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Actually no, they are not required to offer breaks. Some states have passed laws requiring meal and rest breaks during certain periods of work, but Ohio has not done so. Because they have not passed their own law on the matter, Federal law applies.
Federal law does not require meal breaks or rest breaks either. All the Federal law does is state how those breaks, if offered, are to be considered in terms of pay. Short breaks of less than 30 minutes (like the typical 10 minute break here and there), if offered, are to be paid time and the employer can't dock your pay for those. A bona fide meal period, if offered, has to be at least 30 minutes long and you have to be relieved of all duties in order for it to be unpaid time.
However, again, those rules only apply to how the breaks are treated IF the employer offers them. Federal law doesn't mandate that they be offered and, unfortunately, neither does your state law.