Solve the Fraction Division: Find the Missing Number in 5/5 ÷ ? = 5/10

To solve the problem, let's perform the following steps:

• Step 1: Understand the problem: We need to find $x$ such that $\frac{5}{5} \div x = \frac{5}{10}$.
• Step 2: Transform the division into a multiplication by the reciprocal: $\frac{5}{5} \div x = \frac{5}{5} \times \frac{1}{x} = \frac{5}{10}$.
• Step 3: Set up the equation: $\frac{5}{5} \times \frac{1}{x} = \frac{5}{10}$.
• Step 4: Since $\frac{5}{5} = 1$, simplify the expression to $\frac{1}{x} = \frac{5}{10}$.
• Step 5: Solve for $x$: Take the reciprocal of both sides, leading to $x = \frac{10}{5} = \frac{5}{10} \times 2 = \frac{1}{\frac{5}{10}}$.
• Step 6: Recognize that $2$ is equivalent to the reciprocal of $\frac{1}{2}$, conclude $x = \frac{1}{2}$.

Therefore, the missing number is $\frac{1}{2}$ (Choice 2).