Mixed Number to Improper Fraction Calculator
A mixed number like 3 2/5 combines a whole number and a proper fraction. This calculator converts it to an improper fraction (17/5) by reversing the process, shows every step, and simplifies the result using the greatest common divisor.
17/5
- 1
Multiply whole number by denominator
3 × 5 = 15 - 2
Add the numerator
15 + 2 = 17/5 - 3
Simplify and convert to decimal
17 ÷ 5 = 3.400000
How does this calculator work?
Multiply the whole number by the denominator and add the numerator to get the improper numerator; keep the denominator. For 3 2/5: (3 × 5) + 2 = 17 → 17/5. The calculator then simplifies using GCD. Instant conversion with full step-by-step working.
Formula
How this is calculated
To convert a mixed number to an improper fraction, multiply the whole-number part by the denominator of the fractional part, then add the numerator. This total becomes the new numerator of the improper fraction, and the denominator stays the same. For 3 2/5: (3 × 5) + 2 = 17, so the result is 17/5.
The calculator then checks whether the improper fraction can be simplified by finding the greatest common divisor (GCD) of the new numerator and the denominator using the Euclidean algorithm. If the GCD is greater than 1, both are divided by it to give the fully simplified form. For example 2 4/6 → (2 × 6 + 4)/6 = 16/6, and GCD(16, 6) = 2, giving 8/3.
Negative mixed numbers work by treating the whole-number part as negative — the fractional part is always entered as a positive proper fraction. The sign is applied to the final improper numerator.
Frequently asked questions
An improper fraction is one where the numerator is greater than or equal to the denominator — for example 17/5 or 7/3. It represents a value ≥ 1 and is the standard form used in arithmetic operations on fractions.
Multiply the whole number by the denominator, then add the numerator — this gives the new numerator. Keep the denominator the same. For 4 3/7: (4 × 7) + 3 = 31, so the result is 31/7.
Yes. After conversion it divides both the numerator and denominator by their greatest common divisor (GCD) to produce the simplest form. If the GCD is 1, the fraction is already fully reduced.
Also known as
TG we-Calculate Editorial Team. (2026). Mixed Number to Improper Fraction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/mixed-number-to-improper-fraction-calculator
TG we-Calculate Editorial Team. "Mixed Number to Improper Fraction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/mixed-number-to-improper-fraction-calculator.
TG we-Calculate Editorial Team, "Mixed Number to Improper Fraction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/mixed-number-to-improper-fraction-calculator
@misc{wecalculate_mixed_number_to_improper_fraction_calculator, title = {Mixed Number to Improper Fraction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/mixed-number-to-improper-fraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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