FractionReference

Add fractions

Two values in, one exact sum out, with the common-denominator work shown underneath.

Try: — fractions, mixed numbers and decimals all work, negatives included.

Common questions

How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. For 3/8 + 1/4: the least common multiple of 8 and 4 is 8, so 1/4 = 2/8, and 3/8 + 2/8 = 5/8.
Do I have to use the least common denominator?
Any common denominator works — the product always does — but the least one keeps the numbers small. Either way the reduced answer is the same, and this page reduces at the end.
Can I add mixed numbers directly?
Type them as they are — 1 3/4 + 2 1/2 works. Internally they become improper fractions, are added exactly, and come back as both an improper fraction and a mixed number.
Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. See the full methodology.