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

\frac x 2 =5

2x-3=7

x^2 -2x-8=0