Fractions and Mixed Numbers

Equivalent Fractions

Mixed Numbers and Top Heavy Fractions

Calculating a Fraction of an Amount

Adding and subtracting fractions with different denominators

Addition and Subtraction with Fractions and Mixed Numbers

Multiplying Fractions and Mixed Numbers

Dividing Fractions and Mixed Numbers

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.