Solve Compound Division: 42÷(7÷2½) Step-by-Step Solution

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Simplify the inner division using fraction rules.
• Step 3: Simplify the outer division with the result obtained from Step 2.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{2}$ to an improper fraction. We have: $\large 2\frac{1}{2} = \frac{5}{2}$
Step 2: Simplify the inner division $7 \div 2\frac{1}{2}$. This becomes: $\large 7 \div \frac{5}{2} = 7 \times \frac{2}{5} = \frac{14}{5}$
Step 3: Now, simplify the overall expression $42 \div$ $\frac{14}{5}$. This converts to multiplication: $\large 42 \times \frac{5}{14}$
Calculating this gives: $42 \times \frac{5}{14} = \frac{42 \times 5}{14} = \frac{210}{14} = 15$

Therefore, the solution to the problem is $15$.