Solve Mixed Number Addition: 3⅗ + 1 1/15

To solve the problem $3\frac{3}{5} + 1\frac{1}{15}$, we'll follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
  - For $3\frac{3}{5}$: Multiply the whole number $3$ by the denominator $5$ and add the numerator $3$: $(3 \times 5) + 3 = 15 + 3 = 18$, so we have $\frac{18}{5}$.
  - For $1\frac{1}{15}$: Multiply the whole number $1$ by the denominator $15$ and add the numerator $1$: $(1 \times 15) + 1 = 15 + 1 = 16$, so we have $\frac{16}{15}$.
• Step 2: Find the least common denominator (LCD).
  - The denominators are $5$ and $15$, the LCD is $15$.
• Step 3: Convert fractions to have the same denominator.
  - $\frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15}$
  - $\frac{16}{15}$ is already expressed with the denominator $15$.
• Step 4: Add the fractions.
  - $\frac{54}{15} + \frac{16}{15} = \frac{54 + 16}{15} = \frac{70}{15}$
• Step 5: Simplify the fraction.
  - Simplify $\frac{70}{15}$. The greatest common divisor of $70$ and $15$ is $5$. So, $\frac{70}{15} = \frac{70 \div 5}{15 \div 5} = \frac{14}{3}$.
• Step 6: Convert the improper fraction back to a mixed number.
  - $\frac{14}{3} = 4\frac{2}{3}$ (since $14 \div 3 = 4$ remainder $2$)

Therefore, the sum of $3\frac{3}{5} + 1\frac{1}{15}$ is $\mathbf{4\frac{2}{3}}$.