Solve: 1/2 + 3/4 + 2/5 - Adding Three Fractions with Different Denominators

To solve this problem, we will add the fractions by finding a common denominator:

• Step 1: Identify the denominators: 2, 4, and 5. Find the least common multiple (LCM) of these denominators.
• Step 2: The LCM of 2, 4, and 5 is 20. Use this as the common denominator.
• Step 3: Convert each fraction to have a denominator of 20:
• Convert $\frac{1}{2}$ to $\frac{10}{20}$ by multiplying the numerator and denominator by 10.
• Convert $\frac{3}{4}$ to $\frac{15}{20}$ by multiplying the numerator and denominator by 5.
• Convert $\frac{2}{5}$ to $\frac{8}{20}$ by multiplying the numerator and denominator by 4.
• Step 4: Add the three fractions: $\frac{10}{20} + \frac{15}{20} + \frac{8}{20}$.
• Step 5: Add the numerators: $10 + 15 + 8 = 33$.
• Step 6: Write the result as a single fraction: $\frac{33}{20}$.
• Step 7: Check if the fraction can be simplified. Since 33 and 20 have no common factors other than 1, $\frac{33}{20}$ is in its simplest form.
• Step 8: Confirm this matches choice (4): $\frac{33}{20}$.

Therefore, the solution to the problem is $\frac{33}{20}$.