Fractions Calculator – Add, Subtract, Multiply, Divide & Simplify Fractions
This free fractions calculator solves any fraction problem in real time. Use it as a fraction cal to add, subtract, multiply, or divide two fractions, or as a fraction solver that shows every step of the working process. The calculator automatically simplifies the result, displays the decimal and percentage equivalent, and converts improper fractions to mixed numbers. It supports proper fractions, improper fractions, negative fractions, and mixed numbers.
Fractions Calculator
Fraction Calculator
Enter two fractions, select an operation, and get an instant result with full working steps.
The calculator works in real time — adjust any value and the result updates instantly. Enable Mixed Number Mode to enter fractions like 2½ or 3¼ as whole-number and fraction components. The Show Steps button reveals the full working for the selected operation, making this a complete fraction solver for learning and checking work.
Simplify Fractions – Quick Simplifier Tool
Enter any fraction below to reduce it to its simplest form. The tool divides both numerator and denominator by their Greatest Common Factor (GCF) to find the lowest terms.
Simplify a Fraction
Enter a fraction to reduce it to lowest terms instantly.
How Simplification Works
To simplify a fraction, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it.
A fraction is in simplest form (also called lowest terms) when the GCF of the numerator and denominator is exactly 1. No further simplification is possible at that point.
Fractions Chart – Common Fractions, Decimals & Percentages
This fractions chart lists common fractions alongside their decimal and percentage equivalents. Use it as a quick-reference table when working with fractions, decimals, or percentages interchangeably.
| Fraction | Simplified | Decimal | Percentage |
|---|---|---|---|
| Halves | |||
| 1/2 | 1/2 | 0.5 | 50% |
| Thirds | |||
| 1/3 | 1/3 | 0.3333… | 33.33% |
| 2/3 | 2/3 | 0.6667… | 66.67% |
| Quarters (Fourths) | |||
| 1/4 | 1/4 | 0.25 | 25% |
| 2/4 | 1/2 | 0.5 | 50% |
| 3/4 | 3/4 | 0.75 | 75% |
| Fifths | |||
| 1/5 | 1/5 | 0.2 | 20% |
| 2/5 | 2/5 | 0.4 | 40% |
| 3/5 | 3/5 | 0.6 | 60% |
| 4/5 | 4/5 | 0.8 | 80% |
| Sixths | |||
| 1/6 | 1/6 | 0.1667… | 16.67% |
| 2/6 | 1/3 | 0.3333… | 33.33% |
| 3/6 | 1/2 | 0.5 | 50% |
| 4/6 | 2/3 | 0.6667… | 66.67% |
| 5/6 | 5/6 | 0.8333… | 83.33% |
| Eighths | |||
| 1/8 | 1/8 | 0.125 | 12.5% |
| 2/8 | 1/4 | 0.25 | 25% |
| 3/8 | 3/8 | 0.375 | 37.5% |
| 4/8 | 1/2 | 0.5 | 50% |
| 5/8 | 5/8 | 0.625 | 62.5% |
| 6/8 | 3/4 | 0.75 | 75% |
| 7/8 | 7/8 | 0.875 | 87.5% |
| Tenths | |||
| 1/10 | 1/10 | 0.1 | 10% |
| 3/10 | 3/10 | 0.3 | 30% |
| 7/10 | 7/10 | 0.7 | 70% |
| 9/10 | 9/10 | 0.9 | 90% |
| Twelfths | |||
| 1/12 | 1/12 | 0.0833… | 8.33% |
| 3/12 | 1/4 | 0.25 | 25% |
| 4/12 | 1/3 | 0.3333… | 33.33% |
| 6/12 | 1/2 | 0.5 | 50% |
| 8/12 | 2/3 | 0.6667… | 66.67% |
| 9/12 | 3/4 | 0.75 | 75% |
| 11/12 | 11/12 | 0.9167… | 91.67% |
| Sixteenths | |||
| 1/16 | 1/16 | 0.0625 | 6.25% |
| 3/16 | 3/16 | 0.1875 | 18.75% |
| 5/16 | 5/16 | 0.3125 | 31.25% |
| 7/16 | 7/16 | 0.4375 | 43.75% |
| 9/16 | 9/16 | 0.5625 | 56.25% |
| 11/16 | 11/16 | 0.6875 | 68.75% |
| 13/16 | 13/16 | 0.8125 | 81.25% |
| 15/16 | 15/16 | 0.9375 | 93.75% |
How to Calculate Fractions – Step-by-Step Guide
How to Add Fractions
Adding fractions requires a common denominator — both fractions must have the same denominator before you can add the numerators.
