3 can be illustrated by a cube with the side a.   Is it possible to add a length with the square or a cube?

The answer is no. We can’t add and simplify these terms.  