How sound are common sayings such as "The working hand is better in the sight of Allah than the prostrating hand" or "The supporting hand is better than the prostrating hand," and are they considered Islamically correct based on the premise that work is better than passive worship that hinders people's interests?

Islam is a balanced religion that has given everything its due measure. Statements that suggest earning a living is better than worship, or that helping people is better than prayer, are incorrect, and are only true in one case: if a servant neglects obligatory duties for the sake of voluntary acts. Whoever neglects obligatory duties, using earning a living as an excuse, is in grave danger. It is obligatory to perform all the rituals of religion, as Allah Almighty said: "Men whom neither commerce nor selling distracts from the remembrance of Allah." Work is not an act of worship except with a righteous intention. The ranks of deeds are determined by the Sharia (definition), and prayer is the best of deeds.