Fraction Calculator
Type two fractions or mixed numbers, choose +, −, × or ÷ and get the answer as a simplified fraction, a mixed number and a decimal, with every step of the working shown.
The small box on the left of each fraction is an optional whole number for mixed numbers like 1 ½. Use a minus sign for negative numbers.
Step-by-step working
Simplify a fraction
Decimal to fraction
Put repeating digits in brackets: 0.(3) = 1/3, 0.1(6) = 1/6.
How to use the Fraction Calculator
- Enter the first fraction: numerator on top, denominator below, and an optional whole number on the left for mixed numbers.
- Choose the operation: +, −, × or ÷.
- Enter the second fraction the same way. Use a minus sign for negative numbers.
- Press Solve to see the simplified answer, mixed number, decimal and the full working.
- Use the mini tools below to simplify a single fraction or turn a decimal into a fraction.
Fraction rules with worked examples
| Operation | Rule | Example |
|---|---|---|
| Addition | a/b + c/d = (a·d + c·b) / (b·d), or use the LCM of b and d | 1/4 + 1/6 = 3/12 + 2/12 = 5/12 |
| Subtraction | a/b − c/d = (a·d − c·b) / (b·d) | 3/4 − 1/3 = 9/12 − 4/12 = 5/12 |
| Multiplication | a/b × c/d = (a·c) / (b·d) | 2/3 × 3/4 = 6/12 = 1/2 |
| Division | a/b ÷ c/d = a/b × d/c | 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 |
| Mixed to improper | w n/d = (w·d + n) / d | 2 3/5 = (2·5 + 3)/5 = 13/5 |
| Simplify | Divide top and bottom by the GCD | 18/24 ÷ 6 = 3/4 |
Example: adding mixed numbers step by step
Work out 1 1/2 + 2/3:
- Convert the mixed number to an improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
- Find the least common multiple of the denominators: LCM(2, 3) = 6.
- Rewrite both fractions over 6: 3/2 = 9/6 and 2/3 = 4/6.
- Add the numerators: 9/6 + 4/6 = 13/6.
- GCD(13, 6) = 1, so 13/6 is already simplified. As a mixed number, 13 ÷ 6 = 2 remainder 1, so the answer is 2 1/6, or 2.1666… as a decimal.
Common fractions as decimals and percentages
| Fraction | Decimal | Percent | Fraction | Decimal | Percent |
|---|---|---|---|---|---|
| 1/2 | 0.5 | 50% | 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333… | 33.3% | 3/8 | 0.375 | 37.5% |
| 2/3 | 0.666… | 66.7% | 5/8 | 0.625 | 62.5% |
| 1/4 | 0.25 | 25% | 1/10 | 0.1 | 10% |
| 3/4 | 0.75 | 75% | 1/12 | 0.0833… | 8.33% |
| 1/5 | 0.2 | 20% | 1/16 | 0.0625 | 6.25% |
| 1/6 | 0.1666… | 16.7% | 1/20 | 0.05 | 5% |
Frequently asked questions
How do you add fractions with different denominators?
Find the least common multiple (LCM) of the denominators, rewrite each fraction with that denominator, then add the numerators. For example 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 1/6.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example 2/3 × 3/4 = 6/12 = 1/2. Mixed numbers must be converted to improper fractions first.
How do you divide fractions?
Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). For example 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
How do I enter a mixed number?
Type the whole number in the small box to the left of the fraction and the fractional part in the numerator and denominator boxes. For a negative mixed number such as −2 1/3, put the minus sign on the whole number only.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD). For 18/24 the GCD is 6, so 18/24 = 3/4.
Why do I get an error about dividing by zero?
A fraction with a denominator of 0 is undefined, and you cannot divide by a fraction that equals 0. Change the values and the calculator will update straight away.
How do I convert a repeating decimal to a fraction?
Type the repeating digits in brackets in the decimal to fraction tool. For example 0.(3) gives 1/3 and 0.1(6) gives 1/6.