To address your question, let’s clarify the context. You are likely discussing the properties of rational numbers and using a proof structure involving the sum of two rational numbers.
If you're considering the expression \(\frac{a + c}{BD}\) where:
- \(a\) and \(c\) are rational numbers,
- \(B\) and \(D\) are non-zero rational numbers,
then we can analyze how to select \(a\).
If you want \(a\) to be a rational number, then you can choose any rational value for \(a\). The properties of rational numbers state that the sum of two rational numbers is rational.
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Choose \(a\): You can choose \(a\) to be any rational number. For example, you might choose \(a = 1\) or \(a = \frac{3}{4}\).
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Use the property of rational numbers: Now, if you want to demonstrate that the entire expression \(\frac{a + c}{BD}\) is rational, just ensure that \(c\) is also a rational number. If both \(a\) and \(c\) are rational, then their sum \(a + c\) is rational.
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Check \(BD\): Finally, ensure that \(BD\) (the product of \(B\) and \(D\)) is not zero, as division by zero is undefined.
So, if you're looking to apply the proof that the sum of two rational numbers is rational and subsequently analyze the expression \(\frac{a + c}{BD}\), you can utilize any rational number for \(a\).