(1) Find the quotient. \( 2 \frac{1}{2} \div \frac{1}{5}=\square \)

To find the quotient of \( 2 \frac{1}{2} \div \frac{1}{5} \), follow these steps: ### Step 1: Convert the Mixed Number to an Improper Fraction First, convert \( 2 \frac{1}{2} \) to an improper fraction. \[ 2 \frac{1}{2} = \left(2 \times 2 + 1\right) \div 2 = \frac{5}{2} \] ### Step 2: Set Up the Division Problem Now, the problem becomes: \[ \frac{5}{2} \div \frac{1}{5} \] ### Step 3: Multiply by the Reciprocal Dividing by a fraction is the same as multiplying by its reciprocal. So, multiply \( \frac{5}{2} \) by the reciprocal of \( \frac{1}{5} \), which is \( \frac{5}{1} \): \[ \frac{5}{2} \times \frac{5}{1} = \frac{25}{2} \] ### Step 4: Convert Back to a Mixed Number (Optional) If you prefer the answer as a mixed number: \[ \frac{25}{2} = 12 \frac{1}{2} \] ### Final Answer \[ 2 \frac{1}{2} \div \frac{1}{5} = 12 \frac{1}{2} \]