The Fraction Calculator adds, subtracts, multiplies and divides two fractions and gives the answer reduced to its simplest form. You also get the answer as a mixed number, a decimal and a percentage. It works for proper fractions (3/4), improper fractions (11/4) and negative fractions. It is useful for homework, recipe scaling, carpentry measurements in inches and checking answers in competitive-exam practice.
How to use the fraction calculator
- Enter the numerator (top) and denominator (bottom) of the first fraction.
- Choose the operation: + − × ÷.
- Enter the second fraction, then press Calculate.
- For a whole number, use a denominator of 1 (5 = 5/1). For a mixed number such as 2¾, convert it first: (2 × 4 + 3)/4 = 11/4.
Rules for each operation
Adding and subtracting
Example: 1/2 + 1/3 = (1·3 + 1·2)/(2·3) = 5/6. When the denominators share a factor, use the least common denominator (LCD) to keep the numbers small: 5/12 + 1/8 → LCD 24 → 10/24 + 3/24 = 13/24.
Multiplying
Example: 2/3 × 9/10 = 18/30 = 3/5. Tip: cancel common factors before multiplying, 2/3 × 9/10 → 1/1 × 3/5.
Dividing
Example: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. In other words, there are six eighths in three quarters.
Simplifying fractions
A fraction is in its simplest form when the numerator and denominator have no common factor except 1. Divide both by their greatest common divisor (GCD):
Simplify 84/126. GCD(84, 126) = 42, so 84 ÷ 42 / 126 ÷ 42 = 2/3.
To find the GCD quickly, use Euclid’s method: 126 mod 84 = 42, then 84 mod 42 = 0, so the GCD is 42. The calculator uses the same algorithm.
Improper fractions and mixed numbers
- Improper → mixed: divide the numerator by the denominator. The quotient is the whole number and the remainder goes over the denominator. 17/5 = 3 remainder 2 = 3 2/5.
- Mixed → improper: whole × denominator + numerator, all over the denominator. 4 1/3 = (4 × 3 + 1)/3 = 13/3.
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… | 33.33% | 3/8 | 0.375 | 37.5% |
| 2/3 | 0.666… | 66.67% | 5/8 | 0.625 | 62.5% |
| 1/4 | 0.25 | 25% | 1/12 | 0.0833 | 8.33% |
| 3/4 | 0.75 | 75% | 1/16 | 0.0625 | 6.25% |
| 1/5 | 0.2 | 20% | 1/20 | 0.05 | 5% |
Real-life uses
- Cooking: halving a recipe that needs ¾ cup of sugar: ¾ × ½ = ⅜ cup.
- Carpentry and tailoring: inch measurements are often fractions. 5 ⅜″ + 2 ¾″ = 43/8 + 22/8 = 65/8 = 8 ⅛″.
- Sharing: if one partner owns ⅖ of a business and buys ⅓ of the other partner’s ⅗, they now own ⅖ + ⅕ = ⅗.
- Time: 1¾ hours = 1 hour 45 minutes, because ¾ × 60 = 45.
Common mistakes
- Adding the tops and the bottoms: 1/2 + 1/3 ≠ 2/5. You need a common denominator first.
- Flipping the wrong fraction when dividing. Only the second fraction (the divisor) is flipped.
- Forgetting to simplify the final answer, which loses marks in school exams.
- Using a zero denominator, which is undefined. The calculator will warn you.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, ideally the least common multiple of the denominators, then add the numerators. 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second (keep, change, flip). 2/5 ÷ 3/4 = 2/5 × 4/3 = 8/15.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. 45/60 has a GCD of 15, so it simplifies to 3/4.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 7/8 = 7 ÷ 8 = 0.875. Multiply by 100 to get a percentage: 87.5%.
Can I enter mixed numbers?
Convert them to improper fractions first: 3 1/2 becomes 7/2. The result is shown as a simplified fraction and as a mixed number.