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 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:

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:


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

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 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


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