By This fraction calculator adds, subtracts, multiplies and divides fractions, mixed numbers and whole numbers. It shows the working (the common denominator for adding and subtracting, or the reciprocal for dividing), then gives the answer in lowest terms, as a mixed number when it’s more than 1, and as a decimal.
It’s free and needs no sign-up.
How to use it
- Type the first fraction:
3/4, a mixed number like1 1/2(with a space), a whole number like5, or a negative like-2/3. - Choose +, −, × or ÷.
- Type the second fraction and press Calculate.
Fraction rules
| Operation | Rule | Example |
|---|---|---|
| Add | common denominator, add numerators | \( \frac12 + \frac13 = \frac36 + \frac26 = \frac56 \) |
| Subtract | common denominator, subtract numerators | \( \frac23 - \frac14 = \frac{8}{12} - \frac{3}{12} = \frac{5}{12} \) |
| Multiply | multiply tops, multiply bottoms | \( \frac35 \times \frac{10}{9} = \frac{30}{45} = \frac23 \) |
| Divide | multiply by the reciprocal | \( \frac34 \div \frac56 = \frac34 \times \frac65 = \frac{9}{10} \) |
Worked example: adding
\( \frac12 + \frac13 \) (as loaded above). The least common denominator of 2 and 3 is 6, so \( \frac12 = \frac36 \) and \( \frac13 = \frac26 \). Adding gives \( \frac56 \approx 0.833 \).
Worked example: mixed numbers
\( 1\frac12 \times \frac23 \). Convert to an improper fraction first: \( 1\frac12 = \frac32 \). Then \( \frac32 \times \frac23 = \frac66 = 1 \).
Worked example: an improper result
\( \frac53 + \frac12 = \frac{10}{6} + \frac36 = \frac{13}{6} = 2\frac16 \approx 2.167 \).
Simplifying
Divide the numerator and denominator by their greatest common factor: \( \frac{30}{45} \), with GCF 15, becomes \( \frac23 \). The calculator always simplifies fully.
Common mistakes
- Adding denominators. \( \frac12 + \frac13 \neq \frac25 \).
- Forgetting to flip the second fraction when dividing.
- Multiplying mixed numbers directly. Convert to improper fractions first: \( 1\frac12 \times 2 \) is 3, not \( 2\frac12 \).
- Leaving answers unsimplified.
Fractions in algebra and calculus
The same rules work with variables: \( \frac1x + \frac1{x + 1} = \frac{2x + 1}{x(x + 1)} \). Running that in reverse (splitting a fraction into simpler ones) is partial fraction decomposition, a key integration technique.
Related guides
- Fractions: How to Add, Subtract, Multiply and Divide
- Percentage Formula
- Exponent Rules
- Partial Fraction Decomposition
Further reading
- Fraction (Wikipedia) — definitions, arithmetic with fractions and history.
FAQ
How do you add fractions with different denominators?
Rewrite both with a common denominator (the least common multiple of the denominators), then add the numerators.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second: “keep, change, flip”.
How do you simplify a fraction?
Divide top and bottom by their greatest common factor.
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator: the quotient is the whole number and the remainder is the new numerator. \( \frac{13}{6} = 2\frac16 \).