Rearranging Formulas

If balancing equations is about fairness, rearranging formulas is about flexibility. It’s the ability to take an existing relationship and look at it from a new angle. Rearranging lets you solve for a different variable – changing who’s “in charge” of the formula – while keeping the logic identical. It’s the mathematical version of seeing a problem from someone else’s perspective.

Take a simple formula from physics: v = u + at. It describes how velocity changes with acceleration and time. But what if you don’t need velocity – you need time? With a few precise steps, you can rearrange it to t = (v − u)/a. You haven’t changed the meaning, just the focus. Rearranging is about manipulating the structure so that one variable becomes the subject – the one that stands alone.

This skill is vital across maths, science, and engineering. Whether you’re calculating distance, pressure, or current, you’ll often need to isolate a particular value. The process always follows the same logic: perform inverse operations to move terms across the equals sign until your chosen variable is free. What starts as a tangle of letters becomes a clean, useful formula.

The beauty of rearranging is that it builds confidence. Once you realise that formulas are flexible, they stop feeling intimidating. You learn that algebra isn’t about memorising patterns but understanding relationships. Rearranging gives you control – it’s how you make maths work for you rather than the other way around.

Hints and Tips:

• Work step by step, applying the same operation to both sides.
• Use inverse operations to move terms across the equals sign.
• Keep fractions and negatives tidy by simplifying as you go.
• Always double-check your rearranged formula by substituting values.