Year 7 - Maths
Simplifying fractions
Comparing and ordering fractions and decimals (positive and negative)
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
This unit develops understanding and manipulation of fractions, including conversion between fractions to terminating and recurring decimals. Pupils then learn strategies to order fractions of increasing complexity.
Lesson Summary
You will learn to simplify fractions by dividing both the numerator and denominator by common factors and know why this works.
Key Notes
- When a fraction is multiplied by 1 it remains the same but may look different.
- Simplifying fractions can be shown to be the inverse of multiplying to find equivalent fractions.
- A fraction can be written more simply but remain equivalent by dividing the numerator and denominator by a common factor
- A fraction can be written in simplest form by dividing the numerator.
Vocabulary To Learn
- Factor: A factor is a term which exactly divides another term.
- Highest common factor: The highest common factor is the common factor which can be divided by all other possible common factors.
- Product of primes: Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.
Common Mistakes To Avoid
- Pupils may think they just 'get rid' of integers which appear in both numerator and denominator.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When a fraction is multiplied by 1 it remains the same but may look different. Simplifying fractions can be shown to be the inverse of multiplying to find equivalent fractions.
2. Use this key word in a maths sentence and explain it clearly. 'Factor'
A factor is a term which exactly divides another term. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think they just 'get rid' of integers which appear in both numerator and denominator. Correction: Reinforce that you are multiplying by 1, which doesn't change the value and therefore can be omitted from further calculations.
More Lessons In This Unit
- Between numbers Study Guide
- Checking and securing converting improper fractions to mixed numbers Study Guide
- Checking and securing converting mixed numbers to improper fractions Study Guide
- Checking and securing understanding of fractions Study Guide
- Converting fractions to recurring decimals Study Guide
- Converting fractions to terminating decimals Study Guide
- Converting fractions with technology Study Guide
- Converting terminating decimals to fractions Study Guide
- Limitations of technology in calculations Study Guide
- Ordering decimals Study Guide
- Ordering fractions by converting Study Guide
- Ordering fractions by way of a common denominator Study Guide
- Ordering fractions in different ways Study Guide
- Ordering negative integers Study Guide
- Ordering positive and negative fractions and decimals Study Guide
- Problem solving with fractions and decimals Study Guide
- The identity property of multiplication and division Study Guide
Browse all guides in the Year 7 Maths guide library.