Fractions and Mixed Numbers

August 23, 2016

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

Equivalent Fractions

Mixed Numbers and Top Heavy Fractions

Calculating a Fraction of an Amount

Adding and subtracting fractions with different denominators

Adding Fractions with Different Denominators

Addition and Subtraction with Fractions and Mixed Numbers

Multiplying Fractions and Mixed Numbers

Dividing Fractions and Mixed Numbers

Revision Lessons

Equivalent Fractions and Mixed Numbers

Fractions of an Amount

Adding and Subtracting Fractions with the same Denominator

Multiplication and Division of Fractions

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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