Mrs Soh wants to buy 1 watermelon ($5 each) and some mangoes ($2 each). She doesn't know yet how many mangoes she'll get — it depends on what looks fresh today.
In arithmetic, we could only say: “if she gets 3 mangoes, she pays $11”, “if she gets 4, she pays $13”, “if she gets 7, she pays $19”… one specific case at a time.
Algebra gives us a way to say all of these at once with a single letter:
What does the letter n mean in “5 + 2 × n”?
n is called a variable — a letter that can stand for any number we choose.
The expression 5 + 2 × n is an algebraic expression; once we know what n is,
we can evaluate it. If n = 3, the price = $(5 + 2×3) = $11. If n = 4, the price = $13.
One expression captures every possible case.
In this chapter you'll learn to write, evaluate, simplify, expand, and factorise algebraic expressions — the basic vocabulary of all higher math.
📚 本章学习目标 · Learning objectives
Write algebraic expressions and formulae from real-world descriptions
Evaluate algebraic expressions and formulae by substitution
Simplify linear expressions by collecting like terms
Expand linear expressions using the distributive law