Learning Objectives
You should be able to:
- Explain what an algebraic expression is.
- Write algebraic expressions from words.
- Identify parts of an expression.
- Tell the difference between an expression and an equation.
Introduction
This lesson develops Algebraic Expressions from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
🎬 Build an algebraic expression
Mathematical words are compressed into symbols.
🤔 Think About This...
Imagine you walk into a supermarket and buy:
- 3 bottles of Mazoe
- 2 loaves of bread
You do not know the price of either item.
Instead of writing:
Mathematicians can simply write:
Here, m represents the price of one bottle of Mazoe, and b represents the price of one loaf of bread.
📖 What is an Algebraic Expression?
An algebraic expression is a mathematical phrase made up of numbers, variables and operation signs.
Examples of operation signs include:
Examples of algebraic expressions are:
⭐ Expression or Equation?
This is very important.
📌 Expression
An expression describes something.
No equals sign.
📌 Equation
An equation says two things are equal.
It has an equals sign.
🌍 Real-Life Examples
🍞 Bread
If one loaf costs b, then 5 loaves cost:
🚌 Kombi Trips
If one trip costs k, then 4 trips cost:
📱 Airtime
If one airtime voucher costs a, then 2 vouchers plus $5 cost:
⚽ Football
If one ticket costs t and one drink costs d, then 3 tickets and 2 drinks cost:
📝 Worked Examples
Example 1
Write an expression for:
Thinking...
The unknown number is x. Five more means add 5.
Example 2
Write an expression for:
Thinking...
The unknown number is n. Seven times means multiply by 7.
Example 3
Write an expression for:
Thinking...
The unknown number is x. Three less means subtract 3.
Example 4
Write an expression for:
Thinking...
Twice a number means 2x. Then add 8.
Practice Questions
Write an algebraic expression for each statement.
- A number plus 9
- Six times a number
- Ten less than a number
- Three times a number plus four
- Half a number
✅ Show Answers
- x + 9
- 6x
- x − 10
- 3x + 4
- x ÷ 2
🧠 Did You Know?
⭐ What You Can Do Now
- ✅ I know what an algebraic expression is.
- ✅ I know expressions do not have an equals sign.
- ✅ I can write expressions from words.
- ✅ I can recognise expressions in everyday life.
🎉 Well Done!
You now know how to turn words into algebraic expressions. This skill will help you in almost every Algebra topic that comes next.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
📈 Your Progress
Lesson 3 of 22
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.