# Changing the Subject of a Formula

Determine the missing quantities in your study schedule with Beyond Revision and tuition-style posts like this one on changing the subject of a formula.

The best way to learn and improve is to get right into it so let’s start with a simple exercise.

### Getting Started on Changing the Subject of a Formula

Exam Tip
The inverse of an operation will undo the operation.
• The inverse of multiply is divide.
• The inverse of divide is multiply.
• The inverse of add is subtract.
• The inverse of subtract is add.
• The following examples contain everything you need to know about changing the subject of a formula.

This is very similar to solving linear equations so you may want to revise the two topics together.

Example 1
Make 𝑝 the subject of 𝑥 = 4𝑝 + 𝑦.

Making 𝑝 the subject means we want a formula in the form 𝑝 = _. We do this by using inverse operations to manipulate the formula until we have 𝑝 on its own.

First, we want to get the term including 𝑝 on its own. We can do this by subtracting 𝑦 from both sides.

It doesn’t matter that we have 𝑝 on the right-hand side rather than the left-hand side. Both sides of the formula are equal, so 𝑝 is the subject of this formula. If you prefer, you can swap the sides and write the formula as 𝑝 = $\frac{x - y}{4}$ but there is no need to.

Example 2
Make 𝑘 the subject of $\frac{𝑘}{3}$ – 𝑝 = 𝑚

This example is very similar to example 3. The key difference is the order in which we perform our manipulation. In this case, 𝑘 is divided by 3 and then 𝑝 is subtracted. To change the subject, we need to undo each of these in reverse order.

Example 3
Make 𝑘 the subject of $\frac{𝑘 – 𝑝}{3}$ = 𝑚

This example is very similar to example 2. The key difference is the order in which we perform our manipulation. In this case, we subtract 𝑝 and then divide by 3. To change the subject we need to undo each of these in reverse order.

Exam Tip
• The inverse of squaring is square rooting
• The inverse of square rooting is squaring
• Example 4
Make 𝑥 the subject of 𝑏 = $\sqrt{x^2 - 3a}$

This time, we need to start by eliminating the square root.

When you’re finished changing the subject of a formula, why not check out more of our blogs here!? You can also subscribe to Beyond for access to thousands of secondary teaching resources. You can sign up for a free account here and take a look around at our free KS3/GCSE Maths resources before you subscribe too.