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# 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.

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# 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?

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- 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?

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- 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
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- A4h – Multiplying and dividing algebraic fractions
- R3a – Expressing one quantity as a fraction of another
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