Changing the Subject of a Formula

≈ 30 min

A formula is an equation with several letters: $v = u + at$ relates speed, time and acceleration. Changing the subject means solving for one chosen letter — exactly the same inverse-operation moves, just with letters left in the answer.

Worked example. Make $t$ the subject of $v = u + at$ .

v = u + at

v - u = at \qquad \text{(subtract } u\text{)}

t = \frac{v - u}{a} \qquad \text{(divide by } a\text{)}

Every step is one you already know — subtract from both sides, divide both sides.

Make $t$ the subject of $v = u + at$ . Answer in the form t=… (use brackets and / for division).

The area of a rectangle is $A = lw$ . Make $w$ the subject. Answer in the form w=….

The perimeter of a rectangle is $P = 2l + 2w$ . Which is a correct expression for $l$ ?

$l = P - 2w$

$l = \dfrac{P - 2w}{2}$

$l = \dfrac{P}{2} + w$

$l = 2P - w$

The circumference of a circle is $C = 2\pi r$ . Make $r$ the subject. Answer in the form r=… (write $\pi$ as pi).