Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer in lowest terms — with the mixed number, the decimal and the working that gets you there.
Addition and subtraction put both fractions over a common denominator (d₁ × d₂), then the numerators are added or subtracted.
How the fraction calculator works
Addition and subtraction put both fractions over a common denominator (d₁ × d₂), then the numerators are added or subtracted. Multiplication multiplies across the top and the bottom. Division multiplies by the reciprocal — flip the second fraction and multiply. The answer is then reduced by dividing the top and bottom by their greatest common divisor, which is what "lowest terms" means.
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 × 2/3 | 1/2 | 1/2 — the sixes cancel |
| 1/2 ÷ 1/4 | 2 | 2 — a half holds two quarters |
| 7/8 − 1/4 | 5/8 | 5/8 |
FAQFrequently asked questions
How do I add fractions with different denominators?
Put them over a common denominator first: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. The calculator uses d₁ × d₂ as the common denominator, then reduces.
What does "lowest terms" mean?
Top and bottom share no factor other than 1. 6/12 reduces to 1/2 by dividing both by 6, their greatest common divisor.
How do you divide fractions?
Flip the second fraction and multiply: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
What is a mixed number?
A whole number beside a proper fraction: 7/3 is 2 1/3. The row shows it whenever the answer is bigger than one.
Can I use negative fractions?
Yes — put the minus sign on either numerator; the answer carries the sign.
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)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.