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How do I add fractions with different denominators?

Short answer

Rewrite both fractions over a common denominator, add the numerators, then simplify. For 1/3 + 1/4, the least common denominator is 12, so 4/12 + 3/12 = 7/12. A free fraction calculator shows the common denominator and the simplified answer step by step, right in your browser.

Finding the common denominator

The least common denominator is the least common multiple of the two denominators. For 3 and 4 it is 12; for 6 and 8 it is 24. Multiplying both the top and bottom of each fraction by the same factor changes its appearance but not its value, which is why 1/3 can become 4/12. Any common multiple works, the least one just keeps the numbers small and the simplification easy.

The classic mistake

Adding tops and bottoms separately, 1/3 + 1/4 = 2/7, is wrong because the pieces are different sizes: thirds are bigger than quarters. The common denominator step converts both into twelfths, pieces of equal size, and only then can the counts be added. Subtraction works identically, and mixed numbers should be converted to improper fractions before starting.

Step by step

  1. Enter both fractions. Type the numerators and denominators, mixed numbers included.
  2. Pick the operation. Add, subtract, multiply or divide.
  3. Read the worked answer. The calculator shows the common denominator, the raw result and the simplified fraction.

Frequently asked questions

What is 1/3 plus 1/4?

7/12. Over the common denominator 12, the sum is 4/12 + 3/12.

Why can I not just add the denominators?

Because the fractions count pieces of different sizes. Only after rewriting them with a common denominator do the numerators count equal pieces.

How do I add mixed numbers?

Convert each to an improper fraction first, add as usual, then convert back and simplify.

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