Changing the Subject — the Basics
Grade 4What the subject is
The subject of a formula is the single letter on its own, on one side of the equation. In v = u + at, the subject is v. To change the subject, you use inverse operations to isolate a different letter.
Think of it as the same skill as solving an equation — but with letters everywhere instead of numbers.
The golden rule
Whatever you do to one side of the equation, do to the other. Work in reverse BIDMAS: undo additions/subtractions first, then multiplications/divisions, then powers/roots.
Worked example — straightforward rearrangement
EXAMPLE
Make u the subject of v = u + at.
Subtract at from both sides: v − at = u. Rewrite with u on the left: u = v − at.
Worked example — involving a fraction
EXAMPLE
Make r the subject of A = πr².
Divide both sides by π: A/π = r². Take the positive square root of both sides: √(A/π) = r. Rewrite: r = √(A/π).
Try this one
The area of a circle is given by \( A = \pi r^2 \).
Make \( r \) the subject of the formula.
[2]
Nova's hint:
Try to Solve it with Nova?
This is rearranging a formula where the wanted letter is squared.
Ask yourself: 'once the squared letter is on its own, what operation undoes squaring?' Remember the opposite of squaring is taking a square root, as in \( V = k n^2 \) leading to \( n = \sqrt{\tfrac{V}{k}} \).
