What is a formula?
An algebraic formula is an equation that shows the relationship between two or more quantities using letters. For example, the area of a rectangle is A = l × w, where A is the area, l is the length and w is the width. Every letter stands for a value that can change.
The letter that stands alone on one side of the equals sign is called the subject of the formula. In A = l × w, the subject is A.
Key idea / Key idea
To find a formula, describe the relationship in words first, then replace the words with letters and operations (+, −, ×, ÷).
Changing the subject
Often we need a different letter to be the subject. We do this by keeping the equation balanced: whatever we do to one side, we do to the other. Use inverse operations to move terms across the equals sign.
Worked example / Worked example
Make w the subject of P = 2(l + w).
Step 1: Divide both sides by 2 → P ÷ 2 = l + w, so P/2 = l + w.
Step 2: Subtract l from both sides → w = P/2 − l.
Check with l = 5, P = 16: w = 16/2 − 5 = 8 − 5 = 3.
Substituting values
Once a formula is written, substitute known numbers to find an unknown. Replace each letter with its value, then calculate carefully following the order of operations.
Worked example / Worked example
Given v = u + at, find v when u = 4, a = 3, t = 5.
v = 4 + (3 × 5) = 4 + 15 = 19.
Remember / Remember
- The subject appears once, on its own, on one side.
- Use inverse operations: + ↔ −, × ↔ ÷.
- Do the same operation to both sides to keep balance.
- Substitute, then follow order of operations.