1. **State the problem:** Add the mixed numbers $3 \frac{1}{4}$ and $2 \frac{3}{5}$ and express the sum as a mixed number in simplest form. 2. **Convert mixed numbers to improper fractions:** - $3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}$ - $2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}$ 3. **Find a common denominator:** - The denominators are 4 and 5. - The least common denominator (LCD) is $20$. 4. **Convert fractions to have the LCD:** - $\frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20}$ - $\frac{13}{5} = \frac{13 \times 4}{5 \times 4} = \frac{52}{20}$ 5. **Add the fractions:** $$\frac{65}{20} + \frac{52}{20} = \frac{65 + 52}{20} = \frac{117}{20}$$ 6. **Convert the improper fraction back to a mixed number:** - Divide 117 by 20: $117 \div 20 = 5$ remainder $17$ - So, $\frac{117}{20} = 5 \frac{17}{20}$ 7. **Simplify the fraction if possible:** - $\frac{17}{20}$ is already in simplest form. **Final answer:** $$3 \frac{1}{4} + 2 \frac{3}{5} = 5 \frac{17}{20}$$