Writing Expressions
Practise writing expressions with this free Foundation GCSE Maths worksheet from Virtus Academy. You'll work through writing algebraic expressions, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Use a letter for the unknown and translate each phrase into algebra.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Writing expressions means turning words into algebra. A letter stands for an unknown quantity, and the operations in the sentence become the operations in the expression.
The usual convention is to drop the multiplication sign, so three lots of \(n\) is written \(3n\) rather than \(3 \times n\). Division is normally written as a fraction, so \(n\) divided by four becomes \(\frac{n}{4}\).
Order matters when subtraction is involved. Five less than \(n\) is \(n - 5\), not \(5 - n\), and those two expressions have completely different values. Reading the sentence slowly and identifying what is being taken from what avoids the mistake.
Revision notes
Turning words into symbols
Choose a letter for the unknown, then translate each operation in turn.
A number multiplied by four and then increased by three becomes \(4n + 3\). The multiplication happens first because the sentence says so, and the expression preserves that order.
Subtraction and division order
Five less than \(n\) means you start with \(n\) and remove five, giving \(n - 5\).
Similarly, \(n\) divided by three is \(\frac{n}{3}\), whereas three divided by \(n\) is \(\frac{3}{n}\). Read carefully which quantity is being acted on.
Expressions with more than one unknown
Use a different letter for each unknown quantity, and define what each represents.
If apples cost \(a\) pence and pears cost \(p\) pence, then three apples and two pears cost \(3a + 2p\). Stating what the letters mean is part of a full answer.
Key points
- A letter represents an unknown quantity.
- Drop the multiplication sign, writing \(3n\) not \(3 \times n\).
- Write division as a fraction.
- Five less than \(n\) is \(n - 5\).
- Use different letters for different unknowns.
- State what each letter represents.
Worked examples
Example 1
Write an expression for a number \(n\) multiplied by five then decreased by two.
Working
Example 2
A pen costs \(p\) pence. Write an expression for the cost of four pens and a \(50\)p ruler.
Working
Example 3
Write an expression for seven less than three times a number \(x\).
Working
Common mistakes
Writing \(5 - n\) for five less than \(n\).
The five is removed from n, so the expression is n − 5. The two are not the same.
Keeping the multiplication sign.
Write 3n rather than 3 × n. The sign is dropped by convention in algebra.
Using the same letter for different quantities.
If apples and pears cost different amounts, they need different letters.
Not defining the letters.
A full answer says what each letter stands for, such as let n be the number.
Exam tips
- Read the sentence in order and translate one operation at a time.
- Say what each letter represents before writing the expression.
- Take particular care with the order in subtraction and division.
- Check by substituting a simple number to see if the expression behaves correctly.
Key terms
- Expression
- A collection of terms with no equals sign.
- Variable
- A letter representing an unknown or changing quantity.
- Term
- A single part of an expression, such as \(3n\).
- Coefficient
- The number in front of a variable.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.