A person who is extremely clumsy, or who often is sporting bandages covering minor injuries, might be said to be incapable of "walking and chewing gum at the same time".
After the third time in one month that the new office assistant was electrocuted while trying to clear a paper jam in the office copier, the supervisor shook his head and asked the Personnel office to move the employee to another department with no machinery in it, as "this guy can't walk and chew gum at the same time".
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