Solve: 2/5 + 1/2 - 1/3 Fraction Addition and Subtraction

To solve the problem $\frac{2}{5} + \frac{1}{2} - \frac{1}{3}$, we will follow these steps:

• Step 1: Find the least common denominator (LCD) for $\frac{2}{5}$, $\frac{1}{2}$, and $\frac{1}{3}$.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Perform the arithmetic operations.
• Step 4: Simplify the result if necessary.

Now, let's proceed with the solution:
Step 1: The denominators are 5, 2, and 3. The least common multiple of these numbers is 30. Thus, the LCD is 30.

Step 2: Convert each fraction to have the common denominator of 30:
- Convert $\frac{2}{5}$ to a fraction with denominator 30: $\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}$.
- Convert $\frac{1}{2}$ to a fraction with denominator 30: $\frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30}$.
- Convert $\frac{1}{3}$ to a fraction with denominator 30: $\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}$.

Step 3: With all fractions having the same denominator, perform the operations:
$\frac{12}{30} + \frac{15}{30} - \frac{10}{30} = \frac{12 + 15 - 10}{30} = \frac{17}{30}$.

Step 4: Since $\frac{17}{30}$ is in its simplest form, no further simplification is needed.

Therefore, the correct answer is $\frac{17}{30}$.