Question

find the quotient. $\frac{1}{2} div \frac{1}{5} =$ $\frac{1}{2} div \frac{1}{5} = \frac{1}{2} \times \frac{5}{1}$

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal:
$$2\frac{1}{2} \div \frac{1}{5} = 2\frac{1}{2} \times \frac{5}{1}$$

Step2: Convert mixed number to improper fraction

$$2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2}$$

Step3: Multiply the fractions

$$\frac{5}{2} \times \frac{5}{1} = \frac{5\times5}{2\times1} = \frac{25}{2}$$

Step4: Convert to mixed number (optional)

$$\frac{25}{2} = 12\frac{1}{2}$$

Answer:

$\frac{25}{2}$ or $12\frac{1}{2}$