Rearranging Formulae

What is Rearranging Formulae?

Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Rearranging Formulae. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.

Check that you can explain Rearranging Formulae in your own words and give one example from everyday life. If you can do that, you have understood the core idea.

Understanding Rearranging Formulae gives you a reliable method you will reuse in later maths units, in science lessons and in data work.

Rearranging Formulae in detail

Rearranging, or changing the subject of a formula, uses the same balancing steps as solving an equation but with letters instead of numbers. To make x the subject of y = 3x + 2, subtract 2 to get y − 2 = 3x, then divide to get x = (y − 2)/3.

When the subject appears in more than one place, collect those terms on one side and factorise. With squares and roots, take care to apply inverse operations in the correct order. Rearranging is used in science, finance and engineering, for example to find time from distance and speed or the radius from an area.

How the interactive helps you understand Rearranging Formulae

Click a step, or use the Previous and Next buttons, to move through the sequence one stage at a time. Auto-play moves on for you.

Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Rearranging Formulae.

Real-life uses and examples

• Explain Rearranging Formulae to a friend with a simple picture, such as a row of tiles or a bag of sweets.
• Spot Rearranging Formulae in exam questions, where it often sits inside a short word problem.
• Check a homework answer about Rearranging Formulae by estimating first, then working it out step by step.

Common mistakes to avoid

• Memorising the steps for Rearranging Formulae without checking why they work.
• Forgetting units, signs or brackets when you apply Rearranging Formulae.
• Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.