Fraction Calculator with Simplified Steps
Add, subtract, multiply or divide proper fractions, improper fractions, mixed numbers and integers. Get an exact simplified answer, mixed-number form, decimal value, percentage and clear calculation steps.
Last Updated: July 25, 2026
Online Fraction Calculator
Enter values such as 3/4, -5/6, 2 1/3 or 7. Select an operation, then calculate. Use the second mode to simplify or convert one value.
Calculation steps
- Your exact calculation steps will appear here.
Try an example
Recent calculations
- Your last eight results will appear here.
How to Use This Fraction Calculator
- Choose Calculate two fractions to perform arithmetic, or choose Simplify or convert to work with one value.
- Enter each value as an integer, fraction or mixed number. Valid examples include
7,3/4,-5/6and2 1/3. - For two values, select addition, subtraction, multiplication or division. The selected operation appears with a pine background.
- Select the calculation button or press Enter. The answer panel appears after the buttons and shows exact and converted forms.
- Review the steps. They identify the least common denominator for addition or subtraction, cross-cancellation for multiplication or division, and the greatest common divisor used for simplification.
You may place spaces around the slash. A negative sign before a mixed number applies to the entire value, so -2 1/3 means negative seven-thirds. The tool also normalizes a negative denominator. For example, 1/-2 becomes -1/2. Do not enter decimals, commas, variables or full expressions in a fraction field.
1/2 + 1/3 equals 5/6. The least common denominator is 6, so the equivalent fractions are 3/6 and 2/6. Adding their numerators gives 5/6.What Is a Fraction Calculator?
A fraction calculator performs exact arithmetic on ratios of integers. This page handles proper fractions, improper fractions, mixed numbers and whole numbers. It reduces the final value to lowest terms and then presents the same result as an improper fraction, a mixed number, a decimal and a percentage.
The exact fraction remains the main answer because a decimal may repeat or require rounding. One-third is exactly 1/3, while its decimal expansion continues as 0.3333. The tool keeps integer numerators and denominators throughout the calculation. It does not convert the operands to floating-point values before finding the exact result.
Fraction Terms You Should Know
| Term | Meaning | Example |
|---|---|---|
| Numerator | The top number, showing how many selected parts are present. | 3 in 3/5 |
| Denominator | The bottom number, showing how many equal parts make one whole. It cannot be zero. | 5 in 3/5 |
| Proper fraction | A non-zero fraction whose numerator magnitude is smaller than its denominator. | 3/5 |
| Improper fraction | A fraction whose numerator magnitude is at least as large as its denominator. | 8/5 |
| Mixed number | A whole-number part written beside a proper fractional part. | 1 3/5 |
| Equivalent fractions | Different numerator and denominator pairs representing the same value. | 1/2 and 3/6 |
| Reciprocal | A non-zero fraction with its numerator and denominator exchanged. | 5/3 is the reciprocal of 3/5 |
Fraction Formulas Used by the Calculator
Suppose the two fractions are a/b and c/d. The denominators b and d must be non-zero. The calculator first normalizes signs and reduces entered values. It then applies the selected rule.
Adding and subtracting fractions
a/b - c/d = (a × d - c × b) / (b × d)
Fractions must refer to equal-sized parts before their numerators can be added or subtracted. The calculator finds the least common multiple of the denominators and uses it as the least common denominator. Each fraction is scaled to that denominator, then the adjusted numerators are combined.
If the denominators already match, only the numerators change. For example, 7/12 - 5/12 = 2/12 = 1/6. When they differ, 3/4 + 2/3 becomes 9/12 + 8/12 = 17/12, or 1 5/12.
Multiplying fractions
Multiply the numerators and multiply the denominators. The tool cross-cancels common factors before multiplication. Cross-cancellation does not change the value. It reduces intermediate numbers and makes the calculation easier to inspect. For 2/3 × 9/4, cancel 2 with 4 and 3 with 9, leaving 1/1 × 3/2 = 3/2.
