Compare Fractions: Find the Missing Symbol Between 1/3 and 3/10

To solve this problem, we'll compare the fractions $\frac{1}{3}$ and $\frac{3}{10}$ by finding a common denominator.

Let's follow these steps:

• Step 1: Identify the denominators of the given fractions, which are 3 and 10.
• Step 2: Calculate the least common denominator (LCD) of 3 and 10. Since 3 and 10 are co-prime, their product, 30, is the LCD.
• Step 3: Adjust the fractions to have a common denominator of 30:
• Convert $\frac{1}{3}$ to a fraction with denominator 30 by multiplying the numerator and the denominator by 10:
$\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}$
• Convert $\frac{3}{10}$ to a fraction with denominator 30 by multiplying the numerator and the denominator by 3:
$\frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}$
• Step 4: Compare the numerators of the fractions: 10 (from $\frac{10}{30}$) and 9 (from $\frac{9}{30}$).
• Since 10 is greater than 9, $\frac{10}{30}$ is greater than $\frac{9}{30}$.
• Thus, $\frac{1}{3}$ is greater than $\frac{3}{10}$.

Therefore, the correct comparison sign is $>$.