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

That's actually the correct approach! When you have $a \div x = b$, then $x = a \div b$. So $x = \frac{5}{5} \div \frac{5}{10} = 1 \times \frac{10}{5} = 2$. But wait, that gives us 2, not $\frac{1}{2}$!

Check your arithmetic! $\frac{5}{10} = \frac{1}{2}$, so we need $\frac{5}{5} \div x = \frac{1}{2}$. Since $\frac{5}{5} = 1$, we get $1 \div x = \frac{1}{2}$, which means $x = 1 \div \frac{1}{2} = 2$. Actually, let me recalculate...

Substitute back into the original equation: $\frac{5}{5} \div \frac{1}{2} = 1 \times \frac{2}{1} = 2$. But we need this to equal $\frac{5}{10} = \frac{1}{2}$. Since $2 \neq \frac{1}{2}$, there's an error in our setup!

The colon (:) is another way to write division, just like $\div$. So $\frac{5}{5} : x = \frac{5}{10}$ means the same as $\frac{5}{5} \div x = \frac{5}{10}$.

Method: Start with $\frac{5}{5} \div x = \frac{5}{10}$. Multiply both sides by x: $\frac{5}{5} = \frac{5}{10} \times x$. Since $\frac{5}{5} = 1$ and $\frac{5}{10} = \frac{1}{2}$, we get $1 = \frac{1}{2} \times x$. Therefore $x = 1 \div \frac{1}{2} = 2$. But 2 isn't among the choices...

Let me re-read the problem carefully. If the correct answer is $\frac{1}{2}$, then let's check: $\frac{5}{5} \div \frac{1}{2} = 1 \times 2 = 2$, and $\frac{5}{10} = 0.5$. These don't match, so there might be an error in the problem setup or my understanding.