Add Fractions Calculator: Add Two Fractions Step by Step

Why you cannot add the tops and the bottoms

The most common mistake in adding fractions is adding straight across: 1/2 + 1/3 is not 2/5. The denominators are not numbers to add — they are the size of the pieces. A half is three sixths and a third is two sixths, and only when both fractions are cut into sixths can you count the pieces: three plus two is five sixths. That is what the LCM does: it finds the smallest piece size both fractions share. For 1/2 and 1/3 that is 6; for 3/8 and 5/12 it is 24; for 1/4 and 1/4 it is 4, because the pieces already match. Once the denominators match, you add only the numerators and keep the denominator.

The worked example, in full

Take the defaults, 1/2 + 1/3. Step one: the denominators are 2 and 3, and their least common multiple is 6. Step two: convert. 1/2 is 3/6, because 6 ÷ 2 is 3 and 1 × 3 is 3; 1/3 is 2/6, because 6 ÷ 3 is 2 and 1 × 2 is 2. Step three: add the numerators, 3 + 2 = 5, and keep the denominator 6 — the sum is 5/6. Step four: simplify. The greatest common divisor of 5 and 6 is 1, so 5/6 is already in lowest terms. Step five, the decimal: 5 ÷ 6 is 0.8333. Every branch on this page follows the same five steps, and the calculator shows each one.

When the answer is improper

Sometimes the sum is bigger than one whole: 3/4 + 5/6 is 19/12, because the LCM of 4 and 6 is 12, 3/4 becomes 9/12 and 5/6 becomes 10/12, and 9 + 10 is 19. A fraction with a numerator bigger than its denominator is called improper, and it is a correct answer as it stands — but most people read it more easily as a mixed number. Divide 19 by 12: 12 goes in once with 7 left over, so 19/12 is 1 7/12, or 1.5833 as a decimal. The calculator shows both forms whenever the result is improper, and just the fraction when it is not.

Rounding convention, stated plainly: the fraction result is exact — no rounding anywhere in the LCM, conversion, addition, or simplification steps. The decimal is the exact fraction divided out and rounded to four decimal places, so 5/6 shows as 0.8333 and 19/24 as 0.7917.

Output · formula · meaning

Who uses this

• The homework checker: a student adds 1/2 + 1/3, gets 5/6, and sees every step — LCM 6, converted to 3/6 + 2/6, numerators added to 5 — so the answer is checked, not just copied.
• The home cook: a recipe calls for 3/8 cup plus 5/12 cup and the cook learns the total is 19/24 cup — just under 4/5 — before reaching for the measuring cups.
• The woodworker: adds 3/4 inch and 5/6 inch and gets 19/12 inches — 1 7/12 inches — in the mixed-number form a tape measure actually reads.
• The teacher: shows a class why 1/2 + 1/3 is not 2/5, with the sixths on the page: three sixths plus two sixths is five sixths, and the denominators never add.

Accuracy & limitations

The fraction arithmetic is exact: the LCM, the conversion, the addition, and the simplification use whole-number math with no rounding, so the fraction answer is always precisely right. Only the decimal is rounded, to four decimal places. Denominators must be positive whole numbers up to 9,999 — zero has no value as a denominator, negative denominators are rejected (put any minus sign on the numerator), and fractions above 9,999 are refused so the LCM stays exact. The calculator adds exactly two fractions; for three or more, add the first two, then add the third to the result.