Mixed Number Calculator

A mixed number is a whole number and a proper fraction written together: 2 1/3 means 2 + 1/3. Every operation on mixed numbers starts the same way, by turning each one into an improper fraction.

Converting. Multiply the whole number by the denominator, add the numerator, and keep the denominator. 2 1/3 becomes (2 x 3 + 1)/3 = 7/3, and 1 3/4 becomes (1 x 4 + 3)/4 = 7/4.

Adding and subtracting. Put both improper fractions over a common denominator. For 7/3 + 7/4 the least common denominator is 12, so the sum is 28/12 + 21/12 = 49/12. Some people add the whole numbers and the fractions separately instead (2 + 1 = 3, then 1/3 + 3/4 = 13/12, then carry the extra 1 to get 4 1/12). That works for addition and gets messy for subtraction when the second fraction is the larger one, which is why converting first is the safer habit.

Multiplying and dividing. Never multiply the whole parts and the fractions separately: 2 1/2 x 2 1/2 is not 4 1/4. Convert first, 5/2 x 5/2 = 25/4, which is 6 1/4. To divide, multiply by the reciprocal of the second improper fraction.

Converting back. Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator: 49 / 12 = 4 remainder 1, so 49/12 = 4 1/12. The calculator shows the answer both ways, along with the exact decimal, 4.08(3), where the bracketed 3 repeats forever.

Negative mixed numbers. The minus sign applies to the whole thing: -2 1/3 is -(2 + 1/3) = -7/3, not -2 + 1/3. Enter it as whole number -2, numerator 1, denominator 3.