Mixed Number to Improper Fraction Calculator
Convert a mixed number to an improper fraction and back — 2⅓ becomes 7/3.
A mixed number writes a quantity as a whole part plus a proper fraction: 2⅓.
How the mixed number to improper fraction calculator works
A mixed number writes a quantity as a whole part plus a proper fraction: 2⅓. An improper fraction writes the same quantity with a numerator larger than its denominator: 7/3.
Going one way, multiply the whole number by the denominator and add the numerator, keeping the denominator: 2 × 3 + 1 = 7, so 7/3. Going back, divide and keep the remainder: 7 ÷ 3 is 2 remainder 1, so 2⅓.
Mixed numbers are easier to picture; improper fractions are easier to compute with, which is why arithmetic converts to improper form first and back at the end.
Formula: improper = (whole × denominator + numerator) / denominator
Worked examples
| Inputs | Improper fraction | Note |
|---|---|---|
| 2 and 1/3 | 7/3 | 7/3 |
| 5 and 3/4 | 23/4 | 23/4 |
| A negative mixed number | -7/3 | −7/3 |
FAQFrequently asked questions
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the denominator. 2⅓ becomes (2×3+1)/3 = 7/3.
How do I convert back?
Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator.
Why use improper fractions?
Because arithmetic is far easier on them. Adding or multiplying mixed numbers means converting anyway.
Is 7/3 wrong to leave as it is?
No. "Improper" is a name, not a criticism — it is a perfectly correct way to write the number, and often the more useful one.
How do negative mixed numbers work?
The minus applies to the whole quantity, so −2⅓ is −7/3, not −2 + ⅓.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.