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:
- 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
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: