Improper fraction to a mixed number
Divide the numerator by the denominator and keep both parts of the answer. Seventeen divided by five is three with two left over, so 17/5 is 3 and 2/5. The remainder always sits over the original denominator and is always smaller than it; a remainder equal to or larger than the denominator means the whole part is at least one short. Cancel the fraction first if it will cancel, because 34/10 and 17/5 give the same mixed number but only one of them is in lowest terms.
Euclid's algorithm, step by step
| 1 | 17 | 5 | 3 | 2 |
| 2 | 5 | 2 | 2 | 1 |
| 3 | 2 | 1 | 2 | 0 |
Results are provided as-is, with no warranty of accuracy. The method and its sources are published below so you can check the working.
The remainder is always smaller than the denominator. A remainder equal to or larger than it means the whole part came out one short.
Simplifying first changes how the answer is written, not what it is: 34/10 and 17/5 both come to 3 and 2/5.
A negative improper fraction carries its sign across the whole thing. Minus 17/5 is -3 and 2/5, meaning -(3 + 2/5) rather than -3 + 2/5.
How it works
How it is done
- Read each box as the exact decimal that was typed rather than as the binary number a browser stores it in, and count how many decimal places the longer of the two has.
- Multiply both the top and the bottom by ten to the power of that count. Scaling both halves by the same amount leaves the value of the fraction untouched while turning both into whole numbers.
- Run Euclid's algorithm on the two whole numbers with their signs removed — divide the larger by the smaller, then the smaller by the remainder, and keep going until a remainder of zero. The last divisor used is the greatest common divisor.
- Divide the top and the bottom by that divisor. What is left is the fraction in its lowest terms, with any minus sign moved onto the numerator so that -3/4 and 3/-4 come out the same way.
- Divide the numerator by the denominator once more for the mixed number — the quotient is the whole part and the remainder sits over the same denominator.
- Produce the decimal by long division, recording every remainder as it appears. A remainder of zero ends the expansion. A remainder that has already been seen means the digits from that point repeat forever, and they are shown in brackets.
What it assumes
- A minus sign always ends up on the numerator, so -3/4 and 3/-4 both come out as -3/4. They are the same number, and one canonical form is what makes two answers comparable.
- A fraction that divides exactly is written as a plain whole number rather than as something over one, so 10/5 comes out as 2 and never as 2/1.
- Decimal inputs are multiplied by a power of ten before anything else happens, so 2.5/0.75 is treated as 250/75. The answer is exact, but a value with many decimal places produces very large lowest terms.
- The repeating block of a decimal is only bracketed if it both starts and finishes within the number of places set under More options. Beyond that the expansion is cut off with an ellipsis rather than guessed at.
- Whole numbers above 9,007,199,254,740,991 cannot be shown in the numeric boxes without losing digits, so those boxes show a dash. The fraction itself is text and stays exact whatever its size.
- The rounded decimal and the percentage are rounded, to eight and four places. A value smaller than that rounds to zero in those two boxes while the exact form beside them is unchanged.
Common questions
Is an improper fraction wrong?
No — the name is a historical accident. 7/4 and 1¾ are the same number, and 7/4 is the form you want for arithmetic, because multiplying or dividing mixed numbers means converting them back first. Mixed numbers are for reading aloud and for measurements.
How do I turn a mixed number back into an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the denominator: 2⅗ is (2 × 5 + 3)/5 = 13/5. Type the improper form in to check that it simplifies back to the mixed number you started with.
Sources
Method written and checked by Tessalor on Jul 30, 2026.
The full method, worked example and every assumption behind this figure are on Fraction Simplifier.