Skip to main content
Academy11+

11+ Maths · Topic explained

Algebra: what letters stand for

Why does maths suddenly have letters in it? What is x, anyway?

The big idea

A letter stands for a number we don't know yet, or one that can change.

Picture it

Think of closed bags of sweets: each holds the same number, so call it n. 3 bags and 2 loose sweets is 3n + 2.

Key words

unknown
A number we don't know yet, written as a letter.
expression
Numbers and letters joined by + − × ÷, with no equals sign: 3n + 2.
term
One part of an expression: 3n and 2 are the terms of 3n + 2.
3n
3 × n. We leave out the × sign.

Worked examples

  1. 1Warm-up

    Write 'a number add 5' using n

    • The number is n
    • Add 5: n + 5
  2. 211+ standard

    Pencils cost p pence each. What do 4 pencils cost?

    • 4 lots of p
    • 4 × p = 4p pence
  3. 311+ standard

    Simplify a + a + a + 2b + b

    • a + a + a = 3a
    • 2b + b = 3b
    • 3a + 3b
  4. 411+ standard

    Ali is y years old. His sister is 3 years older. How old will she be in 2 years?

    • Sister now: y + 3
    • In 2 years: y + 3 + 2
    • = y + 5

The common mistake

The mistake

3n means 3 and n stuck together, so if n = 5, 3n = 35.

Instead

3n means 3 × n, so if n = 5, 3n = 15.

Why: In algebra, a number next to a letter means multiply.

Where it comes up in the 11+

Writing expressions from words, simplifying, and the first step of 'I think of a number' puzzles.

The video

Video coming soon

We're making a short video that explains algebra: what letters stand for step by step. Until then, everything it covers is on this page.

Free printable

Algebra: what letters stand for worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

Free account needed: it takes a minute.

Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Which means 'double a number, then take away 3'?

    • 2n − 3
    • 2(n − 3)
    • n − 6
    • 3 − 2n
    Show the answer

    2n − 3

    Double n is 2n; then take away 3.

  2. 2. Simplify 4x + 2 + x − 1.

    • 5x + 1
    • 4x + 1
    • 5x + 3
    • 6x
    Show the answer

    5x + 1

    4x + x = 5x and 2 − 1 = 1.

  3. 3. Bags hold b sweets each. Sara has 3 bags and 4 loose sweets. How many sweets does she have?

    • 7b
    • 3b + 4
    • 3 + 4b
    • b + 7
    Show the answer

    3b + 4

    3 bags of b is 3b, plus 4 more.