To turn an improper fraction into a mixed number, divide the numerator by the denominator: the quotient is the whole part and the remainder goes over the same denominator. So 11/4 is two wholes and three fourths. This page collects 25 PDF worksheets for practicing the conversion in both directions, with a worked problem and problems of several kinds.
What worksheets there are
Each worksheet comes with its answer key as a separate file. The level sets the size of the denominator: up to 10 in level 1, up to 12 in level 2, up to 20 in level 3 and up to 30 in level 4. The table counts the worksheets in each direction and level, with the number of problems on each:
| Level | Converting to a mixed number | Converting to an improper fraction | Both directions |
|---|---|---|---|
| 1 | 8, 12 | 8, 12 | 12 |
| 2 | 8, 12, 20 | 8, 12, 20 | 8, 12 |
| 3 | 12, 20 | 12, 20 | 8, 12 |
| 4 | 12, 20 | 12, 20 | 12, 20 |
The 8-problem worksheets work as a warm-up and the 20-problem ones as a long review. The ones that mix both directions make the student decide which operation is needed before doing it. If you need different numbers, the fraction worksheet generator creates another sheet, and for instant checking there is fraction practice, with the level already chosen.
Worked problem: a ribbon 11/4 of a yard long
A ribbon is 11/4 of a yard long. How many whole yards does it have, and what fraction of a yard is left over?
- Divide. 11 ÷ 4 = 2 with 3 left over, because 4 × 2 = 8 and 11 − 8 = 3.
- Place the quotient. The whole part is 2.
- Place the remainder. The 3 is the numerator of the fraction part, and the denominator stays 4.
Result: 2 3/4 yards, that is, 2 whole yards and 3/4 of a yard.
Check: go back with 2 × 4 + 3 = 11, and you recover 11/4.
A model answer for a test: “The ribbon is 2 3/4 yd: 11 ÷ 4 gives quotient 2 and remainder 3, and 2 × 4 + 3 = 11 confirms the result.” Writing the check on one line is usually enough to show that the procedure is understood.
Six problems of different kinds
Not all of them ask for a direct conversion: some look for a part, others for a total, others compare or chain two steps.
Practice
- Convert 19/6 into a mixed number.
- A rope 3 1/4 yards long is cut into pieces of 1/4 yard. How many pieces do you get?
- Which amount is greater, 17/5 or 3 1/2?
- Two sections of a trail measure 9/4 miles and 7/4 miles. Write the total length as a mixed number or a whole number.
- A rod measures 5 3/8 inches. How many eighths of an inch does it have?
- Convert 26/8 into a mixed number and leave the fraction part simplified.
Show the answers
- 3 1/6, because 19 = 3 × 6 + 1.
- 13 pieces: 3 1/4 = (3 × 4 + 1)/4 = 13/4, and that is 13 fourths.
- 3 1/2. Since 17/5 = 3 2/5 and 2/5 = 0.4 is less than 1/2, 3 1/2 wins.
- 4 miles: 9/4 + 7/4 = 16/4 = 4, with no fraction part.
- 43 eighths: 5 × 8 + 3 = 43.
- 3 1/4: the remainder is 2, so you get 3 2/8, and 2/8 = 1/4.
A mistake that shows up with large denominators
With denominators of 12 or more, the quotient is harder to work out and it is easy to fall short. In 35/12, a student who subtracts a single 12 gets 1 and a remainder of 23, and writes an improper fraction inside the mixed number.
Two other mistakes are common. One is changing the denominator: in 19/6 the denominator stays 6 and does not become the quotient. The other is writing 3 0/4 when the remainder is zero. If the remainder is 0, the result is a whole number and no fraction is left.
Notes for the teacher
- Always ask for the reverse check on the worksheets that go both ways: from 2 3/4 you go back to 2 × 4 + 3 = 11.
- For a student who is unsure, drawing shapes helps: 11/4 is two whole shapes cut into fourths and three fourths more.
- A student who moves fast can make up fractions with a given quotient and remainder, and a partner converts them.
- The conversions prepare for work with mixed number operations. Before that, the proper and improper worksheet fixes what an improper fraction is; the guide to types of fractions explains the convention for 5/5.
- To check a single conversion, use the improper fraction to mixed number calculator or its inverse, mixed number to fraction.
Sources
The Wikipedia article Fraction defines an improper fraction as one whose absolute value is greater than or equal to 1, and says that any improper fraction can be converted to a mixed number (an integer plus a proper fraction) and vice versa (consulted October 17, 2026).