Given the image, what is the mathematical expression shown?

The mathematical expression shown in the image is:

\( \frac{5}{10} \div \frac{3}{15} \times \frac{1}{2} \)

Step-by-step solution:

1. Step 1: Solve the expression inside the parentheses first. In this case, it is the division of two fractions: \( \frac{5}{10} \div \frac{3}{15} \). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: \( \frac{5}{10} \times \frac{15}{3} \).
2. Step 2: Simplify the multiplication. We can simplify before multiplying: \( \frac{5}{10} \) simplifies to \( \frac{1}{2} \), and \( \frac{15}{3} \) simplifies to \( 5 \). So the expression becomes \( \frac{1}{2} \times 5 \) which is \( \frac{5}{2} \).
3. Step 3: Now, multiply the result by the third fraction: \( \frac{5}{2} \times \frac{1}{2} \).
4. Step 4: Multiply the numerators together and the denominators together: \( \frac{5 \times 1}{2 \times 2} = \frac{5}{4} \).

Answer: \( \frac{5}{4} \)