How can you divide a fraction by a fraction?

Question

Review dividing ________ and whole numbers

Answer 1

To divide a fraction by a fraction, you can follow these steps:

1. Keep the first fraction as it is: This is the fraction you want to divide.

2. Change the division to multiplication: Instead of dividing by the second fraction, you multiply by its reciprocal (you flip the second fraction).

3. Multiply the numerators: Multiply the top numbers of the fractions together to get the new numerator.

4. Multiply the denominators: Multiply the bottom numbers of the fractions together to get the new denominator.

5. Simplify if necessary: If possible, simplify the resulting fraction by reducing it to its lowest terms.

For example, to divide \( \frac{2}{3} \) by \( \frac{4}{5} \):

1. Keep the first fraction: \( \frac{2}{3} \)
2. Change division to multiplication: \( \frac{2}{3} \times \frac{5}{4} \)
3. Multiply the numerators: \( 2 \times 5 = 10 \)
4. Multiply the denominators: \( 3 \times 4 = 12 \)
5. Combine: \( \frac{10}{12} \)
6. Simplify: \( \frac{5}{6} \)

So, \( \frac{2}{3} \div \frac{4}{5} = \frac{5}{6} \).

Review Dividing Fractions and Whole Numbers

To divide a fraction by a whole number:

1. Keep the fraction: The fraction you want to divide remains the same.
2. Change the whole number to a fraction: Any whole number can be expressed as a fraction by putting it over 1. For example, the whole number 4 can be written as \( \frac{4}{1} \).
3. Multiply by the reciprocal: Follow the same procedure as dividing a fraction by a fraction—multiply by the reciprocal of the whole number fraction.

For example, to divide \( \frac{3}{4} \) by 2:

1. Write 2 as a fraction: \( 2 = \frac{2}{1} \)
2. Change to multiplication: \( \frac{3}{4} \div \frac{2}{1} = \frac{3}{4} \times \frac{1}{2} \)
3. Multiply: \( \frac{3 \times 1}{4 \times 2} = \frac{3}{8} \)

So, \( \frac{3}{4} \div 2 = \frac{3}{8} \).