π° Mixed Number Calculator
Fraction arithmetic with every conversion and simplification step shown.
Simplified result
How to Use the Mixed Number Calculator
Enter each mixed number as whole, numerator, denominator. For a plain fraction like 3/4, set whole to 0. Pick the operation and calculate: every conversion, the arithmetic, and the simplification are shown.
Enter the first number as whole, numerator, denominator (whole = 0 for a simple fraction).
Choose the operation and enter the second number the same way.
Read the simplified mixed-number answer plus the full step breakdown.
The Method: Improper Fractions First
All mixed-number arithmetic goes through improper fractions. Convert: (whole Γ denominator + numerator) / denominator. Then add/subtract needs a common denominator (multiply the denominators, or better, the least common multiple), while multiply/divide work directly on numerators and denominators. Division flips the second fraction first. Finally, simplify by the GCD and convert back to mixed form by dividing.
Worked Examples
Addition: 1 1/2 + 2 1/3. Convert: 3/2 + 7/3. Common denominator 6: 9/6 + 14/6 = 23/6. Convert back: 23 Γ· 6 = 3 remainder 5, so 3 5/6. Multiplication: 2 1/2 Γ 1 1/4 = 5/2 Γ 5/4 = 25/8 = 3 1/8. Division: 2 1/2 Γ· 1 1/4 = 5/2 Γ 4/5 = 20/10 = 2. Subtraction: 3 1/4 β 1 2/3 = 13/4 β 5/3 = 39/12 β 20/12 = 19/12 = 1 7/12.
Simplifying with the GCD
A fraction is simplest when numerator and denominator share no common factor besides 1. The greatest common divisor is found with Euclid's algorithm: repeatedly replace the larger number with the remainder of dividing by the smaller until the remainder is zero. Example: GCD(25, 8): 25 mod 8 = 1, 8 mod 1 = 0, so GCD = 1 and 25/8 is already simplest. For 20/10 the GCD is 10, giving 2.
Frequently Asked Questions
What is a mixed number?
A mixed number combines a whole number with a fraction, like 2 3/4. It means 2 + 3/4. The mixed form is easy to read ("two and three quarters"), while the improper fraction form (11/4) is easier for arithmetic. This calculator converts between them automatically.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator: 2 3/4 = (2Γ4 + 3)/4 = 11/4. To convert back, divide: 11 Γ· 4 = 2 remainder 3, so 2 3/4. Every calculation here shows the conversion step.
How do you add mixed numbers?
Convert both to improper fractions, find a common denominator, add the numerators, then simplify and convert back. Example: 1 1/2 + 2 1/3 = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6. The calculator shows each of these steps.
How do you divide fractions?
Flip the second fraction (take its reciprocal) and multiply: a/b Γ· c/d = a/b Γ d/c. For mixed numbers, convert to improper fractions first. Example: 2 1/2 Γ· 1 1/4 = 5/2 Γ· 5/4 = 5/2 Γ 4/5 = 20/10 = 2.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common divisor (GCD). For 20/10, GCD is 10, giving 2/1 = 2. For 23/6, GCD is 1, so it is already simplest. Results here are always fully simplified.