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Fractions Calculator

Add, subtract, multiply and divide fractions with step-by-step solutions

Use Mixed Numbers here >>>
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Result:

-3/4 + -5/8 = -11/8 or -1 3/8

Solution Steps:

1. Find Common Denominator

The denominators are 4 and 8. The least common denominator (LCD) is 8.

2. Convert Fractions

Convert -3/4 to equivalent fraction with denominator 8:

-3/4 = -6/8

-5/8 already has denominator 8.

3. Perform Addition

-6/8 + -5/8 = -11/8

4. Simplify Result

-11/8 can be expressed as mixed number:

-11 ÷ 8 = -1 with remainder 3 → -1 3/8

How to Use This Fractions Calculator

Basic Operations

This calculator handles all four basic operations with fractions:

  • Addition (+): Combine fractions with common denominators
  • Subtraction (-): Subtract one fraction from another
  • Multiplication (×): Multiply numerators and denominators
  • Division (÷): Multiply by the reciprocal of the second fraction

Working With Mixed Numbers

Click "Use Mixed Numbers" to input whole numbers with fractions:

  1. Enter the whole number in the first box
  2. Enter numerator and denominator in the fraction boxes
  3. Negative numbers should have the minus sign before the whole number

Fraction Calculation Rules

  • Denominators cannot be zero
  • Results are automatically simplified to lowest terms
  • Negative fractions should have the minus sign in the numerator
  • Mixed numbers in results are shown in reduced form

Mastering Fraction Calculations

Fraction operations visual guide

Visual guide to fraction operations

Working with fractions is a fundamental math skill with applications in everyday life, from cooking measurements to financial calculations. Our fractions calculator provides instant solutions with detailed explanations of each calculation step.

Understanding Fraction Operations

Fraction addition example

Each fraction operation has specific rules:

  • Addition/Subtraction: Requires common denominators
  • Multiplication: Multiply numerators and denominators directly
  • Division: Multiply by the reciprocal (flip the second fraction)
  • Simplification: Divide numerator and denominator by their greatest common factor (GCF)

Working With Mixed Numbers

Mixed numbers combine whole numbers with proper fractions:

  1. To calculate with mixed numbers, first convert them to improper fractions
  2. Multiply the whole number by the denominator
  3. Add the numerator to this product
  4. Keep the same denominator
  5. Perform the operation as with regular fractions
  6. Convert back to mixed number if needed
Mixed numbers conversion

Practical Applications of Fractions

Practical uses of fractions

Fraction calculations are essential in many real-world situations:

  • Cooking/Baking: Adjusting recipe quantities
  • Construction: Measuring materials and dimensions
  • Finance: Calculating interest rates and percentages
  • Medicine: Dosage calculations
  • Sports: Statistics and performance metrics

Common Fraction Mistakes to Avoid

  • Adding denominators when adding fractions (denominators stay the same)
  • Forgetting to find common denominators for addition/subtraction
  • Not converting mixed numbers to improper fractions before calculating
  • Dividing fractions without flipping the second fraction
  • Forgetting to simplify final answers

Frequently Asked Questions

Find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, then add the numerators while keeping the denominator the same.

"Of" means multiplication in math problems. So 1/3 of 3/8 is 1/3 × 3/8 = (1×3)/(3×8) = 3/24 = 1/8 after simplifying.

First convert each mixed number to an improper fraction. Then multiply the first fraction by the reciprocal of the second fraction. Finally, simplify the result and convert back to mixed number if needed.

Division by zero is undefined in mathematics. A fraction represents division (numerator ÷ denominator), so having zero in the denominator would mean dividing by zero, which is impossible.