Fraction Calculator
Add, subtract, multiply, and divide fractions. Get simplified results with decimal and percentage conversions.
Enter Fractions
/
/
Result
12
+14
=34
🔢Decimal
0.75
%Percentage
75.00%
All Formats
Unsimplified6 / 8
Simplified3 / 4
Decimal0.75
Percentage75%
How It Works
1. Find common denominator: 2 × 4 = 8
2. Convert fractions: 1×4 / 2×4 + 1×2 / 4×2
3. Add numerators: 4 + 2 = 6
4. Simplify by dividing by GCD
Understanding Fractions
A fraction represents a part of a whole number. It consists of two parts: the numerator (top number) showing how many parts you have, and the denominator (bottom number) showing how many equal parts make up the whole.
Types of Fractions:
- Proper Fractions: Numerator is less than denominator (3/4, 2/5, 7/8)
- Improper Fractions: Numerator is greater than or equal to denominator (5/3, 9/4, 7/7)
- Mixed Numbers: A whole number combined with a proper fraction (1 2/3, 3 1/4)
- Equivalent Fractions: Different fractions representing the same value (1/2 = 2/4 = 3/6)
- Unit Fractions: Fractions with numerator of 1 (1/2, 1/3, 1/4)
Key Terminology:
- Numerator: The top number (how many parts you have)
- Denominator: The bottom number (how many parts in the whole)
- LCD: Least Common Denominator (smallest shared denominator)
- GCD: Greatest Common Divisor (used to simplify fractions)
Fraction Operations and Formulas
Each arithmetic operation has specific rules for fractions:
Fraction Operation Formulas
Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b - c/d = (ad - bc) / bd
Multiplication: a/b × c/d = (a × c) / (b × d)
Division: a/b ÷ c/d = (a × d) / (b × c)
Simplify: Divide both by GCD(numerator, denominator)
Where:
- a/b= First fraction with numerator a and denominator b
- c/d= Second fraction with numerator c and denominator d
- GCD= Greatest Common Divisor of two numbers
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator:
Same Denominators:
- Simply add or subtract the numerators
- Keep the denominator the same
- Example: 3/8 + 2/8 = 5/8
Different Denominators:
- Find the Least Common Denominator (LCD)
- Convert each fraction to an equivalent fraction with the LCD
- Add or subtract the numerators
- Simplify the result if possible
| Example | Step-by-Step | Result |
|---|---|---|
| 1/3 + 1/4 | LCD=12: 4/12 + 3/12 | 7/12 |
| 5/6 - 1/4 | LCD=12: 10/12 - 3/12 | 7/12 |
| 2/5 + 3/10 | LCD=10: 4/10 + 3/10 | 7/10 |
Multiplying and Dividing Fractions
Multiplication is the simplest fraction operation - no common denominator needed:
- Multiply numerator × numerator
- Multiply denominator × denominator
- Simplify the result
- Tip: Cross-cancel before multiplying to simplify early
Division uses the "Keep, Change, Flip" method:
- Keep the first fraction as is
- Change division to multiplication
- Flip the second fraction (reciprocal)
- Multiply and simplify
Examples:
- 2/3 × 3/4 = 6/12 = 1/2 (or cross-cancel: 2/3 × 3/4 = 1/2)
- 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
- 5/6 × 9/10 = 45/60 = 3/4 (or cross-cancel first)
Cross-Cancellation Tip: Before multiplying, simplify diagonally if possible. In 4/9 × 3/8, the 3 and 9 share factor 3, and 4 and 8 share factor 4, giving 1/3 × 1/2 = 1/6.
Simplifying and Converting Fractions
Simplifying (Reducing) Fractions:
- Find the GCD (Greatest Common Divisor) of numerator and denominator
- Divide both by the GCD
- Result is the fraction in lowest terms
Converting Mixed Numbers to Improper Fractions:
- Multiply whole number by denominator
- Add the numerator
- Put result over original denominator
- Example: 2 3/4 = (2×4 + 3)/4 = 11/4
Converting Improper Fractions to Mixed Numbers:
- Divide numerator by denominator
- Quotient = whole number
- Remainder = new numerator
- Example: 17/5 = 3 R2, so 17/5 = 3 2/5
Converting Fractions to Decimals:
- Divide numerator by denominator
- Example: 3/4 = 3 ÷ 4 = 0.75
- Some fractions give repeating decimals: 1/3 = 0.333...
