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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.

**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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