Mixed Numbers Calculator

A mixed number combines a whole number and a fraction, such as 3 1/2 or 7 3/4. It represents a value greater than one whole. Mixed numbers are common in everyday life, from cooking measurements (2 1/2 cups of flour) to construction (a board that is 6 3/8 inches wide).

To do arithmetic with mixed numbers, you typically convert them to improper fractions first. An improper fraction has a numerator larger than its denominator. For example, 3 1/2 becomes 7/2 (multiply 3 by 2 and add 1 for the numerator, keep the denominator). This calculator handles the conversion and arithmetic automatically.

To add mixed numbers, convert each to an improper fraction, find a common denominator, add the numerators, then simplify back to a mixed number. For example, 2 1/3 + 1 1/4: convert to 7/3 and 5/4, find common denominator 12, add 28/12 + 15/12 = 43/12, then simplify to 3 7/12.

Subtraction works the same way. Convert to improper fractions, find a common denominator, subtract the numerators. If the result is an improper fraction, convert it back to a mixed number. This calculator shows each step so you can follow the working.

To multiply mixed numbers, convert both to improper fractions and multiply straight across (numerator times numerator, denominator times denominator). For example, 2 1/2 times 1 1/3: convert to 5/2 and 4/3, multiply to get 20/6, then simplify to 3 2/6 which reduces to 3 1/3.

To divide mixed numbers, convert to improper fractions, flip the second fraction (take the reciprocal), and multiply. For example, 3 1/2 divided by 1 1/4: convert to 7/2 and 5/4, flip to 7/2 times 4/5 = 28/10 = 2 4/5.