12 min read
Introduction
Why algebra exists — letters standing for numbers you do not know yet — and a real problem that needs it.
A Bill You Cannot Finish Yet
A phone plan costs £ a month plus £ for every gigabyte over the free allowance. You do not know how many gigabytes you will use yet — call that number .
Without algebra you are stuck writing a new total for every possible . With algebra you write one short rule:
Monthly bill =
That single expression works for every value of . Algebra is arithmetic with a placeholder for a number you do not know yet — or for a number that can change.
Example 1 — Try a value
If gigabytes over:
- Substitute:
- Multiply first:
- Total: £
The same expression gives £ when , and £ when .
What You Will Practise
Next you build the tools this bill needs: directed numbers, order of operations, expressions, simplifying, substitution, expanding brackets, factorising, indices, and solving equations and inequalities.
Each lesson is short. Read the idea, follow the worked examples, then try the exercises before moving on.
Practice
More lessons in Basic Concepts of Algebra · Next: Directed Numbers