How to use
- Enter the first fraction. For a mixed number such as 1 1/2, put 1 in Whole.
- Choose add, subtract, multiply or divide.
- Enter the second fraction.
- Read the simplified answer, the mixed number, the decimal and the step-by-step working.
How fraction arithmetic works
- Add or subtract: rewrite both fractions over the least common denominator (LCD), then add or subtract the numerators.
- Multiply: multiply the tops together and the bottoms together.
- Divide: flip the second fraction (its reciprocal) and multiply.
- Simplify: divide the top and bottom by their greatest common divisor (GCD), found with Euclid’s algorithm.
Mixed numbers become improper fractions first: 1 1/2 = 3/2.
Examples
- 1/2 + 1/3: the LCD is 6, so 3/6 + 2/6 = 5/6.
- 3/4 + 5/6: 9/12 + 10/12 = 19/12 = 1 7/12 ≈ 1.583333333.
- 1 1/2 × 2/3: 3/2 × 2/3 = 6/6 = 1.
- 3/4 ÷ 1/8: 3/4 × 8/1 = 24/4 = 6.
- 3 5/11 − 4 3/4: 152/44 − 209/44 = −57/44 = −1 13/44.
Common fractions as decimals
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.33% |
| 2/3 | 0.(6) | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1(6) | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/12 | 0.08(3) | 8.33% |
Digits in brackets repeat forever: 0.1(6) means 0.1666…
Negative numbers and exact answers
For a negative mixed number, put the minus sign on the whole number. −2 1/4 means −(2 + 1/4) = −9/4.
The calculator works with whole numbers throughout, so answers are exact. A denominator of 0, or dividing by a fraction equal to 0, is undefined and shows an error.
Comparing two quantities instead? The ratio calculator simplifies ratios the same way, with the GCD.