A formula is an equation that expresses a relationship between variables, each of which represents a quantity.

Consider the formula for the perimeter of a rectangle.

l: The length of the rectangle (in units)

w: The width of the rectangle (in units)

P: The perimeter of the rectangle (in square units)

P = 2l + 2w

The formula for the perimeter of a rectangle has three variables with each variable representing a quantity. A single formula can be represented many ways. Usually one of the variables is isolated. In the formula for the perimeter of a rectangle, the variable P is isolated, although it could be expressed with the variable l or the variable w isolated (below).

Given the formula can be expressed three ways, use:

Note that formulas are usually expressed one way, with a chosen variable isolated.

Algebraic manipulations are generally used to express the formula other ways, with different variables isolated.

Mathematicians usually prefer to isolate the required variable before substituting numbers. When numbers are substituted, no calculations are generaly done till the required variable is isolated. Substituting before isolating the desired variable can lead to intermediate rounding errors.

EXAMPLE

What is the radius of a circle that has a circumference of 100 cm?

SOLUTION

Recall the following:

r: The radius of a circle

C: The circumference of the circle