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"
(Note: this equation has the solution x=4, read how to solve equations.)
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.
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:
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
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 when you want a box with a volume of 12m3, a length of 2m, and a height of 2m, you can calculate its width:
w = V/(hl)
w = 12m3 / (2m × 2m) = 12/4 = 3m