How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

When dividing fractions, the key step is to use the reciprocal of the second fraction. The reciprocal of a fraction is simply flipping its numerator and denominator. For example, the reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\).

Let's say you need to divide \(\frac{2}{5}\) by \(\frac{3}{7}\). First, find the reciprocal of \(\frac{3}{7}\), which is \(\frac{7}{3}\). Then, multiply \(\frac{2}{5}\) by \(\frac{7}{3}\). To multiply fractions, multiply the numerators together and the denominators together. So, \(\frac{2}{5} \times \frac{7}{3} = \frac{2 \times 7}{5 \times 3} = \frac{14}{15}\).

Remember to simplify the fractions if possible. In this case, \(\frac{14}{15}\) is already in its simplest form. If you had a fraction like \(\frac{8}{12}\), you would simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 4, resulting in \(\frac{2}{3}\).

This method works for all fractions, including mixed numbers. If you have a mixed number, convert it to an improper fraction first. For example, to divide \(1 \frac{1}{2}\) by \(\frac{3}{4}\), convert \(1 \frac{1}{2}\) to \(\frac{3}{2}\), then proceed with the reciprocal method: \(\frac{3}{2} \div \frac{3}{4} = \frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2\).

By following these steps, you can confidently divide any fractions you encounter.