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- Changing the subject of a formula
Changing the subject of a formula
Rearranging a formula is just solving an equation with letters. Use the same balancing moves.
The idea
The subject is the letter on its own on one side: in v = u + at, v is the subject.
To make another letter the subject, undo the operations around it, doing the same to both sides.
To make another letter the subject, undo the operations around it, doing the same to both sides.
Example
Make t the subject of v = u + at
Subtract u: v − u = at
Divide by a: t = (v − u)a
Subtract u: v − u = at
Divide by a: t = (v − u)a
Powers and roots
Make r the subject of A = πr2
Divide by π: Aπ = r2
Square root: r = √Aπ
Divide by π: Aπ = r2
Square root: r = √Aπ
Make x the subject of y = 3x − 7.
- Add 7 to both sides: y + 7 = 3x
- Divide by 3: x = (y + 7)3
Answer: x = (y + 7)3
Undo the operations around the new subject in reverse order, doing the same to both sides. Squares are undone by square roots.
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