Multiplying and Dividing with Fractions

Prerequisite Knowledge

• Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
• Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Key Concepts

• When multiplying and dividing with fractions students should cross-simplify the question to cancel out common terms.
• Being able to visualise division with fractions and mixed numbers helps students understand the written methods.
• To divide with fractions students need to understand reciprocals and how to multiply and divide with 0.1 and 0.01.
• Answers should be left in their simplest terms.

Working mathematically

Develop fluency

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals and fractions.

Reason mathematically

• Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

Solve problems

• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

Subject Content

Number

• Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
• Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
• Use a calculator and other technologies to calculate results accurately and then interpret them appropriately