Fraction Calculator
Add, subtract, multiply or divide fractions with step-by-step working shown
calculateFraction Operation
Fraction 1
Fraction 2
Leave Whole blank or 0 for simple fractions (e.g. 3/4). For mixed numbers enter whole part (e.g. 2 and 1/3).
How It Works
Add/Sub: Find LCD, convert both fractions, add/subtract numerators
Multiply: (n1 × n2) / (d1 × d2) then simplify
Divide: Multiply first fraction by reciprocal of second
Simplify: Divide numerator and denominator by their GCD
Result (Fraction)
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Decimal
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Simplified Fraction
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Decimal Equivalent
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Mixed Number
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GCD Used
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Step-by-step Working
What is a Fraction Calculator?
A fraction calculator performs arithmetic on fractions — addition, subtraction, multiplication, and division — and automatically simplifies the result to its lowest terms using the Greatest Common Divisor (GCD). It also converts fractions to decimals and mixed numbers.
Working with fractions manually can be error-prone, especially when finding common denominators. This calculator handles all steps automatically: finding the LCD, computing the result, and reducing to the simplest form.
lightbulb Example Calculation
Scenario: Neha, Class 8 student from Mumbai — working on a maths problem: "Ravi ate 3/4 of a pizza and Priya ate 2/6 of the remaining. What fraction did they eat in total?"
1Find LCD of 4 and 6: LCD = 12
2Convert: 9/12 + 4/12 = 13/12
3As mixed number: 1 and 1/12 ≈ 1.0833
✓ Result: 13/12 = 1 1/12 ≈ 1.0833
help_outlineHow to Use the Fraction Calculator
- Select the operation — Add (+), Subtract (−), Multiply (×), or Divide (÷) — from the dropdown at the top.
- For Fraction 1: enter the Whole number (leave blank or 0 for proper fractions like 3/4), Numerator, and Denominator.
- For Fraction 2: enter the same fields. For a mixed number like 2¾, enter Whole = 2, Numerator = 3, Denominator = 4.
- Click "Calculate" — the result appears as a simplified fraction, decimal equivalent, and mixed number (if applicable).
- Expand the Step-by-step Working section to see how the LCD was found, fractions adjusted, result computed, and simplified using GCD.
Benefits
- Step-by-step method shown — learn the approach for homework, not just the final answer
- Supports mixed numbers — enter whole + fractional parts directly without pre-conversion
- Automatically simplifies to lowest terms using GCD — no manual reduction required
- Result shown in three forms: simplified fraction, decimal, and mixed number for full clarity
- Division via reciprocal handled correctly — common source of student errors eliminated
Key Terms
- Numerator
- The top number of a fraction — the part being counted (e.g., 3 in 3/4)
- Denominator
- The bottom number — total equal parts (e.g., 4 in 3/4); can never be zero
- Proper Fraction
- Numerator < Denominator (e.g., 3/4); value is between 0 and 1
- Improper Fraction
- Numerator ≥ Denominator (e.g., 7/4 = 1¾); value ≥ 1; converts to a mixed number
- LCD
- Lowest Common Denominator — smallest number divisible by both denominators; used for addition and subtraction
- GCD
- Greatest Common Divisor — largest number dividing both numerator and denominator; used to simplify fractions
quizFrequently Asked Questions
Why do we need a common denominator to add or subtract fractions?
Fractions with different denominators represent parts of different-sized wholes — 1/4 is one quarter while 1/3 is one third. You can only add quantities of the same size. Converting both to the same denominator (LCD) makes them comparable: 1/4 = 3/12 and 1/3 = 4/12, so 1/4 + 1/3 = 7/12. Multiplication and division don't require a common denominator because those operations inherently transform both numerator and denominator.
How do I divide fractions?
Dividing by a fraction equals multiplying by its reciprocal (flip numerator and denominator of the second fraction): (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1⅞. The memory trick is "Keep, Change, Flip" — keep the first fraction unchanged, change ÷ to ×, flip the second fraction. The calculator applies this automatically and shows the reciprocal step in the working for clarity.
How are fractions simplified to their lowest terms?
A fraction a/b is in lowest terms when GCD(a, b) = 1 (no common factor other than 1). To simplify: find the GCD of numerator and denominator, then divide both by it. Example: 12/18 → GCD(12, 18) = 6 → 12÷6 = 2, 18÷6 = 3 → simplified to 2/3. The calculator uses the Euclidean algorithm (repeatedly taking the remainder) to find GCD efficiently for any size numbers.
What is a mixed number and how do I convert between forms?
A mixed number has a whole part plus a proper fraction (e.g., 2¾). To convert an improper fraction to a mixed number: divide numerator by denominator; the quotient is the whole part, remainder is the new numerator. Example: 11/4 → 11 ÷ 4 = 2 remainder 3 → mixed number is 2¾. To reverse: (2 × 4) + 3 = 11 → 11/4. The calculator converts automatically and shows all three forms in the result.
Can I enter negative fractions?
Yes. Enter a negative numerator (e.g., −3 with denominator 4 represents −3/4). The calculator correctly handles negative numerators and denominators: if both are negative, the result is positive (−3/−4 = 3/4); if only one is negative, the result is negative. Simplification works normally on negative fractions — GCD is computed from the absolute values and the sign is preserved in the result.