Dividing fractions
Division by a fraction is multiplication by its reciprocal. The second fraction must not equal zero because zero has no reciprocal. For example, 7/8 ÷ 14/3 becomes 7/8 × 3/14. After cancellation, the result is 3/16.
GCD, LCM and the Common Denominator
The greatest common divisor, also called the greatest common factor, is the largest positive integer that divides two integers without a remainder. The calculator uses the Euclidean algorithm to find it. Dividing the numerator and denominator by their GCD reduces a fraction to lowest terms.
The least common multiple is the smallest positive integer divisible by both inputs. For addition and subtraction, the LCM of the denominators is the least common denominator. If the denominators are 12 and 18, their GCD is 6 and their LCM is 36.
Simplified fraction = (numerator ÷ GCD) / (denominator ÷ GCD)
A common denominator formed by multiplying both denominators will work, but it may be larger than necessary. Using the LCM produces smaller equivalent fractions and shorter steps.
How to Simplify a Fraction
A fraction is in simplest form when its numerator and denominator share no factor greater than 1. Find their GCD, divide both by it and keep the denominator positive. For 84/126, the GCD is 42. Dividing both parts by 42 gives 2/3.
The calculator simplifies every entered value and every result automatically. In single-value mode, it also explains the reduction directly. If the numerator is zero, the canonical result is 0 because every valid zero fraction has the same value. A whole-number result is displayed without /1.
Mixed Numbers and Improper Fractions
To convert a positive mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Keep the original denominator. Therefore, 2 1/3 = (2 × 3 + 1)/3 = 7/3.
For a negative mixed number, the sign applies to the complete magnitude. Thus, -2 1/3 = -(2 × 3 + 1)/3 = -7/3. Writing the sign only on the fractional part would describe a different calculation, so the input parser rejects ambiguous forms such as 2 -1/3.
To convert an improper fraction to a mixed number, divide the numerator magnitude by the denominator. The quotient is the whole-number magnitude and the remainder becomes the new numerator. For 17/5, the quotient is 3 and the remainder is 2, producing 3 2/5. The exact improper form remains useful for further arithmetic.
Worked Fraction Calculator Example
Add 2/3 + 5/8. The denominators differ, so begin with their least common multiple.
| Step | Calculation | Result |
|---|---|---|
| Find the denominator GCD | GCD(3, 8) | 1 |
| Find the least common denominator | LCM(3, 8) | 24 |
| Rewrite the first fraction | 2/3 × 8/8 | 16/24 |
| Rewrite the second fraction | 5/8 × 3/3 | 15/24 |
| Add the numerators | 16/24 + 15/24 | 31/24 |
| Convert to a mixed number | 31 ÷ 24 = 1 remainder 7 | 1 7/24 |
The exact answer is 31/24, which is already in lowest terms because 31 and 24 share no factor greater than 1. Its mixed form is 1 7/24, its decimal is approximately 1.291666666666, and its percentage is approximately 129.1666666666%.
Negative Fractions and Zero Rules
- A negative sign may appear in the numerator or denominator of a simple fraction. The calculator moves the sign to the numerator.
- Two negative signs cancel, so
-3/-4becomes3/4. - A zero numerator with a non-zero denominator equals zero.
- A zero denominator is undefined and always returns an error.
- Dividing by a fraction whose value is zero is also undefined.
- The result
-0is normalized to 0.
These sign rules let equivalent fractions share one standard display. For example, 1/-2, -1/2 and -3/6 all normalize to -1/2.
Converting Fractions to Decimals and Percentages
Divide the numerator by the denominator to obtain a decimal. Multiply that value by 100 to obtain a percentage. Some fractions terminate, such as 1/8 = 0.125. Others repeat, such as 1/3 = 0.3333.... The calculator shows up to 12 decimal places and adds an ellipsis when more digits remain.
