Fractions and Mixed Numbers

Students learn how to calculate equivalent fractions and convert between mixed numbers as a top-heavy fractions.  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 properties of number.


Fractions and Mixed Numbers Lessons
Revision Lessons


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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