Mixed Number Calculator: Convert, Add, Subtract & Simplify Fractions
A mixed number combines a whole number and a proper fraction — like 3 1/2 or 7 2/5. A free mixed number calculator converts between mixed and improper forms, then adds, subtracts, multiplies, or divides and simplifies the answer for you.
This guide covers the conversion rules, the four operations step by step, and when simplification matters — so you understand the math even when you use the ToolMars solver.
Convert, add, subtract, multiply & divide mixed numbers
Free mixed number calculator — improper fractions, simplification, private results.
Mixed Numbers vs Improper Fractions
A mixed number is whole + proper fraction (numerator < denominator). An improper fraction has a numerator greater than or equal to the denominator (like 11/4). Both represent the same value; improper fractions are usually easier for multiply and divide.
How to Convert Mixed ↔ Improper
Mixed → improper: (whole × denominator) + numerator, over the same denominator.
- Example: 3 2/5 → (3 × 5 + 2) / 5 = 17/5
Improper → mixed: divide numerator by denominator; write quotient as the whole number and remainder over the denominator.
- Example: 17/5 → 5 goes into 17 three times with remainder 2 → 3 2/5
Add, Subtract, Multiply & Divide Mixed Numbers
For reliable results, convert to improper fractions first, operate, then convert back and simplify:
Worked operations
- Add: 1 1/2 + 2 1/4 = 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3 3/4
- Subtract: 4 1/3 − 1 1/2 = 13/3 − 3/2 = 26/6 − 9/6 = 17/6 = 2 5/6
- Multiply: 2 1/3 × 1 1/2 = 7/3 × 3/2 = 7/2 = 3 1/2
- Divide: 3 1/2 ÷ 1 1/4 = 7/2 ÷ 5/4 = 7/2 × 4/5 = 14/5 = 2 4/5
Check any homework problem instantly with the ToolMars mixed number calculator.
How to Simplify Fractions (and Mixed Answers)
Divide numerator and denominator by their greatest common divisor (GCD). If the fraction is still improper, rewrite it as a mixed number. A fully simplified mixed answer has a proper fraction part in lowest terms — for example 10/4 becomes 5/2, then 2 1/2.
Convert, add, subtract, multiply & divide mixed numbers
Free mixed number calculator — improper fractions, simplification, private results.
Frequently Asked Questions
How do you convert a mixed number to an improper fraction?
Multiply whole × denominator, add the numerator, keep the denominator. Example: 2 3/4 = 11/4.
How do you convert an improper fraction to a mixed number?
Divide; quotient is the whole number, remainder over denominator is the fraction.
Can you add mixed numbers without converting to improper fractions?
Yes — add wholes and fractions separately, then regroup. Improper conversion is often safer.
What does it mean to simplify a mixed number?
Reduce the fraction part to lowest terms and ensure it is proper (numerator < denominator).
Does a mixed number calculator handle multiply and divide?
Yes — convert, operate on improper fractions, then convert back and simplify.