Mixed Numbers and Improper Fractions
Mixed number to improper fraction: multiply the whole number by the denominator, add the numerator, and keep the denominator. 2 3/4 = (2 × 4 + 3) over 4 = 11/4.
Improper fraction to mixed number: divide the numerator by the denominator. The answer is the whole number and the remainder goes over the same denominator. 11/4: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.
Mixed number and improper fraction converter
Type a number to see the steps, and the bars that show why it works.
2 3/4 = 11/4
How to convert a mixed number to an improper fraction
- Multiply the whole number by the denominator. That counts the parts in the wholes: in 3 2/5, 3 wholes of 5 fifths is 15 fifths.
- Add the numerator: 15 + 2 = 17.
- Keep the denominator. The parts are still fifths, so 3 2/5 = 17/5.
| Mixed number | Working | Improper fraction |
|---|---|---|
| 1 1/2 | 1 × 2 + 1 = 3 | 3/2 |
| 2 3/4 | 2 × 4 + 3 = 11 | 11/4 |
| 4 5/6 | 4 × 6 + 5 = 29 | 29/6 |
| 7 3/8 | 7 × 8 + 3 = 59 | 59/8 |
How to convert an improper fraction to a mixed number
- Divide the numerator by the denominator: for 17/5, 17 ÷ 5 = 3 remainder 2.
- The answer, 3, is the whole number.
- The remainder, 2, goes over the same denominator: 17/5 = 3 2/5.
- If there is no remainder, the fraction is a whole number: 12/4 = 3.
Check either way by converting back. The two methods undo each other, which is why the mixed practice sheet alternates them.
Practice: convert it
Press Enter to check. It alternates both directions.
Proper, improper and mixed
| Kind | What it means | Examples |
|---|---|---|
| Proper fraction | Numerator smaller than the denominator; less than 1 | 3/4 2/5 |
| Improper fraction | Numerator equal to or bigger than the denominator; 1 or more | 7/4 5/5 |
| Mixed number | A whole number and a proper fraction | 1 3/4 2 1/5 |
5/5 catches people out: the top equals the bottom, so it is improper, and it equals 1. On a number line, improper fractions are the ones at or past 1.
Mistakes to watch for
- Adding the whole number to the numerator: 2 3/4 becomes 5/4 instead of 11/4. The whole number has to be turned into quarters first.
- Changing the denominator: the size of the parts never changes, so the denominator stays the same both ways.
- Forgetting to simplify: 14/4 = 3 2/4, which simplifies to 3 1/2.
Mixed numbers and improper fractions worksheets
Free PDFs, each with an answer key on page 2.
Converting Mixed Numbers to Improper Fractions
Grades 4–5
Eighteen mixed numbers like 3 2/5 to write as improper fractions.
Download PDF (18 problems · 47 KB)
Converting Improper Fractions to Mixed Numbers
Grades 4–5
Eighteen improper fractions like 17/5 to write as mixed numbers, a few of them whole numbers.
Download PDF (18 problems · 46 KB)
Proper, Improper or Mixed?
Grades 3–4
Eighteen numbers to label proper fraction, improper fraction or mixed number.
Download PDF (18 problems · 46 KB)
Mixed Numbers and Improper Fractions
Grades 4–5
Twelve conversions, alternating mixed number to improper fraction and back.
Download PDF (12 problems · 46 KB)When kids learn it
Mixed numbers start in 4th grade, when students write a fraction like 9/8 as 1 1/8 and add and subtract mixed numbers with like denominators. In 5th grade they use the conversion to add, subtract and multiply mixed numbers with unlike denominators, which is why improper fractions get practiced so much. See 4th grade and 5th grade math practice.
Common questions
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2 3/4: 2 × 4 + 3 = 11, so 2 3/4 = 11/4.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The answer is the whole number and the remainder goes over the same denominator. 17/5 is 17 ÷ 5 = 3 remainder 2, so 3 2/5.
What is an improper fraction?
A fraction whose numerator is equal to or bigger than its denominator, like 7/4 or 5/5. It is worth 1 or more.
What is a mixed number?
A whole number and a proper fraction written together, like 1 3/4. It means 1 + 3/4.
What grade learns mixed numbers and improper fractions?
4th grade introduces mixed numbers and converting between them and improper fractions; 5th grade uses the conversion to add, subtract and multiply them.
Related: fraction worksheets · fractions practice · fraction chart · mixed number calculator · fractions on a number line · adding fractions · all printable worksheets