1. **State the problem:** Divide 35,830 by 750 and find the quotient and remainder. 2. **Formula and rules:** Division can be expressed as $$\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$$ where the remainder is less than the divisor. 3. **Perform the division:** Calculate the quotient by dividing 35,830 by 750: $$\frac{35830}{750} = 47.7733...$$ The integer quotient is 47. 4. **Calculate the remainder:** $$\text{Remainder} = 35830 - (750 \times 47)$$ $$= 35830 - 35250$$ $$= 580$$ 5. **Check remainder:** Since 580 is less than 750, this is valid. 6. **Final answer:** $$35,830 \div 750 = 47 \text{ remainder } 580$$