Fraction Calculator

How to add, subtract, multiply, or divide fractions

Enter each fraction as an optional whole number plus a numerator and a denominator. Both are converted to improper fractions, the chosen operation is applied, and the result is reduced by its greatest common divisor.

You get the answer as an improper fraction, as a mixed number, and as a decimal, along with the working that produced it.

• Enter fraction A: whole number (optional), numerator, denominator.
• Enter fraction B the same way.
• Choose add, subtract, multiply, or divide.
• Read the reduced result, the mixed-number form, and the decimal equivalent.
• Follow the step lines if you need to show your working, since they list the common denominator and the reduction.

Mixed numbers, improper fractions, and negatives

The whole box turns a plain fraction into a mixed number. Enter 2 as the whole, 3 as the numerator, and 4 as the denominator, and the tool converts it internally to the improper fraction 11/4 before any arithmetic runs. Add 1/2 to that and the working shows 11/4 and 1/2, a common denominator of 8, and a reduced answer of 13/4, displayed as the mixed number 3 1/4 and the decimal 3.25.

Signs follow the standard convention. When a whole part is present it carries the sign for the whole quantity, so -2 with 1 and 2 means minus two and a half rather than minus two plus a half. With the whole box empty, a negative numerator makes the fraction negative, and a negative denominator is normalized into the numerator when the answer is reduced.

The result panel always shows all three forms at once, so you can quote whichever the question asked for. An answer of 2/1 is shown as 2 in the mixed line, and an answer that stays a proper fraction repeats itself in the mixed line rather than being blanked out.

• Mixed number: whole 2, numerator 3, denominator 4 means 11/4.
• Negative mixed number: whole -2, numerator 1, denominator 2 means -5/2.
• Negative simple fraction: leave the whole box empty and use a negative numerator.
• Every answer appears reduced, as a mixed number, and as a decimal.

Reading the steps, and where the method differs from a textbook

For addition and subtraction the calculator uses the product of the two denominators as the common denominator, not the least common multiple. Adding 1/4 and 1/6 it writes 4 x 6 = 24, rewrites the pair as 6/24 and 4/24, gets 10/24, and then simplifies by 2 to reach 5/12. A textbook would have used 12 from the start and reached the same 5/12 in one fewer reduction.

That is a deliberate trade: the intermediate numbers are larger, but the method is the same for every pair and the final answer is always fully reduced by the greatest common divisor. If you are copying the working into homework, expect the middle line to look bigger than the one in the answer key, and expect the last line to match.

Division is implemented as multiplication by the reciprocal, and the step line says so: 1/2 divided by 1/4 is shown as 1/2 x 4/1 = 4/2, then simplified to 2/1. Because the reciprocal of zero does not exist, dividing by a fraction whose numerator is zero is refused with a message rather than producing an infinity, and a zero denominator anywhere is rejected before any arithmetic runs.

• Common denominator is the product of the denominators, then reduced by the GCD.
• 1/4 plus 1/6 goes through 24 and lands on 5/12.
• Division is shown explicitly as multiplication by the reciprocal.
• Zero denominators and division by zero are refused with a message.