Adding Fractions with Different Denominators: 1/5 and 1/3

To solve the problem of adding the fractions $\frac{1}{5}$ and $\frac{1}{3}$, we follow these steps:

• Step 1: Find a common denominator for the fractions. Since the denominators are $5$ and $3$, the least common multiple is $15$.
• Step 2: Convert each fraction to this common denominator:
  - For $\frac{1}{5}$, multiply both numerator and denominator by $3$ (the denominator of the other fraction), resulting in $\frac{3}{15}$.
  - For $\frac{1}{3}$, multiply both numerator and denominator by $5$ (the denominator of the other fraction), resulting in $\frac{5}{15}$.
• Step 3: Add the fractions now that they have a common denominator:
  $\frac{3}{15} + \frac{5}{15} = \frac{3+5}{15} = \frac{8}{15}$.

Therefore, when you add $\frac{1}{5}$ and $\frac{1}{3}$, the solution is $\frac{8}{15}$.