Fraction Calculator
Add, subtract, multiply, and divide fractions instantly â with simplified results and step-by-step working
Calculate Fractions
Results
Step-by-Step Working
How to Use the Fraction Calculator
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1Enter the First Fraction
Type the numerator and denominator of your first fraction into the two fields labelled Numerator 1 and Denominator 1.
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2Select the Operation
Choose the arithmetic operation you need: Addition (+), Subtraction (â), Multiplication (Ã), or Division (Ãˇ).
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3Enter the Second Fraction
Type the numerator and denominator of your second fraction into the fields labelled Numerator 2 and Denominator 2.
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4Click Calculate
Press the Calculate button or hit Enter. The tool computes the result instantly.
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5Review Results and Steps
See the simplified fraction result, the decimal equivalent, and the full step-by-step working below.
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6Clear and Try Again
Click Clear to reset all fields and enter a new fraction problem.
Key Features
All Four Operations
Add, subtract, multiply, and divide any two fractions â including improper fractions and negative values.
Auto-Simplification
Every result is automatically reduced to its lowest terms using the GCD â no extra steps needed from you.
Step-by-Step Working
See exactly how the answer was reached â from finding the LCD to cross-multiplying and simplifying.
Decimal Equivalent
Every result includes the decimal form alongside the fraction â helpful for quick real-world comparisons.
Smart Validation
Empty fields, zero denominators, and division by zero are all caught with clear, helpful error messages.
Works Everywhere
Fully responsive on mobile, tablet, and desktop. All logic runs in your browser â no data sent anywhere.
Formulas & How It Works
Every fraction operation follows a specific mathematical rule. Here is exactly what this calculator applies for each operation.
a/b + c/d = (aÃd + cÃb) / (bÃd) â simplify by GCD
Better: find LCD = LCM(b,d), then (aÃLCD/b + cÃLCD/d) / LCD
Subtraction:
a/b â c/d = (aÃd â cÃb) / (bÃd) â simplify by GCD
Multiplication:
a/b à c/d = (aÃc) / (bÃd) â simplify by GCD
Division (Keep-Change-Flip):
a/b Ãˇ c/d = a/b à d/c = (aÃd) / (bÃc) â simplify by GCD
Simplification (GCD â Euclidean Algorithm):
GCD(a, b) = GCD(b, a mod b) until b = 0 â result = a
- a, c
- Numerators of the first and second fractions
- b, d
- Denominators of the first and second fractions
- GCD
- Greatest Common Divisor â used to reduce fractions to lowest terms
- LCM
- Least Common Multiple â used as the common denominator for addition and subtraction
- LCD
- Least Common Denominator = LCM of both denominators
The Euclidean algorithm is the most efficient way to find the GCD. It repeatedly replaces the larger number with the remainder of dividing the two numbers until the remainder is zero â at which point the non-zero number is the GCD.
Practical Examples
- đŽđŗRiya Sharma â Class 6 StudentJaipur, India
Problem: Riya has eaten 3/8 of a pizza and her brother ate 1/4. How much pizza did they eat together?
3/8 + 1/4 â LCD = 8 â 3/8 + 2/8 = 5/8
Result: 5/8 (0.625) â more than half the pizza is gone! - đŽđŗArun Patel â Civil EngineerAhmedabad, India
Problem: A pipe is 7/10 metres long. Arun needs to cut off 2/5 metres. How much remains?
7/10 â 2/5 â LCD = 10 â 7/10 â 4/10 = 3/10
Result: 3/10 metres (0.3m) remaining after the cut - đŽđŗPriya Menon â Home BakerKochi, India
Problem: A cake recipe needs 2/3 cup of sugar. Priya wants to make 3/2 times the recipe. How much sugar does she need?
2/3 Ã 3/2 = (2Ã3)/(3Ã2) = 6/6 â simplify: GCD(6,6) = 6 â 1/1
Result: 1 cup of sugar â the fractions cancel out perfectly - đēđ¸Mark Collins â Carpentry InstructorChicago, USA
Problem: Mark needs to divide a 5/6 foot plank into pieces of 1/3 foot each. How many pieces can he cut?
5/6 Ãˇ 1/3 â Keep-Change-Flip â 5/6 à 3/1 = 15/6 â GCD(15,6)=3 â 5/2
Result: 5/2 = 2.5 â meaning 2 full pieces and one half piece
What Is a Fraction Calculator?
A fraction calculator is a tool that performs arithmetic operations on fractions â numbers expressed as one integer divided by another. Fractions appear constantly in everyday life: cooking recipes, measurements, finance, probability, and school mathematics. Calculating them by hand requires finding common denominators, cross-multiplying, and simplifying â steps that are easy to get wrong under pressure.
This tool handles the entire process automatically: it identifies the correct method for each operation, executes the calculation precisely, and reduces the result to its simplest form. The step-by-step breakdown means students can follow along and learn the method, not just copy the answer.
Whether you are a student in Class 5 working through your first fraction problems, a teacher checking homework answers, an engineer dealing with unit conversions, or a home cook scaling recipes â this calculator handles your fraction arithmetic accurately and instantly.
Fractions in Multiple Languages
Want a complete guide to fractions â types, rules, common mistakes, and real-world uses? Read our in-depth blog post.
Read the Full Guide âFrequently Asked Questions
Is this fraction calculator free to use?
Can I calculate mixed numbers with this tool?
How does the calculator simplify fractions?
What happens if I divide by zero?
Can I use negative fractions?
How does fraction addition work?
How does fraction subtraction work?
How does fraction multiplication work?
How does fraction division work?
Does the calculator show step-by-step working?
Can I enter whole numbers as fractions?
Does this work on mobile phones and tablets?
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