Fractions and Decimals

Students learn how to solve problems with long multiplication and division using written methods.  They use this knowledge to add, subtract, multiply and divide with fractions and mixed numbers.  Finally, students learn the difference between terminating and recurring decimals and how to convert a recurring decimal to a simplified fraction.

This unit takes place in Term 1 of Year 9 and is followed by algebraic fractions.


Fractions and Decimals Lessons
Revision Lessons


Prerequisite Knowledge
  • express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
  • interpret fractions as operators
  • estimate answers; check calculations using approximation and estimation, including answers obtained using technology
  • order positive and negative decimals

Success Criteria
  • 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;
  • calculate exactly with fractions


Key Concepts
  • 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.
  • When calculating with decimal numbers encourage students to estimate the solution as means to check their working.
  • Students may need to recap multiplying and diving by powers of ten when calculating the product of decimal numbers.
  • Use equivalent fractions when performing long division. Simplifying the fractions help to break down the calculation.

Common Misconceptions
  • A fraction with a smaller denominator has a lesser value.
  • Fractions such as 3/5 can incorrectly assumed to have a decimal equivalence of 3.5.
  • Students incorrectly consider multiplications to always increase a number and divisions to decrease.
  • Students fail to spot incorrect calculations due to not estimating solutions.

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