# 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 π the subject of π₯ = 4π + π¦.

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

First, we want to get the term including π on its own. We can do this by subtracting π¦ from both sides.

It doesnβt matter that we have π on the right-hand side rather than the left-hand side. Both sides of the formula are equal, so π is the subject of this formula. If you prefer, you can swap the sides and write the formula as π = $\frac{x - y}{4}$ but there is no need to.

Example 2
Make π the subject of $\frac{\pi }{3}$ – π = π

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

Example 3
Make π the subject of $\frac{\pi  – \pi }{3}$ = π

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 π 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 π₯ the subject of π = $\sqrt{x^2 - 3a}$

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

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