Fractions and Mixed Numbers

Students learn how to calculate equivalent fractions and convert between mixed numbers as a top-heavy fraction.  They use this knowledge to add, subtract, multiply and divide with fractions and mixed numbers.

This topic takes place in Term 4 of Year 9 and follows the properties of numbers.


Fractions and Mixed Numbers Lessons
4 Part Lesson
Addition and Subtraction with Fractions and Mixed Numbers
4 Part Lesson
Multiplying Fractions
4 Part Lesson
Mixed Numbers and Top Heavy Fractions
4 Part Lesson
Calculating a Fraction of an Amount
4 Part Lesson
Equivalent Fractions
4 Part Lesson
Dividing Fractions and Mixed Numbers
4 Part Lesson
Adding Fractions with Different Denominators
Additional Resources
Extended Learning
Dividing with Fractions
Extended Learning
Multiplying Fractions
Extended Learning
Adding and Subtracting Mixed Numbers
Problem Solving
Fractions
Revision
Adding and Subtracting Fractions with the same Denominator
Revision
Fractions of an Amount
Revision
Equivalent Fractions and Mixed Numbers
Revision
Multiplication and Division of Fractions
Revision
Adding and Subtracting Fractions

Prerequisite Knowledge

  • Recognise, find and name a half as one of two equal parts of an object, shape or quantity
  • Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity. 

Success Criteria

  • order positive fractions
  • apply the four operations, including formal written methods, simple fractions (proper and improper)
  • express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
  • apply the four operations, including formal written methods, to mixed numbers both positive and negative;
  • interpret fractions as operators
  • express a multiplicative relationship between two quantities as a fraction
  • calculate exactly with fractions

Key Concepts

  • Fractions represent a proportion of an amount hence the equivalence with decimals and percentages.
  • A fraction is equivalent to a division
  • All rational numbers are written using exact proper or improper fractions.
  • When adding or subtracting fractions the denominators need to be equal.
  • Dividing fractions is equivalent to multiplying by a reciprocal.

Common Misconceptions

  • A shape that is split in two is not necessarily split in half. A half must be two equal proportions of a shape.
  • A fraction with a larger denominator has the greater value.
  • A fraction with a smaller denominator has a lesser value.
  • Fractions such as 3/5 incorrectly have a decimal equivalence of 3.5.

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