Mixed Number Calculator
Perform arithmetic operations with mixed numbers and fractions
Mixed Number Operations
Results
As Improper Fraction
As Decimal
Calculation Summary
Solution Summary
Common Examples
Addition
Subtraction
Multiplication
Division
Key Concepts
Mixed Numbers
Combine whole numbers with proper fractions
Improper Fractions
Numerator is greater than or equal to denominator
Conversion Method
Convert to improper fractions for calculations
Common Denominator
Required for addition and subtraction
Operation Methods
Addition
Find common denominator, add numerators
Subtraction
Find common denominator, subtract numerators
Multiplication
Multiply numerators and denominators
Division
Multiply by reciprocal of divisor
Tips & Applications
Cooking and baking recipe calculations
Construction and carpentry measurements
Always convert to improper fractions first
Simplify results to lowest terms
Convert back to mixed numbers for clarity
Understanding Mixed Numbers
What are Mixed Numbers?
A mixed number combines a whole number with a proper fraction. For example, 2 3/4 represents 2 whole units plus 3/4 of another unit. Mixed numbers are useful for expressing quantities larger than 1 in a more intuitive way.
Why Convert to Improper Fractions?
- • Easier calculations: Standard fraction arithmetic rules apply
- • Avoids regrouping: No borrowing needed in subtraction
- • Consistent method: Same approach for all operations
- • Reduces errors: Fewer steps and special cases
Conversion Formula
Mixed to Improper: (whole × denominator + numerator) / denominator
Improper to Mixed: whole = numerator ÷ denominator, remainder = new numerator
Worked Example: Addition
Calculate: 2 2/5 + 1 1/2
Step 1: Convert to improper fractions
• 2 2/5 = (2×5+2)/5 = 12/5
• 1 1/2 = (1×2+1)/2 = 3/2
Step 2: Find common denominator
• LCM(5,2) = 10
• 12/5 = 24/10, 3/2 = 15/10
Step 3: Add and convert back
• 24/10 + 15/10 = 39/10 = 3 9/10
Common Mistakes
• Don't add whole numbers and fractions separately without considering overflow
• Don't forget to find common denominators for addition/subtraction
• Remember to simplify final answers to lowest terms
• Always convert negative mixed numbers correctly
Real-World Applications
🍰 Cooking & Baking
Recipe adjustments: "I need 2 1/2 cups flour, but the recipe calls for 1 3/4 cups"
🏗️ Construction
Material calculations: "Cut 3 boards of 5 3/4 inches each from a 20-foot board"
⏰ Time Management
Duration calculations: "Meeting ran 1 1/4 hours, presentation was 2 1/2 hours"
Operation Details
Addition & Subtraction
1. Convert both mixed numbers to improper fractions
2. Find the least common multiple of denominators
3. Convert fractions to equivalent fractions with common denominator
4. Add or subtract numerators, keep denominator
5. Simplify and convert back to mixed number if needed
Multiplication & Division
1. Convert both mixed numbers to improper fractions
2. For multiplication: multiply numerators and denominators
3. For division: multiply by reciprocal of second fraction
4. Simplify the result
5. Convert back to mixed number if the result is improper