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"

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.


cuboid 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)
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 you could write V = lwh if you wanted 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

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

w = V / hl

w = 12m3 / (2m×2m) = 12/4 = 3m