Fraction Calculator
Add, subtract, multiply and divide fractions
How Fraction Operations Work
Understanding the mathematical rules behind fraction operations helps you solve problems step-by-step and verify calculator results.
- Addition/Subtraction requires common denominators: multiply by equivalent fractions
- Multiplication multiplies numerators together and denominators together
- Division uses 'multiply by reciprocal' rule: a/b ÷ c/d = a/b × d/c
- Simplification uses Greatest Common Divisor (GCD) to reduce fractions
- Mixed numbers convert from improper fractions when numerator > denominator
What is a Fraction Calculator?
A fraction calculator performs arithmetic operations with fractions (add, subtract, multiply, divide) and automatically simplifies the results. Fractions represent parts of a whole, written as numerator/denominator. This calculator finds common denominators when needed, performs the operation, and reduces the result to lowest terms. It also converts improper fractions to mixed numbers and shows the decimal equivalent, making it perfect for homework, cooking, construction, and any task requiring precise fractional calculations.
Common Use Cases
Cooking & Recipes
Add or scale recipe ingredients: 1/2 cup + 1/3 cup, double a 3/4 teaspoon measurement, etc.
Measurements & Construction
Calculate lumber lengths, fabric cuts, or tool measurements with fractional inches and feet.
Math Homework
Check answers for fraction problems, learn simplification steps, and verify calculations.
Science & Lab Work
Calculate reagent ratios, dilutions, and mixture proportions in fractional amounts.
Financial Calculations
Compute fractional shares, ownership percentages, or divide assets proportionally.
DIY & Crafts
Calculate material amounts, pattern scaling, or dimensional conversions in fractional units.
Fraction Operation Rules
Addition
Formula: a/b + c/d = (ad + bc)/bd
Find common denominator, add numerators, simplify result
Subtraction
Formula: a/b - c/d = (ad - bc)/bd
Find common denominator, subtract numerators, simplify result
Multiplication
Formula: a/b × c/d = (ac)/(bd)
Multiply numerators together, multiply denominators together
Division
Formula: a/b ÷ c/d = a/b × d/c = (ad)/(bc)
Multiply by the reciprocal of the second fraction
Types of Fractions
Proper Fraction
Example: 3/4, 2/5, 7/8
Numerator is smaller than denominator, value less than 1
Improper Fraction
Example: 5/3, 9/4, 11/7
Numerator is greater than or equal to denominator, value ≥ 1
Mixed Number
Example: 2 1/3, 1 3/4, 3 2/5
Whole number plus a proper fraction, converted from improper fractions
Unit Fraction
Example: 1/2, 1/3, 1/10
Numerator is 1, represents one part of the whole
Equivalent Fractions
Example: 1/2 = 2/4 = 3/6
Different fractions that represent the same value
How to Use This Calculator
Step 1: Enter First Fraction
Input the numerator (top number) and denominator (bottom number) of your first fraction.
Step 2: Select Operation
Choose Add (+), Subtract (−), Multiply (×), or Divide (÷) for your calculation.
Step 3: Enter Second Fraction
Input the numerator and denominator of your second fraction.
Step 4: View Results
See the simplified result, original form, mixed number (if applicable), and decimal equivalent.
Step 5: Understand Simplification
The calculator automatically reduces fractions to lowest terms by dividing by the greatest common divisor.
Step 6: Check Decimal
Use the decimal result to verify your fraction or for contexts requiring decimal notation.
Fraction Simplification Tips
Find the GCD
Use the Greatest Common Divisor to reduce fractions: GCD(12,18) = 6, so 12/18 = 2/3
Prime Factorization
Break numbers into prime factors to easily find common divisors
Divisibility Rules
Use shortcuts: numbers ending in 0,2,4,6,8 are divisible by 2; digit sum divisible by 3 means divisible by 3
Cross-Cancel in Multiplication
Cancel common factors before multiplying: (6/8) × (4/9) = (3×1)/(4×3) = 1/4
Work with Smaller Numbers
Always simplify intermediate results to keep calculations manageable
Fraction Calculation Tips
Adding & Subtracting
Requires common denominator. Calculator finds LCD automatically: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Multiplying Fractions
Multiply numerators together and denominators together: 2/3 × 3/4 = 6/12 = 1/2 (simplified).
Dividing Fractions
Multiply by the reciprocal (flip second fraction): 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
Simplifying
Divide numerator and denominator by GCD (greatest common divisor): 6/9 = (6÷3)/(9÷3) = 2/3.
Mixed Numbers
Improper fractions (numerator > denominator) convert to mixed: 7/3 = 2 1/3 (2 whole, 1/3 remaining).
Negative Fractions
Negative sign can go on numerator or whole fraction: -1/2 = 1/(-2). Calculator keeps denominator positive.
Real-World Fraction Applications
Cooking & Baking
Recipe scaling, ingredient ratios, measuring cups and spoons
Construction
Measurements in inches (1/16, 1/8, 1/4), material calculations
Finance
Stock prices, interest rates, percentage calculations
Medicine
Drug dosages, concentration ratios, patient statistics
Music
Note values, time signatures, rhythm calculations
Sports
Statistics, performance ratios, time splits
Interesting Fraction Facts
Ancient Origins
Fractions were used by ancient Egyptians around 2000 BC, but they only used unit fractions (1/n).
Pizza Mathematics
If you eat 3/8 of a pizza and your friend eats 1/4, together you've eaten 5/8 of the pizza.
Music and Fractions
Musical note values are fractions: whole note = 1, half note = 1/2, quarter note = 1/4.
Decimal Connection
Every fraction represents a decimal that either terminates or repeats: 1/4 = 0.25, 1/3 = 0.333...
Farey Sequence
The Farey sequence lists all simplified fractions between 0 and 1 with denominators up to n.
Golden Ratio
The golden ratio φ = (1 + √5)/2 ≈ 1.618 can be expressed as a continued fraction [1; 1, 1, 1, ...].
Common Fraction Mistakes
Adding Denominators
Incorrect: 1/2 + 1/3 = 2/5. Correct: Find common denominator first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Cross Multiplication in Addition
Cross multiplication only works for solving equations, not for adding fractions.
Forgetting to Simplify
Always reduce fractions to lowest terms: 6/8 should be simplified to 3/4.
Division Confusion
Remember 'multiply by reciprocal': a/b ÷ c/d = a/b × d/c, not a/b × c/d.
Mixed Number Conversion Errors
To convert 7/3 to mixed: 7 ÷ 3 = 2 remainder 1, so 2 1/3, not 2 4/3.
Zero Denominator
Never allow zero in the denominator - division by zero is undefined.
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