### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Subject of Formula

Consider the equation . On the left-hand side, we only have y, so we say that y is the subject of the formula. Similarly, in the formula: , S is the subject of the formula.

It is often helpful to express a given equation with a specific variable as the subject. Let’s look at an example:

In the equation , y is the subject of the formula. We can rearrange the equation to make z the subject of the formula:

1. Start with the equation .

2. Subtract 2x from both sides: .

Now z is the subject of the formula.

We can also make x the subject of the formula:

1. Start with the equation .

2. Subtract z from both sides: .

3. Divide both sides by 2: or .

The expressions below are all equivalent but look different:

• • • or Let’s look at more examples that involve changing the subject of a formula.

## Examples

Example 1:

Given the equation , make x the subject of the formula.

Start with the equation .

Subtract from both sides: .

Example 2:

Given the equation , make y the subject of the formula.

1. Start with the equation .

2. Subtract x from both sides: .

3. Divide both sides by 2: .

4. Take the square root of both sides: .

Example 3:

Given the equation , make w the subject of the formula.

1. Start with the equation .

2. Add w to both sides: .

3. Subtract 2x and ay from both sides: .

Example 4:

Make y the subject of formula if  Square both sides to remove the square root: Now subtract x on both sides: Example 5:

Make w the subject of formula from the following:

i) ii) iii) i) Multiply by w on both sides: Re-write this as Now, divide both sides by : ii)  Take w as a common factor:  iii)  Factor out w: Divide by : Example 6:

The formula for the area of a trapezium is: Find an expression for a in terms of A, h, and b.    Example 7:

Make y the subject of formula if  Add and to both sides, and add w: Take the cube root of both sides: 