An important part of learning about fractions is becoming comfortable understanding what they mean. Being able to convert between improper fractions and mixed numbers is a great way to be able to understand fractions and recognize how large or small a fraction is. Here are some math terms that will help you to understand this lesson better:

- Proper Fraction = A fraction whose numerator is smaller than the denominator. Example: \(\dfrac{3}{4}\)
- Improper Fraction = A fraction whose numerator is larger than the denominator. Example: \(\dfrac{4}{3}\)
- Mixed Number = An integer combined with a proper fraction showing how many wholes and how many parts are in the number. Example: \(\displaystyle 2\frac{1}{3}\) means 2 whole and \(\dfrac{1}{3}\) pieces, pronounced two and one-third.

The following video will show how this conversion can be done:

Converting between Improper Fractions and Mixed Numbers

Video Source (10:18 mins) | Transcript

When converting from a Mixed Number to an Improper Fraction:

- Multiply the integer by the denominator and add the numerator to get the new numerator.
- Keep the denominator the same.
- Example: \(\displaystyle2\frac{1}{3}=\left ( \frac{2}{1}\times\frac{3}{3} \right )+\frac{1}{3}=\frac{2\times3}{3}+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}=\frac{7}{3}\)

When converting from an Improper Fraction to a Mixed Number:

- Divide the numerator by the denominator.
- Keep the remainder as the numerator of the new fraction part.
- The denominator stays the same.
- Example: \(\displaystyle \frac{11}{5}=11\div5=2\;\) with 1 divided by 5 left over \(\displaystyle =2\frac{1}{5}\)

## Additional Resources

- Khan Academy: Writing mixed numbers as improper fractions (06:42 mins | Transcript)
- Khan Academy: Writing improper fractions as mixed numbers (04:01 mins | Transcript)

*There are additional resource videos to the left of the screen on each of these links above.*

### Practice Problems

- \(\displaystyle 1\frac{3}{4}\) (Solution
- \(\displaystyle 5\frac{1}{8}\) (Video Solution
- \(\displaystyle 3\frac{2}{5}\) (Solution
- \(\dfrac{11}{4}\) (Video Solution
- \(\dfrac{13}{6}\) (Solution
- \(\dfrac{32}{3}\) (Solution

## Need More Help?

- Study other Math Lessons in the Resource Center.
- Visit the Online Tutoring Resources in the Resource Center.
- Contact your Instructor.
- If you still need help, Schedule a Tutor.