Mixed Number Division: Splitting $2½ Equally Between Two Children

To solve this problem, we will follow these steps:

• Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction.
• Step 2: Divide the improper fraction by 2.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction. This is done by multiplying the whole number 2 by the denominator 2 and adding the numerator 1. Hence, $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$.
Step 2: Divide $\frac{5}{2}$ by 2. Dividing by 2 is equivalent to multiplying by $\frac{1}{2}$. Therefore, $\frac{5}{2} \div 2 = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$.
Step 3: The fraction $\frac{5}{4}$ is already in its simplest form, but it can also be expressed as a mixed number: $1\frac{1}{4}$.

Therefore, each child will receive $1\frac{1}{4}$ dollars.