Solve the Nested Division: 15÷(15÷½) Step-by-Step Solution

To solve this problem, we must first evaluate the nested division expression $15:(15:\frac{1}{2})$.

Let's start by handling the innermost division $15:\frac{1}{2}$. Division by a fraction is equivalent to multiplication by its reciprocal. Therefore:

• The reciprocal of $\frac{1}{2}$ is $2$.
• Hence, $15:\frac{1}{2} = 15 \times 2 = 30$.

Now, we use the result of this inner division, $30$, as the divisor for the outer expression $15:30$.

• Perform the division $15:30$, which simplifies to $\frac{15}{30}$.
• Simplify the fraction $\frac{15}{30}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
• This gives us $\frac{15 \div 15}{30 \div 15} = \frac{1}{2}$.

Therefore, the solution to the problem is $\frac{1}{2}$.