To solve the given expression:

$\left(\frac{1}{2} + \frac{2}{4} + \frac{3}{6} + \frac{4}{8} + \frac{5}{10}\right) - \left(\frac{1}{4} + \frac{2}{8} + \frac{3}{12} + \frac{4}{16}\right)$

Step 1: Simplify each term in the expression

First part:

$\frac{1}{2} = 0.5, \quad \frac{2}{4} = 0.5, \quad \frac{3}{6} = 0.5, \quad \frac{4}{8} = 0.5, \quad \frac{5}{10} = 0.5$ Adding these: $0.5 + 0.5 + 0.5 + 0.5 + 0.5 = 2.5$

Second part:

$\frac{1}{4} = 0.25, \quad \frac{2}{8} = 0.25, \quad \frac{3}{12} = 0.25, \quad \frac{4}{16} = 0.25$ Adding these: $0.25 + 0.25 + 0.25 + 0.25 = 1$

Step 2: Subtract the second part from the first part:

$2.5 - 1 = 1.5$

Final Answer:

The value of the expression is 1.5 (Option A).

Would you like further clarification on any of the steps? Here are some related questions to deepen understanding:

1. How do we simplify fractions in general?
2. Can you explain why all terms in the first part simplify to 0.5?
3. What happens if fractions have different denominators in addition?
4. Why is subtraction done term-by-term when dealing with fractions?
5. How can this problem be solved using the least common denominator?

Tip: Always simplify fractions before summing them up to make calculations easier!