Simple formulae
Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable
What a learner can do afterwards
- Identify the subject of a given formula
- Use inverse operations to rearrange a formula to make a different variable the subject
- Rearrange formulae involving multiple steps including fractions and powers
The lesson
A formula is a rule written with letters, like v = d ÷ t for speed. The subject of a formula is the letter standing alone on one side of the equals sign. In v = d ÷ t, v is the subject.
The formula for speed is v = d ÷ t. If you know distance and time, this formula gives you speed straight away, because v is already the subject.
The area of a circle is A = πr². To make r the subject, first divide both sides by π, then undo the square by taking the square root: r = √(A ÷ π).
Rearranging works like solving an equation: whatever you do to one side, do to the other. Undo operations in reverse order, using the inverse of each one.
To change the subject, undo each operation with its inverse, doing the same thing to both sides.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.