🇺🇸 US: Keep-Change-Flip 🇬🇧 UK: Multiply by reciprocal 🌐 Improper fractions

Mixed Number Calculator

Add, subtract, multiply, and divide mixed numbers (like 2½ and 1¾) with step-by-step working. Converts to/from improper fractions automatically and simplifies results.

Quick Answer
Mixed number a b/c → improper: (a×c+b)/c. To add: find common denominator. To divide: flip and multiply (2½ ÷ 1⅓ = 5/2 × 3/4 = 15/8 = 1⅞). Always simplify the result.

Number A

Number B

Country Mixed Number Style Preferred Form (Higher Grades) Division Method
🇺🇸 United States 2½ (whole + fraction)Mixed numbers preferred'Keep-Change-Flip' (KCF)
🇬🇧 United Kingdom 2½ (same)Improper fractions preferred at A-LevelMultiply by the reciprocal
🇦🇺 Australia 2½ (same)Improper fractions at senior schoolMultiply by the reciprocal
🇩🇪 Germany 2½ (written as 2 1/2)Improper (unechter Bruch) in GymnasiumKehren — multiply by reciprocal
🇫🇷 France 2 et ½ (less common)Improper (fraction impropre) preferredMultiply by the reciprocal
🇯🇵 Japan 2と½ (rare in secondary)Improper fractions standardMultiply by the reciprocal

Frequently Asked Questions

Why does the UK prefer improper fractions over mixed numbers at secondary level?

UK A-Level and GCSE Mathematics increasingly prefer improper fractions (e.g., 7/2 rather than 3½) because they're easier to manipulate algebraically — especially when fractions appear in equations, calculus, or complex expressions. Mixed numbers are useful for representing real-world quantities (2½ cups of flour), but improper fractions are cleaner in mathematical working. US curricula tend to keep mixed numbers longer because textbooks emphasise everyday applications. Both are mathematically equivalent — the choice is pedagogical and cultural.

How do you convert an improper fraction back to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number part; the remainder over the denominator is the fractional part. Example: 17/5 → 17 ÷ 5 = 3 remainder 2 → 3⅖. For negative improper fractions: -17/5 → -(17/5) → -3⅖. Always simplify the fractional part: 15/6 = 5/2 = 2½ (not 2 3/6).