Fraction Calculator
This fraction calculator adds, subtracts, multiplies, and divides two fractions and instantly shows the answer reduced to its lowest terms. Alongside the simplified fraction you also get the equivalent decimal value and, when the result is greater than one, its mixed-number form. Just enter each numerator and denominator, pick an operation, and the result updates as you type — perfect for homework, cooking measurements, woodworking, or any everyday math involving fractions.
Result
The denominator cannot be zero.
As a decimal
Mixed number
The result is always shown reduced to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).
Publicidad
How it works
To add or subtract fractions you need a common denominator. This calculator uses cross-multiplication: for a/b ± c/d the new numerator is a·d ± c·b and the new denominator is b·d. Multiplication is simpler — multiply the numerators together and the denominators together: (a·c)/(b·d). To divide, invert the second fraction and multiply, which gives (a·d)/(b·c). The raw result is then simplified: the calculator finds the greatest common divisor (GCD) of the numerator and denominator with the Euclidean algorithm and divides both by it, so 6/8 becomes 3/4. Any negative sign is moved to the numerator.
Common fractions as decimals and percentages
Some fractions come up so often that it helps to know their decimal and percentage equivalents by heart. To convert any fraction to a decimal you divide the numerator by the denominator, and to get the percentage you multiply that decimal by 100. Fractions like 1/3 and 2/3 give repeating decimals, so they are shown rounded. The table below lists the equivalents you will meet most often in cooking, discounts, test scores and everyday measurements.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 2/3 | 0.667… | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
Adding and subtracting with a common denominator
To add or subtract two fractions they must share the same denominator. Take 1/4 + 2/3: the smallest number both 4 and 3 divide into is 12, so rewrite each fraction over 12. One quarter becomes 3/12 (multiply top and bottom by 3) and two thirds becomes 8/12 (multiply by 4). Now the denominators match, so you simply add the numerators: 3/12 + 8/12 = 11/12. Since 11 and 12 share no common factor, the result is already in its lowest terms. Subtraction works the same way — line up the denominators, then subtract the numerators.
Publicidad
Preguntas frecuentes
- How do I add fractions with different denominators?
- First give both fractions a common denominator. The quickest way is cross-multiplication: for a/b + c/d the sum is (a·d + c·b) / (b·d). For example, 1/2 + 1/3 = (1·3 + 1·2) / (2·3) = 5/6. Then reduce the result if possible. This calculator does all of these steps for you automatically.
- How do I simplify a fraction?
- Divide both the numerator and the denominator by their greatest common divisor (GCD). For 8/12 the GCD is 4, so 8/12 = 2/3. A fraction is fully simplified when the only common factor left between numerator and denominator is 1. The calculator always returns the answer in this reduced form.
- How do I convert a fraction to a decimal?
- Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75, and 1/3 = 0.3333… Some fractions give exact decimals while others repeat. This tool shows the decimal value next to the fraction, rounded to six decimal places for clarity.
- What is a mixed number?
- A mixed number combines a whole number with a proper fraction, such as 1 1/2. It represents an improper fraction whose numerator is larger than its denominator. For instance 7/4 equals 1 3/4 because 4 goes into 7 once with 3 left over. The calculator shows this form whenever the result is greater than one.
- How do I multiply and divide fractions?
- To multiply, multiply the numerators together and the denominators together: 2/3 × 4/5 = 8/15. To divide, flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. You do not need a common denominator for multiplication or division, only for addition and subtraction.