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
Problem Solving and 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.

Go ad-free and get access to over 500 lessons

Mr Mathematics Blog

Two-Way Tables and Frequency Trees

Problem solving lesson on two-way tables and frequency trees.

Plotting Curved Graphs

Three typical exam questions to revise on plotting quadratic, cubic and reciprocal graphs.

Interpreting Cumulative Frequency Graphs

Linking cumulative frequency graphs to ratio, percentages and financial mathematics.