Mixed Fraction Calculator

Four operations, one set of boxes

Add, Subtract, Multiply, and Divide each take two mixed numbers. Every number has a whole, a numerator, and a denominator, so 2 1/2 is whole 2, numerator 1, denominator 2. Leave the whole at 0, or clear it, when you only have a proper or improper fraction such as 3/4. Leave the fraction blank when the value is a whole number and it is read as that number over 1. The Convert tab is separate: it turns a mixed number into an improper fraction, or an improper fraction back into a mixed number.

This mixed fraction calculator has no calculate button. The green result updates as soon as both denominators are valid, and the worked steps appear underneath in the order a teacher writes them: convert each mixed number to an improper fraction, do the operation, simplify, then turn the answer back into a mixed number. Switching between Add, Subtract, Multiply, and Divide keeps the numbers you typed. The boxes start filled with 2 1/2 + 1 3/4, so the steps are visible straight away, and the examples under the tool load a different problem when you click them.

The plus and minus button on each number sets the sign. A negative mixed number is written with the minus on the whole, so −2 1/3 means the whole of 2 1/3 is negative. On a phone the two numbers stack, with the operation sign between them.

Adding and subtracting the way you would on paper

Convert each mixed number first. Multiply the whole by the denominator and add the numerator. 2 1/2 becomes (2 × 2 + 1) / 2, which is 5/2. 1 3/4 becomes (1 × 4 + 3) / 4, which is 7/4. The same rule works when the whole is 0: the fraction is already improper or proper, so there is nothing to convert.

If the denominators differ, build equivalent fractions with the least common denominator. The least common denominator of 2 and 4 is 4, so 5/2 becomes 10/4 and 7/4 stays 7/4. Then add or subtract the numerators only: 10/4 + 7/4 = 17/4. Subtraction is the same line with a minus. 3 1/3 − 1 3/4 converts to 10/3 − 7/4, rewrites as 40/12 − 21/12, and lands on 19/12.

Some classes subtract by regrouping, which means borrowing 1 from the whole number when the first fraction is smaller than the second. That method and the improper-fraction method agree. These steps always convert first, because the same sequence works for addition, subtraction, multiplication, and division. After the arithmetic, divide the numerator and the denominator by their greatest common divisor, then turn an improper result back into a mixed number. 17 ÷ 4 is 4 remainder 1, so 17/4 is 4 1/4. 19 ÷ 12 is 1 remainder 7, so 19/12 is 1 7/12.

Multiplying and dividing mixed numbers

Convert to improper fractions before you multiply. Then multiply the numerators together and the denominators together. 2 1/2 × 1 1/3 is 5/2 × 4/3. Those fractions share a factor, so cancel before you multiply: 2 and 4 share a factor of 2, which leaves 5/1 × 2/3 = 10/3. 10 and 3 have no common factor greater than 1, and 10 ÷ 3 is 3 remainder 1, so the mixed number is 3 1/3. If nothing cancels, multiply straight across and simplify at the end. Both routes give the same fraction.

Division is multiplication by the reciprocal. Keep the first fraction, change the sign to multiplication, and flip the second fraction. 3 1/2 ÷ 1 3/4 becomes 7/2 ÷ 7/4, which is 7/2 × 4/7. Cancel 7 with 7 and 2 with 4, and the product is 2/1, the whole number 2. If the second number is zero, the tool stops, because dividing by zero has no answer.

Converting mixed numbers and improper fractions

A proper fraction has a numerator smaller than its denominator, such as 3/4. An improper fraction has a numerator that is larger than or equal to its denominator, such as 13/5. A mixed number writes the same value as a whole number beside a proper fraction, such as 2 3/5. The Convert tab runs either direction and shows the multiplication or the division you would do by hand.

Mixed to improper uses one formula: whole × denominator + numerator, all over the denominator. 2 3/5 is (2 × 5 + 3) / 5 = 13/5. If the mixed number is negative, the improper fraction is negative too: −1 3/4 = −(1 × 4 + 3) / 4 = −7/4. Improper to mixed is the reverse. Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. 11 ÷ 4 is 2 remainder 3, so 11/4 = 2 3/4. The converter simplifies first, so 8/6 becomes 4/3 and then 1 1/3.

Negative answers, zero, and simplest form

The minus sign sits on the whole number of the result. 1 1/4 − 2 1/2 is −5/4, written −1 1/4, which means the entire value 1 1/4 is negative. When the answer is a proper fraction, there is no whole number to carry the sign, so you see −3/4. A result of zero is just 0, even if a minus button was left on.

A denominator of zero is rejected, because a fraction with a zero denominator is undefined. Simplifying uses the greatest common divisor, also called the greatest common factor: the largest positive integer that divides the numerator and the denominator. If that divisor is 1, the fraction is already in lowest terms and the step says so. The decimal under the answer is exact when the fraction terminates within 18 decimal places. When the decimal repeats, or runs longer than that, it is rounded to six places and labelled about. Everything runs in the browser. The numbers are not sent anywhere, and nothing is stored after you close the tab.