TMUA-P2-PRF1-005 — Paper P2 · Direct proof · Level 2

Options

1. A
   Write them as $\frac{a}{b}$ and $\frac{c}{d}$ with integers $a, c$ and non-zero integers $b, d$; then the product is $\frac{ac}{bd}$ with integer numerator and non-zero integer denominator.
2. B
   Write them as $\frac{a}{b}$ and $\frac{c}{d}$ for any real $a, b, c, d$; then the product is a fraction so it is rational.
3. C
   Check $\frac12 \times \frac13 = \frac16$; one example suffices.
4. D
   Assume the product is irrational and get a contradiction.
5. E
   Write each rational as a terminating decimal and multiply.

Letters only — the answer key is hidden. Work it out, then check the solution below.

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