TMUA-P2-PRF1-010 — Paper P2 · Direct proof · Level 2

Options

1. A
   Write the rationals as $a/b$ and $c/d$ with integers $a,c$ and non-zero integers $b,d$. Then their sum is $(ad+bc)/bd$, a ratio of integers with non-zero denominator.
2. B
   Take $1/2 + 1/4 = 3/4$, which is rational, so all such sums are rational.
3. C
   Write the rationals as $a/b$ and $c/d$. Their sum is $(a+c)/(b+d)$, which is a ratio of integers.
4. D
   Every rational has a terminating decimal, and adding two terminating decimals gives a terminating decimal.

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

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