1. **State the problem:** Add the mixed numbers and fractions: $5 \frac{3}{10} + \frac{1}{12}$. 2. **Convert mixed number to improper fraction:** $$5 \frac{3}{10} = \frac{5 \times 10 + 3}{10} = \frac{50 + 3}{10} = \frac{53}{10}$$ 3. **Find common denominator:** The denominators are 10 and 12. The least common denominator (LCD) is 60. 4. **Convert fractions to have denominator 60:** $$\frac{53}{10} = \frac{53 \times 6}{10 \times 6} = \frac{318}{60}$$ $$\frac{1}{12} = \frac{1 \times 5}{12 \times 5} = \frac{5}{60}$$ 5. **Add the fractions:** $$\frac{318}{60} + \frac{5}{60} = \frac{318 + 5}{60} = \frac{323}{60}$$ 6. **Convert back to mixed number:** Divide 323 by 60: $$323 \div 60 = 5 \text{ remainder } 23$$ So, $$\frac{323}{60} = 5 \frac{23}{60}$$ **Final answer:** $5 \frac{23}{60}$