ClearQuip · Everyday math

Fraction calculator

Two fractions, one operation, lowest terms

This fraction calculator adds, subtracts, multiplies, or divides two fractions and reduces the answer. You enter a numerator and a denominator for each fraction. Mixed numbers should be converted to improper fractions first, so 1 1/2 is entered as 3/2.

Inputs

Result

Fill in the fields and press Calculate.

Disclaimer: Exact fraction arithmetic for the integers you enter.

How to use

  1. Choose add, subtract, multiply, or divide.
  2. Enter the first fraction as numerator over denominator.
  3. Enter the second fraction the same way. Use a negative numerator for a negative fraction.
  4. Press Calculate. The hero shows the reduced fraction and a decimal beside it.

How it's calculated

Addition and subtraction use a common denominator: a/b + c/d = (ad + bc) / bd, and subtraction flips the sign in the middle. Multiplication is (a×c) / (b×d). Division by c/d is multiplication by d/c.

The greatest common divisor of the numerator and the denominator then divides both, so 2/4 becomes 1/2. A negative sign is kept on the numerator.

Worked example

1/2 + 1/3 = (3 + 2) / 6 = 5/6, which is about 0.833. 1/2 ÷ 1/4 = 1/2 × 4/1 = 2/1. Subtracting 3/4 from 1/2 gives (2 − 3) / 4 = −1/4.

Assumptions

Integers in all four boxes. A zero denominator is rejected. Dividing by a zero numerator is rejected. The decimal is the reduced fraction as a number, not a rounded measurement.

FAQ

How do I enter a mixed number?

Convert it first. 2 1/4 is 9/4. The page does not have a whole-number box.

Can denominators be negative?

Yes. The reducer moves a negative sign onto the numerator so the denominator is shown positive.

What is lowest terms?

Numerator and denominator have been divided by the largest integer that goes into both.

Does this handle decimals inside a fraction?

The boxes accept numbers, but the reducer uses integer arithmetic. Use whole numerators and denominators.

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