Enter a mixed number such as 2 3/4 to get the improper fraction 11/4, with every step and a pie model that shows why. Switch the direction to turn an improper fraction like 17/5 back into a mixed number, simplified, with its decimal and percent.
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Convert
Use a minus sign for a negative mixed number, e.g. −3
Enter your values to see the result.
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How to use the Mixed Number to Improper Fraction Converter
Choose the direction: mixed number to improper fraction, or the reverse.
Enter the whole number, numerator and denominator (or just the numerator and denominator for an improper fraction).
Read the answer, already simplified where possible.
Follow the steps and the pie model to see how it works.
Copy the result or use the equivalent fractions table.
The two conversions at a glance
Direction
Rule
Example
Mixed → improper
(whole × denominator + numerator) / denominator
3 2/5 = (15 + 2)/5 = 17/5
Improper → mixed
numerator ÷ denominator = whole, remainder over denominator
17/5 = 3 R 2 = 3 2/5
Negative
convert the positive part, keep the sign
−2 1/3 = −7/3
Whole number
whole × denominator over the denominator
4 = 12/3 = 8/2
Why it works
A mixed number is a whole number plus a fraction: 2 3/4 means 2 + 3/4. Each whole is the same as 4/4, so 2 wholes are 8/4, and 8/4 + 3/4 = 11/4. In the pie model, that is 2 full pies cut into quarters (8 slices) plus 3 more slices, 11 quarter-slices in total. Going the other way, you group the slices back into full pies: 11 quarters make 2 full pies with 3 quarters left over.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and put the result over the same denominator. For 2 3/4: 2 × 4 = 8, 8 + 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 quotient is the whole number, the remainder is the new numerator and the denominator stays the same. 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.
What is an improper fraction?
A fraction whose numerator is equal to or larger than its denominator, such as 7/4 or 5/5. Its value is 1 or more. A proper fraction, like 3/4, is less than 1.
How do I convert a negative mixed number?
Convert the positive version and keep the minus sign in front: −1 5/8 = −(1 × 8 + 5)/8 = −13/8. The minus applies to the whole number and the fraction together, not just to the whole part.
Do I need to simplify the answer?
Converting never creates a common factor that was not already there, but if the fraction part was not in lowest terms, the improper fraction will not be either. For example 22/8 = 2 6/8 simplifies to 2 3/4 (11/4). The converter shows the simplified form.
Why use improper fractions instead of mixed numbers?
Improper fractions are easier to multiply and divide: 2 1/2 × 1 1/3 becomes 5/2 × 4/3 = 20/6 = 10/3. Mixed numbers are easier to read for measurements and recipes, so you often convert back at the end.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.