n + 5
3n
n − 2
n ÷ 2
Learn the 3-Step Method
1Spot the operation words.
‘more than’ → add · ‘less than’ → subtract · ‘lots of / times’ → multiply · ‘shared / half’ → divide.
2Write it compactly.
3 × n is written 3n (number first, no × sign). n ÷ 2 can be written n/2.
3Mind the order in subtraction.
‘2 less than n’ is n − 2, NOT 2 − n. Subtraction order matters.
Worked Example
Tom is t years old. Write expressions for the family's ages.
Watch Out! Common Mistakes
Convention! The number always comes first: 3n.
Order! Start from n and take 2 away: n − 2.
Not yet! An expression just describes the calculation — no equals sign until there’s an equation to state.
⬇ Cheat Sheet
- more than → + · less than → − · lots of → × · shared → ÷
- 3 × n is written 3n (number first).
- '2 less than n' = n − 2 (order matters).
- Expression: no equals sign. Equation: has one.
📖 Continue Your Journey
Quick summary
- Translate operation words: more → +, less → −, lots of → ×, shared → ÷.
- Write 3 × n as 3n, number first with no × sign.
- '2 less than n' is n − 2 — subtraction order matters.
- Expressions describe; equations (with =) state facts.
Frequently asked questions
What does 3n mean?
3 × n — three lots of the unknown number. By convention the number is written first and the multiplication sign is dropped.
What's the difference between an expression and an equation?
An expression describes a calculation with no equals sign (n + 5); an equation says two things are equal (n + 5 = 12) and can be solved.
Why is '2 less than n' written n − 2?
Because you start with n and remove 2. Writing 2 − n calculates something different — the gap below 2, not below n.
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