Changing the subject of a formula means rearranging the formula so that a different variable is on its own on one side of the equals sign. In this topic, the subject appears in one term only, making the rearrangement more straightforward.

 

The goal is to use inverse operations to isolate the required variable.

 

 

Understanding the Structure

If the subject appears in one term, it will usually be:
• multiplied or divided by a number
• added to or subtracted from another term

 

Operations must be undone in the reverse order to which they appear.

 

 

Changing the Subject When the Term Is Added or Subtracted

Consider the formula:

$$
y = x + 5
$$

 

To make \( x \) the subject, subtract \( 5 \) from both sides:

$$
y - 5 = x
$$

 

So the new subject is:

$$
x = y - 5
$$

 

Another example:

$$
A = b - 7
$$

 

Add \( 7 \) to both sides:

$$
A + 7 = b
$$

 

 

Changing the Subject When the Term Is Multiplied

Consider the formula:

$$
y = 3x
$$

 

To make \( x \) the subject, divide both sides by \( 3 \):

$$
\frac{y}{3} = x
$$

 

So:

$$
x = \frac{y}{3}
$$

 

Another example:

$$
P = 5m
$$

 

Divide both sides by \( 5 \):

$$
m = \frac{P}{5}
$$

 

 

Changing the Subject When the Term Is Divided

Consider the formula:

$$
y = \frac{x}{4}
$$

 

Multiply both sides by \( 4 \):

$$
4y = x
$$

 

So:

$$
x = 4y
$$

 

Another example:

$$
A = \frac{b}{6}
$$

 

Multiply both sides by \( 6 \):

$$
b = 6A
$$

 

 

Changing the Subject with Two Operations

If the subject is involved in more than one operation, undo them one at a time.

 

For example:

$$
y = 2x + 3
$$

 

First subtract \( 3 \):

$$
y - 3 = 2x
$$

 

Then divide by \( 2 \):

$$
x = \frac{y - 3}{2}
$$

 

 

Key Points to Remember

Use inverse operations to isolate the variable.
Undo addition and subtraction before multiplication or division.
Carry out the same operation on both sides of the equation.

 

Changing the subject of a formula is an essential algebraic skill used in rearranging equations and solving problems across mathematics and science.