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Math Help - Proof: If p and q are rational numbers then p + q...

  1. #1
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    Proof: If p and q are rational numbers then p + q...

    Hey all,
    I want to prove that:
    If p and q are rational numbers then p + q is also a rational number.

    I have tried through direct proof:
    p = \frac{n}{m} and  q = \frac{r}{s} where m, n \neq 0 Then,

    \frac{n}{m}+\frac{r}{s} \rightarrow \frac{sn}{ms}+\frac{rm}{ms} \rightarrow \frac{sn+rm}{sm} which is rational.

    Is this proof correct ?
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  2. #2
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    This is all on the condition that m,n,r,s are integers. You're proof is correct if the following products sn, rm and sm are also integers.
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