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, where recipes are written in mixed numbers (2½ cups flour, 1¾ tsp salt)
• Woodworking, where board lengths come in feet and fractions (7⅝ inches)
• Medication, dosed in tablet fractions (1½ tablets)
• Algebra, which needs improper fractions before most operations will work

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

What this page does, and what it does not. It converts in both directions and reduces the result. The arithmetic sections above are there because you almost always convert in order to add or multiply, and knowing why makes the conversion stick. For the arithmetic itself, convert both mixed numbers to improper fractions here, then take them to the fraction calculator linked below.