Mathematics ACT Aspire Practice Test 2025 – Complete Study Resource

To divide fractions, the process involves multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is created by flipping the numerator and the denominator. For example, if you have the fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), to divide \( \frac{a}{b} \) by \( \frac{c}{d} \), you would multiply \( \frac{a}{b} \) by \( \frac{d}{c} \). This results in \( \frac{a \times d}{b \times c} \).

This method works seamlessly because it transforms the division operation into a multiplication operation, which is much simpler to execute. Thus, using the reciprocal allows us to handle fraction division without confusion or additional complexity.

Other methods like adding or subtracting fractions or converting them to decimals do not achieve the same result and are unsuitable for dividing fractions, as they do not follow the established arithmetic rules for operations with fractions.