Flip It! Rearranging Formulae

Here is a simple equation: 3 × ? = 12. You probably found the missing number straight away — you divided 12 by 3 to get 4. That move, 'do the opposite to undo', is the exact same idea behind rearranging formulae. Now think about this: the formula for the area of a rectangle is A = l × w (Area equals length times width). If someone tells you the area and the width, how would you find the length? That puzzle is exactly what this lesson is about.

A formula is a mathematical rule that connects two or more variables. A variable is a letter that stands for an unknown or changing number. The subject of a formula is the variable on its own on one side — for example, in A = l × w, the subject is A. Rearranging a formula means rewriting it so a different variable becomes the subject. You do this using inverse operations — the opposite of each operation already in the formula. The golden rule: whatever you do to one side of the formula, you must do to the other side. Here are the key inverse pairs to remember: • Addition ↔ Subtraction • Multiplication ↔ Division • Squaring ↔ Square root Work through each step one at a time, and your rearrangement will always be correct. WORKED EXAMPLE — Rearranging A = l × w to make l the subject: Step 1 — Write the formula: A = l × w Step 2 — You want l on its own. It is multiplied by w, so divide both sides by w: A ÷ w = (l × w) ÷ w Step 3 — On the right, w ÷ w = 1, so it cancels: A ÷ w = l Step 4 — Write neatly with the subject first: l = A ÷ w or l = A/w Check with numbers: if A = 30 and w = 5, then l = 30/5 = 6. Substitute back: A = 6 × 5 = 30 ✓ A slightly harder formula: v = u + at (final speed = starting speed + acceleration × time). Rearrange to make a (acceleration) the subject: Step 1: v = u + at Step 2 — Subtract u from both sides: v − u = at Step 3 — Divide both sides by t: (v − u)/t = a Step 4 — Write neatly: a = (v − u)/t Notice that (v − u) stays together as a group — use brackets to show this.