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Add Fractions Calculator

Sum fractions, simplified.

How it is calculated

The tool adds two fractions by cross-multiplication: n1/d1 + n2/d2 = (n1·d2 + n2·d1) / (d1·d2), then divides top and bottom by their greatest common divisor, so the answer is always in lowest terms. It does not need the least common denominator first; reducing at the end gives the same fraction. All four boxes must be whole numbers with an absolute value below 2 billion. A decimal such as 2.5, a zero denominator, or a value that large gives no result. Numerators may be negative or zero, and a minus sign is always moved to the front. A whole-number answer is shown over 1 (1/2 + 1/2 gives 1/1). The answer is an improper fraction, not a mixed number.

Worked example

Add 3/4 and 5/6. Cross-multiply for the top: 3 × 6 + 5 × 4 = 18 + 20 = 38. The bottom is 4 × 6 = 24, giving 38/24. The greatest common divisor of 38 and 24 is 2, so divide both by 2. The calculator shows 19/12, which is 1 7/12 as a mixed number (about 1.583).

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Common mistakes

  • Adding tops and bottoms separately, so that 1/2 + 1/3 becomes 2/5. Denominators must be matched first, which the tool does.
  • Typing a mixed number such as 1 1/2 in one box. Convert it to an improper fraction (3/2) first.
  • Putting a decimal in a box (like 2.5 in a numerator). The tool shows no result; multiply top and bottom by 2 and enter whole numbers.
  • Entering 0 as a denominator. A fraction cannot have a zero denominator, so there is no result.
  • Reading 19/12 as an error because it is larger than 1. It is a correct improper fraction.

About this calculator

Adding two fractions with different denominators requires first rewriting both over a common denominator, typically the least common denominator (LCD), the smallest number both original denominators divide into evenly, before the numerators can simply be added together; the result is then reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor.

This process is one of the foundational skills in elementary and middle-school arithmetic, and it underlies practical tasks like combining measurements in recipes, adding 1/3 cup and 1/4 cup for example, adding fractional lengths in carpentry and construction measured in inches, and computing combined probabilities or proportions expressed as fractions in early statistics.

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