© Boardworks Ltd 2005 1 of 73

Changing the subject of a formula

1. The subject of a formula

2. Changing the subject of a formula

© Boardworks Ltd 2005 2 of 73

The subject of a formula

Here is a formula you may know from physics:

V = IRV = IR

where V is voltage, I is current and R is resistance.

V is called the subject of the formula.

The subject of a formula always appears in front of the equals sign without any other numbers or operations.

Sometimes it is useful to rearrange a formula so that one of the other variables is the subject of the formula.

Suppose, for example, that we want to make I the subject of the formula V = IR.

© Boardworks Ltd 2005 3 of 73

The formula:

can be written as a function diagram:

I × R V

The inverse of this is:

V÷ RI

So:

Changing the subject of the formula

V is the subject of this formula

I is now the subject of this formula

I = VR

V = IR

© Boardworks Ltd 2005 4 of 73

The formula:

m = 2n + 1 m = 2n + 1

can be written as a function diagram:

n + 1× 2 m

The inverse of this is:

m÷ 2 – 1n

or

m is the subject of this formula

n is the subject of this formula

Changing the subject of the formula

n =m – 1

2

© Boardworks Ltd 2005 5 of 73

Changing the subject of the formula

To find out which pattern will contain 47 matches, substitute 47 into the rearranged formula.

n =m – 1

2

n =47 – 1

2

n =462

n = 23

So, the 23rd pattern will contain 47 matches.

© Boardworks Ltd 2005 6 of 73

Changing the subject of the formula

We can also change the subject by performing the same operations on both sides of the equals sign. For example, to make C the subject of

subtract 32: F – 32 =9C5

multiply by 5: 5(F – 32) = 9C

divide by 9:5(F – 32)

9= C

F = + 329C5

5(F – 32)9

C =

© Boardworks Ltd 2005 7 of 73

Change the subject of the formula 1

© Boardworks Ltd 2005 8 of 73

Find the equivalent formulae