**This is the students’ version of the page. Log in above for the teachers’ version.**

# Part 1 – Adding and subtracting fractions

Between each question and the next, only one aspect is changed. Can you see how this affects the answer in each case? Click the “New questions” button for a new set of randomly generated questions. Click “show all answers” to show all answers at once, or click on each individual question to show answers one at a time.

**Teachers**: log in to access the following:

- Worksheet (with space for student work)
- Handout (slides with exercises only; 4 per page for reduced printing)

- See Teacher resources under Part 3 for a card sort covering all four operations with fractions

- Addition pyramid generator – suitable for use on an interactive whiteboard. Answers available.

**Teachers**: log in to access these.

# Part 2 – Multiplying fractions

Here is a sequence of calculations:

\(12 \times 8 = 96 \)

\(12 \times 4 = 48 \)

\(12 \times 2 = 24 \)

\(12 \times 1 = 12 \)

What are the next three calculations in this sequence?

**Teachers**: log in to access the following:

- Slides in PPTX (with click-to-reveal answers)
- Slides in PDF (one slide per page, suitable for importing into IWB software)

- Worksheet (with space for student work)
- Handout (slides with exercises only; 4 per page for reduced printing)

- See Teacher resources under Part 3 for a card sort covering all four operations with fractions

**Teachers**: log in to access these.

- Consider \(\frac{4}{4} \times \frac{1}{3}\). This is equivalent to \(1 \times \frac{1}{3}\) so we would expect the product to be \(\frac{1}{3}\), as shown in the applet’s initial configuration.
- Tick the box to show the vertical splits.
- Start reducing the numerator of the first fraction while holding everything else constant for a visualisation of \(\frac{3}{4} \times \frac{1}{3}, \frac{2}{4} \times \frac{1}{3},\) and \( \frac{1}{4} \times \frac{1}{3}\).
- Continue to play around with this applet!

# Part 3 – Dividing fractions

1) Here is a sequence of calculations:

\(40 \times 8 = 320 \)

\(40 \times 4 = 160 \)

\(40 \times 2 = 80 \)

\(40 \times 1 = 40 \)

What are the next three calculations in this sequence?

2) Here is a **different** sequence of calculations:

\(40 \div 8 = 5 \)

\(40 \div 4 = 10 \)

\(40 \div 2 = 20 \)

\(40 \div 1 = 40 \)

What are the next three calculations in this sequence?

**Teachers**: log in to access the following:

- Slides in PPTX (with click-to-reveal answers)
- Slides in PDF (one slide per page, suitable for importing into IWB software)

- Worksheet (with space for student work)
- Handout (slides with exercises only; 4 per page for reduced printing)

- Card sort covering all four operations, not just division.

**Teachers**: log in to access these.

**Teachers**: log in to view this content.

- N10a – Converting terminating decimals into fractions and vice versa
- N10b – Converting recurring decimals into fractions and vice versa
- N11a – Identifying and working with fractions in ratio problems
- N12a – Interpreting fractions and percentages as operators
- A4g – Adding and subtracting algebraic fractions
- A4h – Multiplying and dividing algebraic fractions
- R3a – Expressing one quantity as a fraction of another
- P8a – Tree diagrams