Adding fractions is one of the first real arithmetic skills that trips students up, mostly because it looks like ordinary addition but has an extra rule: the denominators have to match first. Here's the method, broken into the two cases you'll actually run into.
Adding Fractions with the Same Denominator
When two fractions already share a denominator, addition is simple: add the numerators and keep the denominator unchanged. For example, 1/5 + 2/5 = 3/5 — three of the same five equal parts.
Adding Fractions with Different Denominators
When the denominators differ, first rewrite both fractions with a common denominator — usually their least common multiple (LCM) — then add the numerators as before. For 1/2 + 1/3, the LCM of 2 and 3 is 6, so the problem becomes 3/6 + 2/6 = 5/6.
Adding Mixed Numbers
For mixed numbers like 1 1/2 + 2 1/3, add the whole numbers and fractional parts separately, then combine — or convert both to improper fractions first if the fractional parts don't simplify neatly. Our Mixed Number Calculator handles both cases automatically and shows every step.