Rearranging Equations

Rearranging an equation means changing its form to make a different letter the subject. The value of the equation stays balanced as long as you do the same thing to both sides.

The basic rules

Addition and subtraction Undo adding by subtracting, and undo subtracting by adding.
Multiplication and division Undo multiplying by dividing, and undo dividing by multiplying.
Powers and roots Undo squaring by taking a square root, and undo a square root by squaring.
  • Choose the letter you want to make the subject.
  • Undo the operations around that letter in reverse order.
  • Whatever operation you do to one side, do to the other side too.
  • Keep the equation balanced, and check your result by substituting values.

Worked examples

Make a the subject: F = ma
Divide both sides by m: a = F ÷ m.
Make t the subject: v = u + at
Subtract u from both sides: v − u = at.
Divide both sides by a: t = (v − u) ÷ a.
Make V the subject: ρ = m ÷ V
Multiply both sides by V, then divide both sides by ρ: V = m ÷ ρ.

Quick check

Put the rearranged expression back into the original equation. If both sides are equal, your rearrangement is consistent. Remember that division by a letter assumes it is not zero.

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