Fraction Arithmetic Calculator
Perform addition, subtraction, multiplication, and division on fractions with automatic simplification to lowest terms. Perfect for students, cooks, and anyone working with fractions.
Calculate with Fractions
Enter two fractions and select an operation:
Addition: a/b + c/d = (a×d + b×c)/(b×d)
Subtraction: a/b - c/d = (a×d - b×c)/(b×d)
Multiplication: a/b × c/d = (a×c)/(b×d)
Division: a/b ÷ c/d = (a×d)/(b×c)
Understanding Fraction Arithmetic
Fractions are essential in mathematics and appear in many real-world applications. This calculator helps you perform all four basic arithmetic operations on fractions with automatic simplification.
Fraction Arithmetic Operations
➕ Addition
a/b + c/d = (a×d + b×c)/(b×d)
Find common denominator (LCM of b and d)
Convert both fractions to equivalent fractions
Add numerators, keep denominator the same
Simplify the result
➖ Subtraction
a/b - c/d = (a×d - b×c)/(b×d)
Same process as addition
Subtract numerators instead of adding
Keep the common denominator
Simplify the result
✖️ Multiplication
a/b × c/d = (a×c)/(b×d)
Multiply numerators together
Multiply denominators together
No common denominator needed
Simplify the result
➗ Division
a/b ÷ c/d = (a×d)/(b×c)
Multiply by the reciprocal of the second fraction
Flip the second fraction: c/d becomes d/c
Then multiply: (a/b) × (d/c) = (a×d)/(b×c)
💡 Pro Tip: Always simplify fractions to their lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). This makes fractions easier to work with and understand.
Worked Examples
| Operation | Example | Step-by-Step | Result |
|---|---|---|---|
| Addition | 1/2 + 1/3 | LCM(2,3)=6 1/2 = 3/6 1/3 = 2/6 3/6 + 2/6 = 5/6 |
5/6 |
| Subtraction | 3/4 - 1/6 | LCM(4,6)=12 3/4 = 9/12 1/6 = 2/12 9/12 - 2/12 = 7/12 |
7/12 |
| Multiplication | 2/3 × 3/4 | 2/3 × 3/4 = (2×3)/(3×4) Multiply numerators: 2×3 = 6 Multiply denominators: 3×4 = 12 Result: 6/12 |
1/2 |
| Division | 5/8 ÷ 3/4 | 5/8 ÷ 3/4 = 5/8 × 4/3 Multiply by reciprocal: 4/3 5/8 × 4/3 = (5×4)/(8×3) Result: 20/24 = 5/6 |
5/6 |
Common Denominators
🔍 Finding LCM
To add or subtract fractions, find the Least Common Multiple (LCM) of the denominators
LCM is the smallest number that both denominators divide into evenly
Example: LCM of 4 and 6 is 12
Because 4×3=12 and 6×2=12
🔄 Equivalent Fractions
Once you have the LCM, convert both fractions to equivalent fractions with the common denominator
Multiply numerator and denominator by the same number
Example: 1/2 = (1×6)/(2×6) = 6/12
1/3 = (1×4)/(3×4) = 4/12
📐 Simplification
Always simplify the final result by dividing numerator and denominator by their GCD
GCD of 8 and 12 is 4
8÷4=2, 12÷4=3
Result: 2/3 instead of 8/12
Makes fractions easier to read and use
Real-World Applications
👩🍳 Cooking & Baking
Recipe adjustments and scaling
Mixing ingredients in proper proportions
Converting between different measurements
Adjusting serving sizes
🏗️ Construction
Measuring materials to fractional lengths
Calculating proportions for mixing concrete
Dividing spaces into equal parts
Working with blueprints and plans
💰 Finance
Splitting costs among multiple people
Calculating fractional ownership shares
Working with percentages and proportions
Financial ratios and analysis
📐 Mathematics Education
Learning fraction operations
Understanding common denominators
Mastering simplification techniques
Building foundation for algebra
Cooking Examples
| Situation | Fraction Calculation | Result | Practical Use |
|---|---|---|---|
| Doubling a recipe | 1/2 × 2 = 1 | 1 cup (whole) | Scale ingredients |
| Halving a recipe | 3/4 × 1/2 = 3/8 | 3/8 cup | Reduce portions |
| Mixing ingredients | 1/3 + 1/4 = 7/12 | 7/12 cup | Combine measurements |
| Dividing dough | 1 ÷ 3 = 1/3 | 1/3 of total | Equal portions |
| Recipe adjustment | 2/3 - 1/4 = 5/12 | 5/12 cup | Fine-tune measurements |
Important Rules to Remember
📏 Common Denominator Rule
For addition and subtraction, always use a common denominator
Find the Least Common Multiple (LCM) of both denominators
Convert both fractions to equivalent fractions
Then add or subtract the numerators
🔄 Reciprocal Rule
Division by a fraction is multiplication by its reciprocal
To divide by a/b, multiply by b/a
The reciprocal of a/b is b/a
This is the key to fraction division
🎯 Simplification Rule
Always simplify fractions to their lowest terms
Divide numerator and denominator by their GCD
This makes fractions easier to read and use
Improves accuracy in further calculations
Common Fraction Equivalents
| Decimal | Fraction | Percentage | Common Use |
|---|---|---|---|
| 0.25 | 1/4 | 25% | Quarter |
| 0.333... | 1/3 | 33.33% | Third |
| 0.5 | 1/2 | 50% | Half |
| 0.666... | 2/3 | 66.67% | Two thirds |
| 0.75 | 3/4 | 75% | Three quarters |
| 0.8 | 4/5 | 80% | Four fifths |
| 0.9 | 9/10 | 90% | Nine tenths |