What is a mixed number?

A mixed number combines a whole-number part and a proper fraction, for example 3 and 1/2. It is shorthand for the sum of the two parts (3 + 1/2 = 7/2 as an improper fraction).

How do you add mixed numbers?

Convert each mixed number to an improper fraction, find the lowest common denominator (LCD), rewrite both fractions over that LCD, add the numerators, then simplify the result and convert back to a mixed number. The calculator shows every one of these steps.

How do you subtract mixed numbers?

The process is the same as addition except you subtract the numerators after rewriting over the LCD. If the result is negative the calculator displays it with a leading minus sign.

How do you multiply mixed numbers?

Convert both to improper fractions, multiply numerator by numerator and denominator by denominator, then simplify using the greatest common divisor (GCD). There is no need to find a common denominator for multiplication.

How do you divide mixed numbers?

Convert the dividend to an improper fraction, flip the divisor (take its reciprocal), then multiply. For example 2 and 1/2 divided by 1 and 1/4 becomes (5/2) times (4/5) = 20/10 = 2.

How is the fraction simplified?

The calculator divides both the numerator and denominator by their greatest common divisor (GCD), found with the Euclidean algorithm. The result is always in lowest terms.

Mixed Number Calculator

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 5/4 is 4/5
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.