# 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

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

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

*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

$\frac x 2 =5$ |

$2x-3=7$ |

$x^2 -2x-8=0$ |