Calculate and simplify fractions
Use integer numerators and nonzero denominators.
Fraction operation rules
Let the fractions be a/b and c/d.
The final numerator and denominator are divided by their greatest common divisor. That creates the simplest form.
Get a clear result
- Enter the top and bottom values for the first fraction.
- Choose addition, subtraction, multiplication, or division.
- Enter the numerator and denominator for the second fraction.
- Select Calculate fraction to show the answer above the form.
- Check the simplified fraction, mixed number, decimal, and working step.
Common fraction calculations
These examples show the simplified output for each operation.
| First fraction | Operation | Second fraction | Simplified result | Decimal |
|---|---|---|---|---|
| 3/4 | + | 2/5 | 23/20 | 1.15 |
| 7/8 | − | 1/6 | 17/24 | 0.7083333333 |
| 7/8 | × | 4/9 | 7/18 | 0.3888888889 |
| 5/6 | ÷ | 10/9 | 3/4 | 0.75 |
Work confidently with simple fractions
Fraction parts and signs
Fractions show parts of a whole. The top value is the numerator. The bottom value is the denominator. A denominator tells you how many equal parts exist. A numerator tells you how many parts are selected.
Start by keeping every denominator nonzero. A zero denominator has no valid value. Negative signs can appear in either part of a fraction. The calculator moves a negative denominator to the numerator. This keeps the displayed answer consistent and easier to read.
Operations and reduction
Addition and subtraction need a common denominator. The calculator multiplies across to create one. It then adds or subtracts the matching numerator values. For example, one half plus one third becomes three sixths plus two sixths. The result is five sixths.
Multiplication is usually faster. Multiply the top numbers together. Then multiply the bottom numbers together. Cross-canceling can reduce numbers before multiplying. The calculator reduces the completed answer automatically. That helps avoid long equivalent fractions.
Division follows a useful rule. Keep the first fraction. Reverse the second fraction. Then multiply. This reversed fraction is called the reciprocal. Division by zero is never allowed. A fraction with zero as its numerator equals zero, so it cannot be used as the divisor.
Simplifying is important because it gives the cleanest equivalent fraction. Find the greatest common divisor of the numerator and denominator. Divide both values by that number. For instance, twelve eighteenth reduces by six. The simple result is two thirds.
Results for practical use
Mixed numbers provide another readable form. A fraction larger than one contains complete wholes and a remainder. Seven thirds becomes two and one third. Decimals are also helpful for measurement, money estimates, and comparisons. Repeating decimals are shown to ten places for a practical check.
Use exact fractions whenever precision matters. Cooking adjustments, classroom exercises, construction measurements, and probability often benefit from exact forms. Use the decimal result when a quick comparison is enough. Always review the working step when learning a new operation.
The calculator accepts negative values and large whole-number inputs. Enter each numerator and denominator carefully. Choose the correct operation before calculating. The result area appears above the form after submission. It includes the reduced result, mixed number, decimal value, and pre-reduction fraction.
Practice with a few known examples before relying on complex entries. Check whether the answer sign makes sense. Check whether division used a reciprocal. Finally, confirm the denominator is positive. These habits make fraction work clearer, faster, and more dependable.
Comparing equivalent values
Equivalent fractions represent the same amount using different numbers. One half equals two fourths and four eighths. Simplification does not change value. It only removes a shared factor. This is why a smaller answer can still be completely accurate.
Comparing fractions becomes easier after matching denominators. The larger numerator then identifies the larger fraction. You can also convert values to decimals. However, exact fractional form avoids rounding and preserves relationships between quantities. This supports careful later calculations.
Simple fraction calculator FAQs
1. What does this calculator do?
It adds, subtracts, multiplies, or divides two fractions. It also reduces the result, shows a mixed number when useful, and provides a decimal equivalent.
2. Can I enter negative fractions?
Yes. You can enter a negative numerator or denominator. The result is normalized so any negative sign appears in the numerator.
3. Why can a denominator not be zero?
Division by zero is undefined. A fraction uses its denominator to divide the numerator, so zero cannot be a valid denominator.
4. How are fractions simplified?
The calculator finds the greatest common divisor of the numerator and denominator. It divides both values by that divisor until the fraction is in simplest form.
5. Why does division reverse the second fraction?
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal swaps the numerator and denominator of the second fraction.
6. What is a mixed number?
A mixed number combines a whole number and a proper fraction. For example, seven thirds can be written as two and one third.
7. Does the calculator handle improper fractions?
Yes. Improper fractions are accepted and simplified. The result panel also converts them into a mixed number where applicable.
8. Are decimal results exact?
Some fractions end exactly, while others repeat forever. The calculator displays decimal values to ten places for a useful practical approximation.
9. Can I use whole numbers?
Yes. Enter a whole number as a fraction with denominator one. For example, use 5/1 to represent five.
10. What happens when I divide by zero?
The calculator stops the calculation and explains the issue. A zero fraction cannot be used as the divisor in a valid fraction division.
11. Why check the working step?
The working step helps you verify the selected operation. It also supports learning by showing whether denominators were combined, multiplied, or inverted correctly.