- Find the Least Common Denominator (LCD) of the two denominators.
- Convert each fraction to an equivalent fraction with the LCD as its denominator by multiplying numerator and denominator by the same value.
- Add the numerators. The denominator stays the same.
- Simplify the result by dividing numerator and denominator by their GCF.
Example: 1/4 + 1/6 → LCD = 12 → 3/12 + 2/12 = 5/12
How to Subtract Fractions
Subtraction follows the exact same steps as addition, using the LCD and subtracting the numerators instead of adding them.
Example: 5/6 − 1/4 → LCD = 12 → 10/12 − 3/12 = 7/12
How to Multiply Fractions
Multiplication is straightforward — no common denominator is needed. Multiply the numerators together and the denominators together, then simplify.
- Multiply the two numerators: a × c
- Multiply the two denominators: b × d
- Write the result as (a×c) / (b×d)
- Simplify by dividing numerator and denominator by their GCF.
Example: 2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2
How to Divide Fractions
To divide fractions, keep the first fraction, change the division sign to multiplication, and flip the second fraction (find its reciprocal). Then follow the multiplication rules.
- Keep the first fraction as it is.
- Change ÷ to ×.
- Flip the second fraction (swap numerator and denominator).
- Multiply numerators and denominators.
- Simplify the result.
Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1½
How to Simplify Fractions After Solving
After performing any fraction operation, always check whether the result can be simplified. Find the GCF of the numerator and denominator and divide both by it. This calculator simplifies every result automatically — you can see the working in the step-by-step panel.
Fraction Rules & Formulas – Quick Reference
Worked Examples
Mixed Numbers & Improper Fractions
A mixed number combines a whole number and a proper fraction (e.g., 2¾). An improper fraction has a numerator greater than or equal to its denominator (e.g., 11/4). Both represent the same value — the calculator works with both forms.
Mixed Number to Improper Fraction
Improper Fraction to Mixed Number
The fractions calculator automatically shows the mixed number form whenever the result is an improper fraction. To enter a mixed number, tick Mixed Number Mode at the top of the calculator and enter the whole number, numerator, and denominator separately.
Fraction to Decimal and Percentage
Converting a Fraction to a Decimal
Divide the numerator by the denominator. The result is the decimal equivalent.
Converting a Fraction to a Percentage
Convert to a decimal first, then multiply by 100 and add the percent symbol.
The fractions calculator displays both the decimal and percentage equivalents for every result automatically. You can use the fractions chart above as a quick-reference for the most common conversions without needing to calculate.
When Are Decimal and Percent Forms Useful?
- Comparing fractions: It is easier to compare 0.667 and 0.75 than 2/3 and 3/4, even though the values are the same.
- Test scores and grades: Scores are usually reported as percentages, so knowing that 7/8 = 87.5% is useful for students.
- Money and measurements: Currency and measurements use decimals more naturally than fractions.
- Recipes and quantities: Some conversions between imperial and metric measurements require fraction-to-decimal skills.
Common Fraction Mistakes to Avoid
- Adding the denominators instead of finding a common one. The most common error. When adding 1/3 + 1/4, the answer is NOT 2/7. You must find the LCD (12), convert both fractions, and then add: 4/12 + 3/12 = 7/12.
- Forgetting to simplify the final answer. A result like 6/8 is technically correct but is not in simplest form. Reduce every answer by dividing numerator and denominator by their GCF (GCF of 6 and 8 is 2, so 6/8 = 3/4).
- Dividing fractions without flipping the second fraction. For division you must take the reciprocal of the divisor before multiplying. 1/2 ÷ 1/4 ≠ 1/2 × 1/4. Correct: 1/2 × 4/1 = 4/2 = 2.
- Confusing mixed numbers with improper fractions when multiplying. Convert any mixed number to an improper fraction before performing multiplication or division. Multiplying whole and fractional parts separately gives the wrong answer.
- Sign errors with negative fractions. A negative sign applies to the entire fraction. −3/4 is not the same as (−3)/(−4) = 3/4. The calculator handles negative signs in the numerator field.
- Forgetting that a fraction with denominator 1 is a whole number. 5/1 = 5 and 0/4 = 0. If the denominator divides the numerator exactly, the result is a whole number, not a fraction.
- Rounding repeating decimals incorrectly. 1/3 = 0.3333… is a repeating decimal, not exactly 0.33. Using 0.33 in calculations that feed back into fractions will introduce rounding errors. Work with the fraction form for accuracy.