Module 3: Algebra basics · Topic 12 of 26
Algebraic expressions
Using letters for numbers and substituting values
VIDEO LESSON Watch Mr Boston explain algebraic expressions
Mr Boston
In algebra a letter stands for a number we do not know yet, or a number that can change.
The language of algebra
- 3n means 3 × n. n/2 means n ÷ 2. n² means n × n.
- A term is a single part, like 5x or −2. An expression is a group of terms, like 5x − 2.
- An equation has an equals sign and can be solved: 5x − 2 = 13.
- Substitute means swap the letter for a number, then use BIDMAS.
Worked examples
Example 1. Write an expression for “4 more than a number n”.
n + 4
Example 2. If a = 5, work out 3a + 2.
3 × 5 + 2 = 15 + 2 = 17.
Example 3. If x = −2 and y = 3, work out x² + 4y.
x² = (−2)² = 4 and 4y = 12, so 4 + 12 = 16.
Top tips and common mistakes
- 3n is 3 × n, so if n = 4, 3n is 12, not 34!
- Put negative numbers in brackets when substituting: (−2)² = 4.
- Tickets cost £t each, so 5 tickets cost £5t.
Tayo
Algebra felt like a secret code at first. Then I realised the letters are just numbers in disguise!
Practise
Answer as many as you like. Every question is new, and you get a “correct” tick for each one you get right first time. Use “Show answer” to see a worked solution.
Quiz: earn your stamp
Printable worksheet
Algebraic expressions worksheet. The questions come first and the answers for grown-ups are on the last page, so you can print just the question pages.
Printing is optional. A4 size.