In order to divide fractions, first we have to learn about inverses. Here are some math terms that will help you to understand this lesson better:

- Reciprocal or Inverse: When the values in the numerator and denominator switch places. \(\displaystyle \frac{3}{4}\) \(\overrightarrow{}\) \(\dfrac{4}{3}\)

The following video will explain what makes inverses special:

Video Source (05:11 mins) | Transcript

How do you divide by a fraction? The next video will show how to use the multiplicative inverse (reciprocal) to divide by a fraction. It will also demonstrate why it works.

Video Source (06:49 mins) | Transcript

The following video has more examples of dividing by fractions:

Video Source (03:52 mins) | Transcript

Dividing by a fraction is the same as multiplying by the inverse of the second fraction. Remember that this does not work if you try using the inverse of the first fraction. Also remember that any whole number can be written as a fraction and then used in the same way.

\(\displaystyle 5 = \frac{5}{1}\)

## Additional Resources

- Khan Academy: Inverse Property of multiplication (03:16 mins, Transcript)
- Khan Academy: Understanding Division of Fractions (05:41 mins, Transcript)
- Khan Academy: Division of Fractions, Example 1 (01:16 mins, Transcript)
- Khan Academy: Division of Fractions, Example 2 (03:35 mins, Transcript)

### Practice Problems

**Divide the following fractions:**

- \(\displaystyle \frac{1}{4}\div\frac{1}{3}= \) (Solution
- \(\displaystyle \frac{1}{4}\div\frac{5}{8}= \) (Solution
- \(\displaystyle \frac{3}{7}\div\frac{2}{5}= \) (Solution
- \(\displaystyle \frac{3}{4}\div\frac{9}{2}= \) (Video Solution
- \(\displaystyle \frac{3}{4}\div6= \) (Solution
- \(\displaystyle 6\div\frac{3}{2}= \) (Video Solution

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