What is the correct method for dividing fractions?

Dividing fractions follows a specific rule that makes the process straightforward and effective. The correct method involves flipping the second fraction, which is referred to as finding its reciprocal, and then changing the division operation into multiplication.

When you have a division of fractions, such as (\frac{a}{b} \div \frac{c}{d}), you can rewrite the expression by multiplying (\frac{a}{b}) by the reciprocal of (\frac{c}{d}). This becomes (\frac{a}{b} \times \frac{d}{c}). Multiplying fractions is simply done by multiplying the numerators together and the denominators together, resulting in (\frac{a \times d}{b \times c}).

This method works because dividing by a number is equivalent to multiplying by its reciprocal. Thus, using the reciprocal ensures the division is correctly carried out, leading to the desired result. This procedural approach is one of the foundational concepts in fraction arithmetic and is essential for solving problems involving multiple fractions.