Fractions turn up constantly in recipes, tape measures and homework. This fraction calculator adds, subtracts, multiplies and divides two fractions or mixed numbers, such as 1 1/2 + 3/4. It shows the cross-multiplication step, reduces the answer to lowest terms using the greatest common divisor, and gives the result as an improper fraction, a mixed number and a decimal.
It is handy for woodworking cut lists measured in inches (for board volume, see the board foot calculator) and for scaling recipes. For part-to-part comparisons, the ratio calculator simplifies and scales ratios.
How to use the fraction calculator
- Enter the first fraction. For a mixed number like 1 1/2, put 1 as the whole number, 1 as the numerator and 2 as the denominator. Leave the whole number at 0 for a simple fraction.
- Choose the operation.
- Enter the second fraction the same way.
- For a negative mixed number, make the whole number negative (−2 1/3). For a negative simple fraction, make the numerator negative.
Formula
Mixed numbers are first converted to improper fractions: w n/d = (w × d + n)/d. The result is simplified by dividing the numerator and denominator by their greatest common divisor (GCD), found with Euclid's algorithm.
Worked example
1 1/2 + 3/4
- Convert: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
- Cross-multiply: (3 × 4 + 3 × 2)/(2 × 4) = (12 + 6)/8 = 18/8.
- Simplify: GCD(18, 8) = 2, so 18/8 = 9/4.
- Mixed number: 9 ÷ 4 = 2 remainder 1, so 2 1/4, or 2.25 as a decimal.
2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2.
Common fraction–decimal equivalents
Tape measures in the US are marked in sixteenths of an inch, so these are worth knowing.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/16 | 0.0625 | 9/16 | 0.5625 |
| 1/8 | 0.125 | 5/8 | 0.625 |
| 3/16 | 0.1875 | 11/16 | 0.6875 |
| 1/4 | 0.25 | 3/4 | 0.75 |
| 5/16 | 0.3125 | 13/16 | 0.8125 |
| 3/8 | 0.375 | 7/8 | 0.875 |
| 7/16 | 0.4375 | 15/16 | 0.9375 |
| 1/2 | 0.5 | 1/3 | 0.333… |
Least common denominator vs simply multiplying
Textbooks often teach adding fractions with the least common denominator (LCD): for 1/6 + 1/4 the LCD is 12, giving 2/12 + 3/12 = 5/12. Multiplying the denominators (6 × 4 = 24) also works, giving 4/24 + 6/24 = 10/24, which simplifies to the same 5/12. The calculator multiplies and then simplifies, so the final answer is identical. The LCD method just keeps the numbers smaller when you work by hand.
To divide by a fraction, multiply by its reciprocal (flip it). You can't divide by zero, or by a fraction equal to zero; there is no answer.
Caveats and assumptions
- Inputs are whole numbers (integers); for decimals, convert to a fraction first (0.25 = 1/4).
- Denominators cannot be zero, and you cannot divide by a fraction equal to zero.
- Very large numerators and denominators can exceed exact integer precision in browsers (above about 9 quadrillion).
- The decimal is rounded to six places; repeating decimals such as 1/3 are not exact.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over a common denominator, add the numerators, then simplify. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. 18/24: the GCD is 6, so it simplifies to 3/4.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 3/5 = (2 × 5 + 3)/5 = 13/5.
How do I turn a fraction into a decimal?
Divide the numerator by the denominator. 5/8 = 5 ÷ 8 = 0.625.
Sources
- OpenStax Prealgebra 2e — 4.1 Visualize Fractions — mixed numbers and improper fractions
- OpenStax Prealgebra 2e — 4.2 Multiply and Divide Fractions — reciprocal method
- OpenStax Prealgebra 2e — 4.5 Add and Subtract Fractions with Different Denominators — least common denominator
This calculator gives estimates for planning and education. Check measurements, local codes, supplier specs and your school's official policy before relying on a result. See our disclaimer and how we build and check calculators.