# Equations and Formulas

## What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

x |
+ |
2 |
= |
6 |

That equations says: **what is on the left (x + 2) is equal to what is on the right (6)**

So an equation is like a **statement** "*this* equals *that*"

*(Note: this equation has the solution x=4, read how to solve equations.)*

## What is a Formula?

A formula is a special type of equation that shows the relationship between different **variables**.

A **variable** is a symbol like x or V that stands in for a number we don't know yet.

### Example: The formula for finding the volume of a box is:

V = lwh

**V** stands for volume, **l** for length, **w** for width, and **h** for height.

When l=10, w=5, and h=4, then:

**V = 10 × 5 × 4 = 200**

A formula will have **more than one variable**.

These are all equations, but only some are formulas:

x = 2y - 7 |
Formula (relating x and y) |

a + ^{2}b = ^{2}c^{2} |
Formula (relating a, b and c) |

x/2 + 7 = 0 |
Not a Formula (just an equation) |

## Without the Equals

Sometimes a formula is written without the "=":

### Example: The formula for the volume of a box is:

**lwh**

But in a way the "=" is still there, because we can write **V = lwh** if we want to.

## Subject of a Formula

The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.

### Example: in the formula

s = ut + ½ at^{2}

"s" is the subject of the formula

## Changing the Subject

One of the very powerful things that Algebra can do is to "rearrange" a formula so that another variable is the subject.

Rearrange the volume of a box formula (**V = lwh**) so that the width is the subject:

Start with: | V = lwh |

divide both sides by h: | V/h = lw |

divide both sides by l: | V/(hl) = w |

swap sides: | w = V/(hl) |

So now when you want a box with a volume of 12m^{3}, a length of 2m, and a height of 2m, you can calculate its width:

**w = V/(hl)**

**w = 12m ^{3} / (2m × 2m) ** =

**12/4**=

**3m**