A mixed number calculator that handles addition, subtraction, multiplication and division of mixed numbers in a single tool. Type in two mixed numbers, pick an operation, and the result appears instantly as a fully simplified mixed number — plus a decimal equivalent and a collapsible step-by-step working panel so you can see exactly how the answer was reached.
Mixed numbers come up constantly in cooking (1 and 3/4 cups), woodworking (2 and 5/8 inches), time management (1 and 1/2 hours), and any area where whole units and fractional remainders naturally occur together. Most calculators only handle pure fractions or decimals; this one works directly in the mixed-number format you already have.
How it works
Every operation follows the same two-stage approach taught in schools.
Stage 1 — convert to improper fractions. A mixed number w n/d (whole part w,
numerator n, denominator d) equals (w*d + n) / d. For example,
2 and 3/4 becomes (2*4 + 3)/4 = 11/4.
Stage 2 — apply the operation.
- Add / Subtract: find the lowest common denominator (LCD) of the two
denominators, rewrite each fraction over that LCD, then add or subtract the
numerators. LCD =
(d1 * d2) / GCD(d1, d2). - Multiply: multiply numerators together and denominators together:
(a/b) * (c/d) = (a*c)/(b*d). No common denominator is needed. - Divide: multiply by the reciprocal of the divisor:
(a/b) / (c/d) = (a/b) * (d/c) = (a*d)/(b*c).
After the operation the result is simplified by dividing numerator and denominator
by their GCD (Euclidean algorithm). Finally, the improper fraction is split back
into a whole part and a remainder fraction: whole = floor(|n| / d),
remainder = |n| mod d.
The tool uses JavaScript BigInt arithmetic throughout, so numerators and denominators never lose precision regardless of how large the intermediate values become.
Worked example
Add 1 and 1/2 to 2 and 3/4.
- Convert:
1 1/2 = 3/2,2 3/4 = 11/4 - LCD of 2 and 4 is 4
- Rewrite:
3/2 = 6/4 - Add numerators:
6 + 11 = 17 - Result:
17/4 - GCD(17, 4) = 1, already simplified
- Mixed number:
4 and 1/4(since 17 = 4*4 + 1)
Another example: divide 3 and 1/3 by 1 and 1/4.
- Convert:
3 1/3 = 10/3,1 1/4 = 5/4 - Flip divisor: reciprocal of
5/4is4/5 - Multiply:
(10/3) * (4/5) = 40/15 - Simplify: GCD(40, 15) = 5, so
40/15 = 8/3 - Mixed number:
2 and 2/3
Formula note
For all four operations the unifying formula is:
- Add:
a/b + c/d = (a*d + b*c) / (b*d) - Subtract:
a/b - c/d = (a*d - b*c) / (b*d) - Multiply:
a/b * c/d = (a*c) / (b*d) - Divide:
a/b / c/d = (a*d) / (b*c)
The LCD optimisation for addition and subtraction reduces the size of intermediate
values: instead of using b*d directly, the calculator divides by GCD(b, d) first,
keeping numbers smaller and simplification faster.
All arithmetic runs locally in your browser. No numbers are sent to a server.