Mixed Number Calculator

How to add, subtract, multiply and divide mixed numbers

A mixed number calculator turns each mixed number into an improper fraction, does the operation and converts back. For 1 1/2 + 2 3/4 the improper fractions are 3/2 and 11/4. Over a common denominator of 4 they are 6/4 + 11/4 = 17/4, which is 4 1/4 as a mixed number. The steps under the result show every one of these moves for your own numbers.

The four operations

To add or subtract, the fractions need a common denominator: a/b ± c/d = (ad ± cb) / bd. To multiply, multiply the tops and the bottoms: 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 3 1/3. To divide, multiply by the reciprocal of the second number: 3 1/2 ÷ 1 3/4 = 7/2 × 4/7 = 28/14 = 2. Every result is reduced by dividing the top and bottom by their greatest common divisor, found with the GCF calculator.

Converting between mixed and improper

Mixed to improper: multiply the whole number by the denominator, add the numerator and keep the denominator, so 2 3/4 = (2 × 4 + 3)/4 = 11/4. Improper to mixed: divide the top by the bottom. The quotient is the whole part and the remainder is the new numerator, so 17 ÷ 4 = 4 remainder 1, giving 4 1/4. Use the fraction to decimal calculator for the decimal value, or the decimal to fraction calculator for the other direction.

Common mistakes

The classic error is to add the whole numbers and the fractions separately without a common denominator, or to multiply whole parts and fraction parts separately: 2 1/2 × 3 1/2 is not 6 1/4. Always go through improper fractions for multiplication and division. When you subtract, the result can be negative, for example 1 1/2 − 3 = −1 1/2. Recipes and woodworking measurements in inches use mixed numbers constantly, and a one-sixteenth slip compounds across several cuts.