# N2f – Applying the four operations to fractions

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.

Teacher resources for Part 1

• Slides in PPTX
• 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
Links to past exam and UKMT questions

# Part 2 – Multiplying fractions

A starting point...

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?

Teacher resources for Part 2

• 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
Links to past exam and UKMT questions

Interactive GeoGebra activity: multiplying fractions ≤ 1
• 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

A starting point...

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?

Teacher resources for Part 3