# 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 fact or rule that uses mathematical symbols.

It will usually have:

- an equals sign (=)
- two or more
**variables**(x, y, etc) that stand in for values we don't know yet

It shows us how things are related to each other.

### 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=4, and h=5, then:

**V = 10 × 4 × 5 = 200**

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

A very powerful thing that Algebra can do is to "rearrange" a formula so that another variable is the subject.

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

**V = lwh**

**V/h = lw**

**V/(hl) = w**

**w = V/(hl)**

So if we want a box with a volume of 12, a length of 2, and a height of 2, we can calculate its width: