Algebraic notation

In a nutshell

Algebra uses letters called 'variables' to represent unknown quantities. The basic rules for algebraic notation help write terms in a concise way. These terms can then be used in expressions, formulae or equations.

Example 1

The letter 'a' could represent an apple. Two apples could be described by $$\underline{2a}$$.​

Basic rules

​​Adding equal variables

​Add the numbers and copy the variable. If there is no number with the variable, it means $$1$$. For example, $$x$$ means $$1x$$

Example

​$$x+x=2x$$

Subtracting equal variables

Subtract the numbers and copy the variable.

Example

​$$7x-5x=2x$$

Multiplying same variables

​Multiplying the same variables changes the power. When multiplying, add the powers. If there is no number with the variable, it means $$1$$​​.

Example

​$$x \times x = x^2$$

Multiplying different variables

Write the letters without the multiplication sign. Multiplying different variables will not change their powers.

Example

$$x \times y = xy$$

Adding/subtracting different variables

These cannot be added or subtracted so they will remain the same.

Example

$$a+b=a+b$$​​

Formulae

Formulae help find quantities.

Examples 

• ​$$F=ma$$ 

Calculate the force ($$F$$​) on an object from its mass ($$m$$​) and acceleration ($$a$$​).

• ​$$P = 2(l+w)$$ 

Calculate the perimeter ($$P$$​) of a rectangle from its length ($$l$$​) and width ($$w$$​).

• ​$$A=\frac{1}{2} bh$$ 

Calculate the area ($$A$$​) of a triangle from its base ($$b$$​) and its height ($$h$$​).​

Equations

An equation is formed when two expressions equal each other.

Examples