# 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