How to Use This Fraction Calculator
Our calculator handles all fraction operations with step-by-step solutions:
- Enter First Fraction: Input numerator and denominator (or a mixed number)
- Select Operation: Choose add (+), subtract (-), multiply (×), or divide (÷)
- Enter Second Fraction: Input the second numerator and denominator
- Calculate: Get the result in simplified form
Features:
- Supports proper fractions, improper fractions, and mixed numbers
- Automatically simplifies results to lowest terms
- Shows step-by-step solution process
- Converts between fraction formats
- Displays decimal equivalent
Tips for Input:
- For mixed numbers, enter whole number separately or use format: 2 3/4
- Negative fractions: Enter negative sign with numerator
- Denominators cannot be zero
Real-World Applications of Fractions
Fractions appear throughout daily life and various professions:
Cooking and Baking:
- Recipe measurements: 3/4 cup flour, 1/2 teaspoon salt
- Scaling recipes up or down
- Dividing portions equally
Construction and DIY:
- Lumber dimensions (2×4 is actually 1 1/2 × 3 1/2 inches)
- Drill bit and screw sizes (5/16", 3/8")
- Cutting materials into equal parts
Music:
- Time signatures (3/4 time, 6/8 time)
- Note durations (quarter notes, eighth notes, half notes)
- Rhythm and beat divisions
Finance:
- Stock prices (historically quoted in fractions)
- Interest rates and partial payments
- Splitting bills and costs
Time:
- Quarter hour (1/4), half hour (1/2)
- Scheduling partial hours
Worked Examples
Adding Fractions with Different Denominators
Problem:
Calculate 2/3 + 3/4
Solution Steps:
- 1Find the LCD of 3 and 4: LCD = 12
- 2Convert 2/3: (2 × 4)/(3 × 4) = 8/12
- 3Convert 3/4: (3 × 3)/(4 × 3) = 9/12
- 4Add numerators: 8/12 + 9/12 = 17/12
- 5Convert to mixed number: 17 ÷ 12 = 1 R5
- 6Final answer: 1 5/12
Result:
2/3 + 3/4 = 17/12 = 1 5/12
Multiplying Mixed Numbers
Problem:
Calculate 1 1/2 × 2 2/3
Solution Steps:
- 1Convert to improper fractions:
- 21 1/2 = (1×2 + 1)/2 = 3/2
- 32 2/3 = (2×3 + 2)/3 = 8/3
- 4Multiply: (3/2) × (8/3) = 24/6
- 5Simplify: 24/6 = 4
Result:
1 1/2 × 2 2/3 = 4
Dividing Fractions
Problem:
Calculate 5/8 ÷ 3/4
Solution Steps:
- 1Keep the first fraction: 5/8
- 2Change division to multiplication
- 3Flip the second fraction: 3/4 becomes 4/3
- 4Multiply: (5/8) × (4/3) = 20/24
- 5Simplify by GCD(20,24) = 4: 20/24 = 5/6
Result:
5/8 ÷ 3/4 = 5/6
Tips & Best Practices
- ✓Always simplify your final answer to lowest terms
- ✓For division, remember 'Keep, Change, Flip' - keep first, change to multiply, flip second
- ✓Cross-cancel before multiplying to make calculations easier
- ✓LCD (Least Common Denominator) = LCM (Least Common Multiple) of the denominators
- ✓When adding mixed numbers, you can add whole parts and fraction parts separately
- ✓Convert mixed numbers to improper fractions before multiplying or dividing
- ✓Check your answer by converting to decimals and verifying the operation
Frequently Asked Questions
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, to simplify 12/18: GCD(12, 18) = 6. Divide both: 12÷6 = 2, 18÷6 = 3. So 12/18 = 2/3. You can also factor both numbers and cancel common factors.
Denominators indicate the size of each piece. You can't add pieces of different sizes directly - it's like adding apples and oranges. The common denominator converts all fractions to the same-sized pieces so they can be combined. For example, 1/2 + 1/3 requires converting to sixths (3/6 + 2/6) before adding.
Count decimal places and put the number over that power of 10. For 0.75: that's 75/100, which simplifies to 3/4. For repeating decimals like 0.333..., recognize common equivalents (1/3) or use algebra: x = 0.333..., 10x = 3.333..., 9x = 3, x = 1/3.
A fraction represents a part of a whole (3/4 means 3 out of 4 parts). A ratio compares two quantities that may or may not be parts of the same whole (3:4 could mean 3 boys to 4 girls). Ratios can be written as fractions, but their interpretations differ. Fractions always relate part to whole; ratios can compare any two quantities.
Division asks 'how many times does the divisor fit into the dividend?' Multiplying by the reciprocal gives the same answer mathematically. Think of it this way: 6 ÷ 2 asks 'how many 2s in 6?' which equals 6 × (1/2) = 3. The reciprocal (flipped fraction) represents 'one divided by that number,' making division equivalent to multiplication.
Convert both fractions to equivalent fractions with a common denominator, then compare numerators. Alternatively, convert both to decimals. For example, to compare 3/4 and 5/7: convert to 21/28 and 20/28, so 3/4 > 5/7. Or as decimals: 0.75 > 0.714.
Sources & References
Last updated: 2026-01-22