Solve the Fraction Addition: 2/5 + 2/6 Step-by-Step

To solve the problem $\frac{2}{5} + \frac{2}{6}$, we need a common denominator:

• Step 1: Find the least common multiple (LCM) of the denominators 5 and 6. The LCM of 5 and 6 is 30.
• Step 2: Rewrite each fraction to have the denominator 30:
  • For $\frac{2}{5}$: Multiply the numerator and denominator by $6$ (since $5 \times 6 = 30$). This gives $\frac{2 \times 6}{5 \times 6} = \frac{12}{30}$.
  • For $\frac{2}{6}$: Multiply the numerator and denominator by $5$ (since $6 \times 5 = 30$). This gives $\frac{2 \times 5}{6 \times 5} = \frac{10}{30}$.
• Step 3: Add the two fractions: $\frac{12}{30} + \frac{10}{30} = \frac{22}{30}$.
• Step 4: Simplify the resulting fraction. Since $\frac{22}{30}$ is already in simplest form, no further simplification is necessary.

Therefore, the sum of $\frac{2}{5}$ and $\frac{2}{6}$ is $\frac{22}{30}$, which corresponds to choice 4.