Fractions, decimals and percentsGrades 4–5
Improper fractions and mixed numbers worksheets
This page opens on improper fractions to mixed numbers, such as 23/6 = 3 5/6. Switch the Skill setting to Mixed numbers to improper fractions for the reverse. Both print with an answer key.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
Two names for the same amount
An improper fraction has a numerator at least as large as its denominator, so it is worth one whole or more. A mixed number writes the same amount as a whole number and a leftover fraction. 23/6 and 3 5/6 are the same quantity. Students need to move freely between the two forms before they can add, subtract or multiply fractions greater than one.
The topic arrives in fourth grade and is used heavily in fifth. Understanding comes before the procedure: if a student can see that 23/6 is three wholes (18 sixths) plus 5 more sixths, the rule that follows is easy to remember.
Settings for this sheet
- Skill is set to Improper fractions to mixed numbers here. Choose Mixed numbers to improper fractions for the other direction. Either one gives you a full sheet of the one conversion, which is better for learning than mixing them.
- Largest denominator can be raised as far as 20. This page starts at 10, so denominators are anywhere from 2 to 10. Keep it small when the concept is new.
- Number of problems has a range of 8 to 30, and the default of 24 prints in three columns.
Every generated fraction has a remainder, so no answer is a plain whole number, and the whole-number part is between 1 and 5. The fraction part of every mixed number is already in lowest terms, and the key writes each answer the same way, such as 2 2/3 for 16/6.
Worked example: 23/6 and back again
To a mixed number. Division is the engine here.
- Divide the numerator by the denominator: 23 ÷ 6 = 3 with a remainder of 5, since 6 × 3 = 18 and 23 − 18 = 5.
- The quotient, 3, is the whole number.
- The remainder, 5, is the new numerator, and the denominator stays at 6.
- The mixed number is 3 5/6.
Back to improper. Use multiplication and addition.
- Multiply the whole number by the denominator: 3 × 6 = 18.
- Add the numerator: 18 + 5 = 23.
- Keep the same denominator: 23/6.
Returning to the start is the best self-check. A student who converts 23/6 to 3 5/6 and cannot get back to 23/6 has made a slip somewhere.
Using the key to find patterns
The answer key prints the converted form for each problem. Compare these against student work.
- Remainder written as a decimal or left next to the quotient. The student wrote 3 R5. The remainder needs to sit over the denominator.
- Changed denominator. Writing 3 5/3, for example, means the child used the quotient as a new denominator. The denominator never changes in this conversion.
- Forgetting to add. In the reverse direction, 3 × 6 = 18 is not the finished numerator. Ask how many sixths are in the fraction part.
- Fraction part not reduced. The key leaves the fraction part as the conversion produces it, so an answer such as 2 4/6 can appear. Decide in advance whether your students must also reduce it to 2 2/3.
Reducing connects to simplifying fractions, a good companion. After conversions are fluent, multiplying fractions with mixed numbers (turn on the Use mixed numbers toggle) is a natural application.