Mixed Number Calculator
Add, subtract, multiply and divide mixed numbers and get the answer as both a mixed number and an improper fraction.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Mixed numbers are easiest to work with if you convert them to improper fractions first, do the arithmetic, then convert back. This calculator does each step for you.
Worked example
calculated with the default values below
First whole number 2 · First numerator 1 · First denominator 2 · Operation Add (+) · Second whole number 1 · Second numerator 3 · Second denominator 4 Mixed number result 4 1/4 · As improper fraction 17/4 · Decimal value 4.25
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
A = w₁D₁ + n₁, B = w₂D₂ + n₂; n = AD₂ ± BD₁, d = D₁D₂; n → n ÷ g, d → d ÷ g, g = gcd(n, d)
- A
- first number as improper numerator
- B
- second improper numerator
- w₁, w₂
- whole-number parts
- n₁, n₂
- fractional numerators
- D₁
- first denominator
- D₂
- second denominator
- n
- result numerator
- d
- result denominator
- g
- gcd for reduction
Sign follows the whole-number component. Improper negative results are split into a signed whole part plus a non-negative remainder; a negative proper fraction with whole part zero keeps its negative sign (for example, −1/2). Division by zero is rejected.
Frequently asked questions
Why does my mixed number result get simplified to smaller fractions than I entered?
The tool first turns each mixed number into an improper fraction using whole times denominator plus numerator, then combines them with the chosen operation and reduces by the greatest common divisor. So 2 and 1/2 plus 1 and 3/4 becomes 5/2 plus 7/4, or 17/4, which it shows as 4 and 1/4 rather than leaving the raw 17/4. Negative wholes are handled by signing the whole fraction before combining, and the Decimal value output is the final improper fraction divided straight through.