Solve the Fraction Addition: 3/7 + 1/3 Step by Step

Solve the following exercise:

$\frac{3}{7}+\frac{1}{3}=\text{?}$

To solve the problem of adding the fractions $\frac{3}{7}$ and $\frac{1}{3}$, we follow these steps:

• Step 1: Find a common denominator for the fractions. The denominators are $7$ and $3$. By multiplying $7$ and $3$, we find the common denominator is $21$.
• Step 2: Convert each fraction to an equivalent fraction with this common denominator.
  • The first fraction: $\frac{3}{7}$. We multiply both the numerator and the denominator by $3$ (since $7 \times 3 = 21$): $\frac{3 \times 3}{7 \times 3} = \frac{9}{21}.$
  • The second fraction: $\frac{1}{3}$. We multiply both the numerator and the denominator by $7$ (since $3 \times 7 = 21$): $\frac{1 \times 7}{3 \times 7} = \frac{7}{21}.$
• Step 3: Add the fractions. Now that both fractions have the same denominator, we can add them: $\frac{9}{21} + \frac{7}{21} = \frac{9 + 7}{21} = \frac{16}{21}.$
• Step 4: Simplify the resulting fraction if necessary. In this case, $\frac{16}{21}$ is already in its simplest form.

Therefore, the final solution to the problem is $\frac{16}{21}$.