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"

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 = 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)
a² + b² = c²	Formula (relating a, b and c)
x/2 + 7 = 0	Not a Formula (just an equation)

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.

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

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:

So now if you have a box with a depth of 2m, a height of 2m and a volume of 12m³, you can calculate its width:

w = V / dh

w = 12m³ / (2m×2m) = 12/4 = 3m