Improper Fraction and Mixed Number Calculator

Add, subtract, multiply, divide Improper Fraction & Mixed Numbers

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About Mixed Numbers

A mixed number is a whole number combined with a proper fraction. For example, 2 3/4 (two and three-quarters) is a mixed number.

Mixed numbers are commonly used in everyday life for measurements, cooking recipes, time calculations, and many practical applications where fractional quantities are needed.

Understanding how to work with mixed numbers is essential for mastering fractions and developing strong mathematical skills.

Components of a Mixed Number

• Whole Number: The integer part (e.g., 2 in 2 3/4)

• Numerator: Top number of the fraction (e.g., 3 in 2 3/4)

• Denominator: Bottom number of the fraction (e.g., 4 in 2 3/4)

Converting Mixed Numbers and Improper Fractions

Mixed to Improper Fraction

Steps:

  1. Multiply the whole number by the denominator
  2. Add the numerator to the result
  3. Keep the same denominator

Example: Convert 2 3/4 to improper fraction

2 × 4 + 3 = 11

Result: 11/4

Improper Fraction to Mixed

Steps:

  1. Divide the numerator by the denominator
  2. The quotient becomes the whole number
  3. The remainder becomes the new numerator
  4. Keep the same denominator

Example: Convert 11/4 to mixed number

11 ÷ 4 = 2 remainder 3

Result: 2 3/4

Operations with Mixed Numbers

Addition & Subtraction

  • 1. Convert both mixed numbers to improper fractions
  • 2. Find common denominator
  • 3. Add or subtract the numerators
  • 4. Simplify and convert back to mixed number

Multiplication & Division

  • 1. Convert both mixed numbers to improper fractions
  • 2. Multiply numerators and denominators (or flip and multiply for division)
  • 3. Simplify the result
  • 4. Convert back to mixed number if needed

Real-World Applications

Cooking & Recipes

Recipes often use mixed numbers for ingredient measurements (e.g., 2 1/2 cups of flour, 1 3/4 teaspoons of salt).

Construction & Carpentry

Measurements in inches are commonly expressed as mixed numbers (e.g., 5 3/4 inches, 12 1/2 feet).

Time Calculations

Time durations are often expressed in mixed numbers (e.g., 2 1/2 hours, 3 3/4 days).