Mixed Number Calculator – Add, Subtract, Multiply & Divide Mixed Numbers
Our mixed number calculator makes it easy to add, subtract, multiply, and divide mixed numbers in seconds. Simply enter the whole number and fraction parts of each mixed number, choose an operation, and get an instant simplified result. Whether you're helping your kids with homework or double-checking a recipe, this free tool handles all the heavy lifting for you.
Enter the whole number part of the first mixed number (can be 0)
Enter the numerator of the first fraction
Enter the denominator of the first fraction (must be positive)
Choose the arithmetic operation to perform
Enter the whole number part of the second mixed number (can be 0)
Enter the numerator of the second fraction
Enter the denominator of the second fraction (must be positive)
Your results will appear here
How to Use This Calculator
1. Enter the whole number part of your first mixed number in the 'First Whole Number' field (enter 0 if you only have a fraction). 2. Enter the numerator and denominator of the first fraction in the corresponding fields. 3. Select the arithmetic operation you want to perform: add, subtract, multiply, or divide. 4. Enter the whole number, numerator, and denominator for the second mixed number. 5. Click Calculate to instantly see the result as a mixed number, an improper fraction, a decimal, and a full step-by-step breakdown.
What Is a Mixed Number?
A mixed number (also called a mixed fraction) is a number that combines a whole number and a proper fraction. For example, 2½ is a mixed number — it means 2 whole units plus one half. Mixed numbers are commonly used in everyday life, from cooking measurements to construction dimensions.
How to Convert a Mixed Number to an Improper Fraction
Before performing arithmetic on mixed numbers, it is easiest to convert them to improper fractions (where the numerator is larger than the denominator). The formula is:
- Improper Numerator = (Whole Number × Denominator) + Numerator
- Keep the same Denominator
Example: 2½ → (2 × 2) + 1 = 5, so 2½ = 5/2
Adding Mixed Numbers
To add mixed numbers, convert each to an improper fraction, then find a common denominator:
- a/b + c/d = (a×d + c×b) / (b×d)
Finally, simplify and convert back to a mixed number.
Subtracting Mixed Numbers
Subtraction follows the same steps as addition, but you subtract the numerators instead:
- a/b − c/d = (a×d − c×b) / (b×d)
Multiplying Mixed Numbers
To multiply mixed numbers, convert to improper fractions and multiply numerators together and denominators together:
- a/b × c/d = (a×c) / (b×d)
Dividing Mixed Numbers
To divide mixed numbers, convert to improper fractions and multiply by the reciprocal of the second fraction:
- a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Simplifying the Result
After performing the operation, always simplify the result by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). Then convert back to a mixed number by dividing the numerator by the denominator to find the whole part, and using the remainder as the new numerator.
Example: 2½ + 1¾
- 2½ = 5/2, 1¾ = 7/4
- 5/2 + 7/4 = 10/4 + 7/4 = 17/4
- 17 ÷ 4 = 4 remainder 1 → 4¼