The exact fraction is not rounded. Decimal and percentage outputs are secondary approximations for comparison and communication. If your class, invoice or measurement requires a specific rounding rule, apply it to the final value at the required number of places.
Common Fraction Mistakes
- Adding denominators:
1/2 + 1/3is not2/5. Rewrite both values with a common denominator. - Skipping the reciprocal: division requires flipping the second non-zero fraction before multiplying.
- Using a zero denominator: no fraction with zero on the bottom is defined.
- Misreading a negative mixed number:
-2 1/3means the entire mixed number is negative. - Rounding too early: keep the exact fraction through intermediate steps, then round only the requested final decimal.
- Forgetting to simplify: equivalent answers may be correct, but lowest terms make comparison easier.
Exact Arithmetic, Privacy and Limits
This calculator uses BigInt integer arithmetic for numerators and denominators. Values larger than JavaScript's ordinary safe-integer limit remain exact within the stated input cap. Each numeric token is limited to 60 digits to keep calculations and displayed steps responsive. The tool never evaluates entered text as code.
Input is checked against specific integer, fraction and mixed-number formats. Results and history are inserted as plain text. Calculator entries, answers and recent history stay in the current browser page and disappear when the page reloads. The calculation does not send your fraction text to a calculation server.
The calculator covers numerical fractions only. It does not simplify algebraic fractions containing variables, solve equations, compare measurement units or decide how many significant figures a real-world result should contain.
Fraction Calculator vs Other Math Tools
| Tool | Best use | Main output |
|---|---|---|
| Fraction Calculator | Exact operations, simplification and mixed-number conversion | Reduced fraction with steps |
| Math Calculator | General arithmetic expressions, parentheses and percentages | Numerical result |
| Scientific Calculator | Trigonometry, logarithms, powers, roots and scientific notation | Advanced numerical result |
| Average Calculator | Summarizing a list of numbers | Mean, sum, count and range |
| Recipe Scaling Calculator | Changing ingredient quantities for a new serving count | Scaled recipe amounts |
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Frequently Asked Questions
How do I add fractions with different denominators?
Find the least common multiple of the denominators, rewrite both fractions with that common denominator, add the adjusted numerators and simplify the result.
How do I subtract fractions?
Use a common denominator, subtract the second adjusted numerator from the first and reduce the answer. A negative result is valid when the second fraction is larger.
How do I multiply two fractions?
Multiply numerator by numerator and denominator by denominator. Cross-cancel common factors before multiplying when possible, then simplify the final fraction.
How do I divide fractions?
Keep the first fraction, replace division with multiplication and use the reciprocal of the second fraction. The second fraction must not equal zero.
How do I simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both by it. The result is in lowest terms when the remaining GCD is 1.
What is the difference between GCD and LCM?
GCD is the largest integer that divides two values without a remainder. LCM is the smallest positive multiple shared by both values. GCD simplifies fractions, while LCM helps find a common denominator.
How do I convert an improper fraction to a mixed number?
Divide the numerator magnitude by the denominator. Use the quotient as the whole-number magnitude and the remainder as the new numerator over the original denominator.
How do I convert a mixed number to an improper fraction?
Multiply the whole-number magnitude by the denominator, add the fractional numerator and place the total over the original denominator. Apply the mixed number's sign to the full result.
Can a fraction have a negative denominator?
It can be written that way, but standard form keeps the denominator positive. This calculator moves a negative denominator sign to the numerator, so 1/-2 becomes -1/2.
Why is a zero denominator undefined?
Division by zero has no defined finite value. The calculator rejects any entered fraction with a zero denominator and also blocks division by a zero-valued second fraction.
Does the calculator round its answers?
The fraction, improper fraction and mixed number remain exact. Only decimal and percentage displays are limited; an ellipsis shows when additional digits continue.
Does it support integers above JavaScript's safe-integer limit?
Yes. The calculator uses BigInt integer arithmetic and accepts numeric tokens up to 60 digits. It keeps fraction operations exact without converting the operands to ordinary floating-point numbers.