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
The inverse of an operation will undo the operation.
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.
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.
|𝑥 = 4𝑝 + 𝑦|
|– 𝑦||– 𝑦|
|𝑥 – 𝑦 = 4𝑝|
|÷ 4||÷ 4|
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 = but there is no need to.
Make 𝑘 the subject of – 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.
|– 𝑝 = 𝑚|
|+ 𝑝||+ 𝑝|
|= 𝑚 + 𝑝|
|× 3||× 3|
|𝑘 = 3(𝑚 + 𝑝)|
Make 𝑘 the subject of = 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.
|× 3||× 3|
|𝑘 – 𝑝 = 3𝑚|
|+ 𝑝||+ 𝑝|
|𝑘 = 3𝑚 + 𝑝|
Make 𝑥 the subject of 𝑏 =
This time, we need to start by eliminating the square root.
|𝑏2 = 𝑥2 – 3𝑎|
|+ 3𝑎||+ 3𝑎|
|𝑏2 + 3𝑎 = 𝑥2|
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