Equations and Formulas
What is an Equation
An equation says that two things are equal. It will have an equals sign "=" like this:
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"
What is a Formula
A formula is a special type of equation that shows the relationship between different variables (a variable is a symbol for a number we don't know yet).
Example:
The formula for finding the volume of a box is
V = wdh
V stands for volume, w for width, d for depth and h for height.
If w=5, d=10 and h=4, then V = 5×10×4 = 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:
wdh
But in a way the "=" is still there, because you could write V = wdh if you wanted to.
Subject of 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 = vt + 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 = wdh) so that the width is the subject:
Start with: 
V = wdh 
divide both sides by d: 
V / d = wh 
divide both sides by h: 
V / dh = w 
swap sides: 
w = V / dh 
So now if you have a box with a depth of 2m, a height of 2m and a volume of 12m^{3}, you can calculate its width:
w = V / dh
w = 12m^{3} / (2m×2m) = 12/4 = 3m
