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Improper fractions to mixed numbers, and back again
An improper fraction has a top number that's bigger than (or equal to) the bottom number, like 11/4. A mixed number shows the same amount as wholes and a fraction, like 2 3/4. Both are correct. Mixed numbers are just easier to picture.
Children usually learn this in 4th grade, and use it a lot when adding and subtracting fractions in 5th grade.
Worked examples
- Improper to mixed: 11/4. Divide the top by the bottom: 11 ÷ 4 = 2 R 3. The 2 is the wholes and the 3 is what's left over, still in fourths. So 11/4 = 2 3/4.
- Mixed to improper: 3 2/5. Multiply the whole number by the bottom and add the top: 3 × 5 + 2 = 17. Keep the same bottom number, so 3 2/5 = 17/5.
- Picture it. 7/3 is seven thirds. Three thirds make one whole, so seven thirds is two wholes and one third: 7/3 = 2 1/3.
6 practice questions
- 7/3 = ?
- 9/2 = ?
- 13/5 = ?
- 2 1/4 = ?/4
- 1 5/6 = ?/6
- 3 3/8 = ?/8
Show answers
- 7/3 = 2 1/3
- 9/2 = 4 1/2
- 13/5 = 2 3/5
- 2 1/4 = 9/4
- 1 5/6 = 11/6
- 3 3/8 = 27/8
Tips for parents
- The bottom number never changes when you convert.
- Check by converting back the other way.
- If the remainder is 0, the answer is a whole number. For example, eight fourths is 2.
Questions parents ask
What is an improper fraction?
A fraction where the top number is bigger than or equal to the bottom number, so it's worth 1 or more. Eleven fourths is an example.