Question

How can you divide a fraction by a fraction

Answer 1

Dividing a fraction by another fraction involves a simple process. Here are the steps:

1. **Keep the First Fraction**: Write down the first fraction (the one you are dividing).

2. **Change Division to Multiplication**: Change the division sign to a multiplication sign.

3. **Flip the Second Fraction**: Take the second fraction (the one you're dividing by) and flip it. This is known as finding the reciprocal of the fraction.

4. **Multiply**: Multiply the first fraction by the reciprocal of the second fraction.

5. **Simplify** (if necessary): If possible, simplify the resulting fraction.

### Example

Let's say you want to divide \( \frac{2}{3} \) by \( \frac{4}{5} \):

1. **Keep the First Fraction**: \( \frac{2}{3} \)
2. **Change Division to Multiplication**: \( \frac{2}{3} \times \)
3. **Flip the Second Fraction**: The reciprocal of \( \frac{4}{5} \) is \( \frac{5}{4} \).
4. **Multiply**:
\[
\frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12}
\]
5. **Simplify**: \( \frac{10}{12} \) can be simplified to \( \frac{5}{6} \) by dividing both numerator and denominator by 2.

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