Expressions, formulae and equations
Constructing expressions
A letter stands for a number you do not know yet. Once you can write the words as algebra, the problem is half solved.
Letters stand for unknown numbers
If Mathew is x years old, you can describe everyone else in terms of x: • David is 4 years OLDER → x + 4 • Adam is 2 years YOUNGER → x − 2 • Kathryn is 3 TIMES his age → 3x • Ella is HALF his age → x/2
How to write it properly
Always write the number BEFORE the letter: write 3x, not x3. Write 3 × x as 3x — you drop the multiplication sign. Write x ÷ 2 as x/2 — you use a fraction rather than a division sign.
A trick if you get stuck
Replace the letter with an easy number, work out what you would do, then put the letter back. 'Sofia has n counters and puts in two more.' Pretend n is 10. You would work out 10 + 2. So with the letter it is n + 2. 'She takes out three.' You would do 10 − 3, so it is n − 3. This works well for simple expressions — though for harder ones you still need to think about the operation itself.
Worked examples
David is 4 years older than Mathew, who is x
- 'Older' means add.
- Add 4 to Mathew's age.
Answer: x + 4
Kathryn is 3 times Mathew's age
- 'Times' means multiply.
- Write the number before the letter.
Answer: 3x, not x3
Ella is half Mathew's age
- 'Half' means divide by 2.
- Write a division as a fraction.
Answer: x/2
Sofia has n counters and puts in two more
- Pretend n is 10: you would work out 10 + 2.
- Put the letter back.
Answer: n + 2
Adam is 2 years younger than Mathew
- 'Younger' means subtract.
- Take 2 off his age.
Answer: x − 2
Writing 3 × x correctly
- Drop the multiplication sign.
- Put the number first.
Answer: 3x
Where you see this in real life
- If a taxi charges £3 plus £2 for every mile, the cost of m miles is 3 + 2m — one expression covering every journey.
- A phone plan of £10 a month plus 5p a text costs 10 + 0.05t pounds, whatever t turns out to be.
Key words
- Expression
- a collection of numbers and letters, with no equals sign
- Unknown
- a number you do not know yet, shown by a letter
- Term
- a single number or letter part of an expression
- Algebra
- using letters to stand for numbers
- Variable
- a letter standing for a value that can change