It depends what the question is. If the question is have you ever been convicted of a crime, then it is accurate to answer that you were convicted of reckless driving. If the question asks whether you've ever been arrested, you would need to say you were arrested for DUI but only convicted of reckless driving. A brief description of the event is fine for the explanation.
Read the question carefully. If it asks for conviction then write down the proper conviction. If it asks for what you were arrested then --you will have to put down the offense.
Make sure you carefully read the wording of the question. If it asks if you have ever been convicted, then you should state Reckless Driving. However if it asks if you have ever been arrested, then you should detail the arrest for DUI and explain that it was subsequently reduced. It is always better to be completely honest and provide an explaination rather than appearing as if you are hiding something. A very brief description should be sufficient.
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