Mixed Number / Improper Fraction Converter

A mixed number combines a whole number and a proper fraction (e.g., 3½). An improper fraction has a numerator larger than or equal to its denominator (e.g., 7/2). Converting between these forms is essential for arithmetic, cooking measurements, and algebra.

Converting mixed number to improper fraction: Improper Fraction = (Whole Number × Denominator + Numerator) ÷ Denominator

Converting improper fraction to mixed number: Whole Part = floor(Numerator ÷ Denominator) Remainder = Numerator mod Denominator Result = Whole Part and Remainder/Denominator

Adding mixed numbers:

1. Convert both to improper fractions
2. Find common denominator
3. Add numerators
4. Convert result back to mixed number

Multiplying mixed numbers:

1. Convert both to improper fractions
2. Multiply numerators together and denominators together
3. Simplify and convert back

Worked examples:

Mixed to improper: 4¾ = (4 × 4 + 3) ÷ 4 = (16 + 3) ÷ 4 = 19/4

Improper to mixed: 17/5 = floor(17 ÷ 5) = 3 remainder 2 = 3 and 2/5

Adding mixed numbers: 2⅓ + 1¾ = 7/3 + 7/4 (convert to improper) = 28/12 + 21/12 (common denominator 12) = 49/12 = 4 and 1/12

Multiplying: 2½ × 1⅓ = 5/2 × 4/3 = 20/6 = 10/3 = 3 and 1/3

Where this matters in real life:

• Cooking — recipes written in mixed numbers (2½ cups flour, 1¾ tsp salt)
• Woodworking — board lengths in feet and fractions (7⅝ inches)
• Medication — dosing in tablet fractions (1½ tablets)
• Algebra — improper fractions are required before most algebraic operations

Simplifying fractions: Always reduce by dividing both numerator and denominator by their Greatest Common Divisor (GCD). Example: 20/6 ÷ 2 = 10/3.