MathematicsChapter 4: Factorization and Algebraic Manipulation
Fractions
For algebraic expressions, factorise first.
Learning objectives
- Define and explain fractions.
- Apply fractions to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
For algebraic expressions, factorise first. HCF is the product of common factors with the lowest powers. LCM is the product of all factors with the highest powers. Then algebraic fractions cancel common factors (never cancel terms across a plus).
Where / symbols
- Fractions
- For algebraic expressions, factorise first. HCF is the product of common factors with the lowest powers. LCM is the product of all factors with the highest powers. Then algebraic fractions cancel common factors (never cancel terms across a plus).
Overview
Learn the idea, then use it:
Core Understanding
For algebraic expressions, factorise first. HCF is the product of common factors with the lowest powers. LCM is the product of all factors with the highest powers. Then algebraic fractions cancel common factors (never cancel terms across a plus).
Examples factorise first · lowest vs highest powers · cancel factors only
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — FRACTIONS
For algebraic expressions, factorise first. HCF is the product of common factors with the lowest powers. LCM is the product of all factors with the highest powers. Then algebraic fractions cancel common factors (never cancel terms across a plus).
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge fractions with a neighbouring idea that uses a different definition, rule, or method.
Key points
- factorise first
- lowest vs highest powers
- cancel factors only
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Fractions
Sticky Notes · Quick Revision
Core Idea
- For algebraic expressions, factorise first.
Key Points
- factorise first
- lowest vs highest powers
- cancel factors only
Simple Check
- Explain fractions in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge fractions with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- For algebraic expressions, factorise first.
- factorise first
- lowest vs highest powers
- cancel factors only
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.