# 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) a2 + b2 = c2 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 at2

"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

divide both sides by h:V/h = lw
divide both sides by l:V/(hl) = w
swap sides: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:

w = V/(hl)
= 12 / (2 × 2)
= 12 / 4
= 3