Solve the Fraction Addition: 1/3 + 1/10 Step-by-Step

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

• Step 1: Find a common denominator.
  Since the denominators are 3 and 10, the least common multiple (LCM) of these numbers is 30. Therefore, the common denominator will be 30.
• Step 2: Convert each fraction to have the common denominator.
  Convert $\frac{1}{3}$ into an equivalent fraction with a denominator of 30:
  $\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}$.
  Convert $\frac{1}{10}$ into an equivalent fraction with a denominator of 30:
  $\frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}$.
• Step 3: Add the equivalent fractions.
  Now that both fractions have the same denominator, add the numerators while keeping the denominator 30:
  $\frac{10}{30} + \frac{3}{30} = \frac{10 + 3}{30} = \frac{13}{30}$.

After calculating, we find that the sum of the fractions is $\frac{13}{30}$.

Therefore, the correct answer to the problem is $\frac{13}{30}$.