# Maths KS2: Multiplying and dividing fractions

In a mysterious crystal cave, Olivia and Hassan get to work dividing and multiplying fractions in order to find their way out.

Archimedes has ²⁄₅ of an emerald and asks how much he would have left if he gave ¹⁄₂ to Hypatia.

After working out the division of this fraction, Olivia and Hassan get to work to divide and multiply fractions.

With a little help from Archimedes, Olivia and Hassan then learn how to multiply and divide more complex fractions.

This short animated film is from the BBC Teach series, Hypatia's Mathematical Maze.

### Teacher Notes

Before watching the film

Prior to this lesson you may wish to introduce pupils to other relevant topics, for example:

• Multiplication and division
• Comparing and ordering fractions
• Simplification of fractions

During watching the film

Depending on the focus of your lesson, you may wish to pause the film at certain points to check for understanding, asking questions such as:

• What is the difference between an integer and a fraction?
• How else can you represent the fractions?
• How would we simplify the fractions that Olivia and Hassan have?
• What different stages will you use to answer Hypatia’s final question?

Final question:
Something divided by four is seven twenty-fourths. Five twentieths divided by something is five eightieths. What are the missing fractions and integers?
? ÷ 4 = ⁷⁄₂₄
5⁄₂₀ ÷ ? = 5⁄₈₀

7⁄₆ ÷ 4 = ⁷⁄₂₄
5⁄₂₀ ÷ 4 = 5⁄₈₀

Following on from the film:

• Use bar models to represent dividing the fractions into further pieces.
• Use examples where the pupils have to explain their thinking in terms of factors, multiples, commutativity and equivalent fractions e.g. Which is larger? ⅘ ÷ 3 or 4⁄₃ ÷ 5? What is larger, ⅔ ÷ 5 or 4⁄₆ ÷ 5?
• Play true or false by exploring the relationship between dividing fractions by integers and multiplying fractions by other fractions, e.g. Which of these statements are true?
• ¹⁄₂ ÷ 2 = ¹⁄₂ x ¹⁄₂
• ¹⁄₂ ÷ 4 = ¹⁄₂ x ³⁄₄
• ¹⁄₂ ÷ 3 = ¹⁄₂ x ¹⁄₃
• ¹⁄₂ ÷ 5 = ¹⁄₂ x ¹⁄₅

### Curriculum Notes

This short film is suitable for teaching maths at KS2 in England, Wales and Northern Ireland and 2nd Level in Scotland.