What is an Equation? Equations and Formulas
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 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)|
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:
=12 / (2 × 2)
=12 / 4