Compare Fractions: Find the Missing Sign Between 2/15 and 1/3

To solve this problem, we'll convert both fractions to have a common denominator and compare:

• Step 1: Identify the denominators $(15$ and $3)$ of the fractions $\frac{2}{15}$ and $\frac{1}{3}$.
• Step 2: Find the common denominator. The least common multiple (LCM) of $15$ and $3$ is $15$.
• Step 3: Convert each fraction to have the common denominator $15$.
• For $\frac{2}{15}$, the fraction is already over $15$, so it stays $\frac{2}{15}$.
• For $\frac{1}{3}$, multiply both the numerator and the denominator by $5$ to get an equivalent fraction: $\frac{1 \times 5}{3 \times 5} = \frac{5}{15}$.
• Step 4: Compare the equivalent fractions $\frac{2}{15}$ and $\frac{5}{15}$.
• Step 5: Since $2 \lt 5$, it follows that $\frac{2}{15} \lt \frac{5}{15}$.

Therefore, the correct sign to fill in the missing slot is $\lt$.

Consequently, the completed expression is $\frac{2}{15} \lt \frac{1}{3}$.

Therefore, the solution to the problem is $\lt$.