# How to make X the subject of a formula

Whatever you do to
one side, you do to the other

Let’s say…….An eye for an eye.

Example 1

Make P the subject of the formula m=3n+2P

Subtract 3n from BOTH SIDES

m-3n=cancel(3n)+2P-cancel(3n)

m-3n=2P

Divide both sides by 2

(m-3n)/2=(cancel2P)/cancel2

(m-3n)/2=P

P=(m-3n)/2

Now P is the subject to the formula.

Example 2

In the following formula:

A=1/2(a+b)h

Rearrange this formula to find the height h.

Multiply both sides by 2

2A=cancel2times1/cancel2(a+b)h

2A=(a+b)h

Divide both sides by (a + b)

(2A)/(a+b)=(cancel((a+b))h)/cancel(a+b)

(2A)/((a+b))=h

h=(2A)/((a+b))

Now the height h is the subject of the formula.

Example 3

The volume V of a cone is given by the formula:

V=1/3pir^2h

Rearrange this formula to find the radius r

Multiply both sides by 3

3V=cancel3times1/cancel3pir^2h

3V=pir^2h

Divide both sides by pih

(3V)/(pih)=(cancelpir^2cancelh)/(cancel(pih)

(3V)/(pih)=r^2

Take the square root of both sides

sqrt(((3V)/(pih)))=cancelsqrt\(r^cancel2)

sqrt(((3V)/(pih)))=r

r=sqrt(((3V)/(pih)))

Now the radius r is the subject of the formula