Year 5 - Maths
Use the relationship between the numerator and denominator to simplify fractions
Comparing fractions using equivalence and decimals
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will use representations to describe and compare two fractions. They will explain the relationship within families of equivalent fractions and use their knowledge of common equivalents to compare fractions with decimals.
Lesson Summary
You will learn to use the relationship between the numerator and denominator to simplify fractions.
Key Notes
- If the multiplicative relationship between the numerator and denominator is the same, the fractions will be equivalent.
- If a fraction has been simplified, the numerator and denominator are as small as they can be to keep the relationship.
- Create an equivalent fraction in a simpler form with lower values of the numerator and denominator.
- Use common factors of the numerator and denominator to simplify fractions.
Vocabulary To Learn
- Common factor: When you are comparing the factors of two numbers, a common factor is one shared by both numbers.
- Simplest form: When a fraction is in its simplest form, the numerator and denominator only share a common factor of one.
- Simplify: To simplify a fraction is to identify the highest common factor shared by the numerator and denominator and to scale down both by that factor.
- Scale up/down: To scale up or down is to multiply or divide by a given number or factor.
Common Mistakes To Avoid
- Pupils may not see that the fraction and its simplified version are equivalent. Pupils may not have a deep understanding of how factors relate to fractions.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
If the multiplicative relationship between the numerator and denominator is the same, the fractions will be equivalent. If a fraction has been simplified, the numerator and denominator are as small as they can be to keep the relationship.
2. Use this key word in a maths sentence and explain it clearly. 'Common factor'
When you are comparing the factors of two numbers, a common factor is one shared by both numbers. 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 not see that the fraction and its simplified version are equivalent. Pupils may not have a deep understanding of how factors relate to fractions. Correction: Stress the equivalence of fractions when simplifying and make use of representations to show that fractions are equivalent using parts of a whole and position on a number line. Discuss the language of factors, common factors and prime numbers.
More Lessons In This Unit
- Explain and represent how to divide 1 into different numbers of equal parts Study Guide
- Explain the relationship between numerators and denominators across equivalent fractions Study Guide
- Explain the relationship between numerators and denominators in equivalent fractions Study Guide
- Explain the relationship within families of equivalent fractions Study Guide
- Identify and describe patterns in the number system Study Guide
- Recall common fraction-decimal equivalents Study Guide
- Solve problems using fraction-decimal equivalents Study Guide
- Use knowledge of common equivalents to compare fractions and decimals Study Guide
- Use representations to describe and compare fractions Study Guide
- Use representations to describe and compare two fractions Study Guide
- Use representations to describe and compare two fractions in a continuous context Study Guide
- Use the language of equivalent fractions correctly Study Guide
- Use the relationship between the numerator and denominator in equivalent fractions to solve problems Study Guide
- Use understanding of equivalent fractions to solve problems Study Guide
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