Adding Fractions Calculator
Add two fractions and get the answer in lowest terms, as a mixed number and as a decimal.
Fractions can only be added once they share a denominator, because a third and a half are different-sized pieces.
How the adding fractions calculator works
Fractions can only be added once they share a denominator, because a third and a half are different-sized pieces. Multiply each fraction by whatever makes the denominators match — d₁ × d₂ always works — add the numerators, then reduce.
1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Using d₁ × d₂ is not always the smallest common denominator, but reducing at the end gets to the same answer.
Formula: a/b + c/d = (ad + cb) / bd; a/b × c/d = ac / bd; a/b ÷ c/d = ad / bc
Worked examples
| Inputs | Answer in lowest terms | Note |
|---|---|---|
| 1/2 + 1/3 | 5/6 | 5/6 |
| 3/4 + 5/6 | 19/12 | 19/12, or 1 7/12 |
| Adding to a whole | 1 | 1 |
FAQFrequently asked questions
How do I add fractions with different denominators?
Give them a common denominator, add the numerators, then reduce: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Do I add the denominators too?
No — that is the classic mistake. 1/2 + 1/3 is not 2/5. Only the numerators add, once the denominators match.
What is the lowest common denominator?
The smallest number both denominators divide into. Multiplying them always works and reducing afterwards gives the same result.
How do I add mixed numbers?
Convert each to an improper fraction first, add, then convert back.
What is 3/4 + 5/6?
19/12, which is 1 7/12.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.