Solve the Fraction Addition: 2/5 + 1/6 + 4/30

To solve this problem, we'll add the fractions $\frac{2}{5}$, $\frac{1}{6}$, and $\frac{4}{30}$. Here's the step-by-step solution:

Step 1: Find a common denominator.

The denominators are 5, 6, and 30. The least common multiple (LCM) of these numbers is 30.

Step 2: Convert each fraction to have the common denominator of 30.

• $\frac{2}{5}$ is converted by multiplying both the numerator and the denominator by 6: $\frac{2 \times 6}{5 \times 6} = \frac{12}{30}$
• $\frac{1}{6}$ is converted by multiplying both the numerator and the denominator by 5: $\frac{1 \times 5}{6 \times 5} = \frac{5}{30}$
• $\frac{4}{30}$ already has the denominator of 30, so it remains $\frac{4}{30}$.

Step 3: Add the converted fractions.

Now, add the numerators while keeping the common denominator: $\frac{12}{30} + \frac{5}{30} + \frac{4}{30} = \frac{12 + 5 + 4}{30} = \frac{21}{30}$

Therefore, the sum of the fractions is $\frac{21}{30}$.

From the provided answer choices, the correct answer is choice 2: $\frac{21}{30}$.