Math
Mixed Number to Improper Fraction Calculator
Enter the whole part, numerator, and denominator of a mixed number and get the improper fraction with every step: multiply the whole by the denominator, add the numerator, keep the denominator.
The simplified fraction, decimal, and percent are included, and negative mixed numbers are handled correctly.
Use a minus sign here for a negative mixed number, for example -3.
The top of the fraction part.
The bottom of the fraction part. Must be positive.
Try an example
Result
Improper fraction
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- Simplified
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- Decimal
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- Percent
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Study path
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How to convert a mixed number to an improper fraction
A A whole number written next to a fraction, like 2 1/3. is a whole number plus a proper fraction. Each whole is worth The bottom number of a fraction; it says how many equal parts make one whole./denominator, so multiply the whole number by the denominator, add the The top number of a fraction; it counts how many parts you have., and put the total over the same denominator. 3 2/5 = (3 × 5 + 2)/5 = 17/5.
| Mixed number | Multiply and add | Improper fraction |
|---|---|---|
| 3 2/5 | 3 × 5 + 2 = 17 | 17/5 |
| 1 1/2 | 1 × 2 + 1 = 3 | 3/2 |
| 4 6/8 | 4 × 8 + 6 = 38 | 38/8 = 19/4 |
| -2 1/3 | 2 × 3 + 1 = 7, keep the sign | -7/3 |
| 5 0/1 | 5 × 1 + 0 = 5 | 5/1 |
Negative mixed numbers
The sign belongs to the whole value: -2 1/3 means -(2 + 1/3) = -7/3. Enter the minus sign on the whole number and keep the numerator positive. Writing -2 + 1/3 would give -5/3, which is a different number.
How to use it
- Type the whole number, then the numerator and denominator of the fraction part.
- For a negative mixed number, put the minus sign on the whole number only.
- Read the improper fraction and its simplified version.
- Open Show the work to see multiply, add, keep-the-denominator, and the check by division.
How to read the answer
The improper fraction has the same value as the mixed number, written as a single fraction. If the simplified version differs, the fraction part of your mixed number was not in lowest terms. The decimal confirms both forms match: 17/5 = 3.4.
Common mistakes and edge cases
- Add the numerator after multiplying, not before: 3 2/5 is (3 × 5) + 2 = 17, not 3 × (5 + 2).
- The denominator stays the same. 3 2/5 is 17/5, not 17/15.
- Keep the sign on the whole value for negative mixed numbers: -2 1/3 = -7/3.
- A denominator of 0 is undefined.
- If the numerator is not smaller than the denominator, the input is not a standard mixed number; the calculator still converts it and warns you.
Worked examples
Typical
3 2/5
Improper fraction
17/5
Fraction part not simplified
4 6/8
Improper fraction
38/8
Negative mixed number
-2 1/3
Improper fraction
-7/3
Whole number only
5 0/1
Improper fraction
5/1
No whole part
0 3/4
Improper fraction
3/4
Large values
125 7/16
Improper fraction
2007/16
Zero denominator
3 2/0
Improper fraction
Error
Negative numerator
Sign in the wrong place
Improper fraction
Error
Frequently asked questions
How do you convert 3 2/5 to an improper fraction?+
Multiply 3 by 5 to get 15, add 2 to get 17, and keep the denominator: 17/5.
Why do you multiply the whole number by the denominator?+
Each whole equals denominator/denominator. Three wholes in fifths is 15/5, and adding the 2/5 gives 17/5.
How do you convert a negative mixed number?+
Convert the positive version and put the minus sign in front of the result: -2 1/3 = -7/3.
Does the improper fraction need simplifying?+
Only if the fraction part was not in lowest terms. 4 6/8 gives 38/8, which simplifies to 19/4. The calculator shows both.
What if the whole number is 0?+
Then the value is already a plain fraction: 0 3/4 = 3/4.
When should I use improper fractions instead of mixed numbers?+
For multiplying, dividing, and comparing. Mixed numbers are better for reading the size of a quantity at a glance.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026