1. **State the problem:** Miguel used $5 \frac{3}{5}$ gallons of gas on Sunday and $3 \frac{1}{4}$ gallons on Monday. We need to find the total gallons used over the two days combined, expressed as a mixed number in simplest form. 2. **Convert mixed numbers to improper fractions:** - For Sunday: $5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5}$ - For Monday: $3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$ 3. **Add the improper fractions:** We need a common denominator. The denominators are 5 and 4, so the least common denominator (LCD) is 20. Convert each fraction: $$\frac{28}{5} = \frac{28 \times 4}{5 \times 4} = \frac{112}{20}$$ $$\frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20}$$ Add them: $$\frac{112}{20} + \frac{65}{20} = \frac{112 + 65}{20} = \frac{177}{20}$$ 4. **Convert the improper fraction back to a mixed number:** Divide 177 by 20: $$177 \div 20 = 8 \text{ remainder } 17$$ So, $$\frac{177}{20} = 8 \frac{17}{20}$$ 5. **Simplify the fraction if possible:** The fraction $\frac{17}{20}$ cannot be simplified further because 17 is a prime number and does not divide evenly into 20. **Final answer:** Miguel used $8 \frac{17}{20}$ gallons of gas in total over the two days.