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Mixed Fraction Calculator
Last updated: June 19, 2026
A mixed fraction calculator is an arithmetic utility that performs addition, subtraction, multiplication, and division on mixed numbers and improper fractions. It automatically converts mixed numbers to improper fractions, computes the selected mathematical operation, reduces the resulting fraction using its greatest common divisor (GCD), and yields both the simplified mixed fraction and its decimal equivalent with step-by-step work.
Add, subtract, multiply, and divide mixed numbers or improper fractions. Renders the simplified mixed number and step-by-step calculations.
Quick Answer
Add, subtract, multiply, or divide mixed numbers and improper fractions. Renders the simplified mixed fraction and improper fraction results.
First Mixed Number
Operation
Second Mixed Number
Simplified Result
3 3/4
Improper Fraction: 15/4
Step-by-Step Solution:
- Convert 1 1/2 to improper fraction: 3/2
- Convert 2 1/4 to improper fraction: 9/4
- Find a common denominator: (3 × 4) / (2 × 4) + (9 × 2) / (4 × 2)
- Calculate: 12/8 + 18/8 = 30/8
- Simplify fraction by dividing by GCD (2): 15/4
- Convert improper fraction back to mixed number: 3 3/4
How it works
How to calculate with mixed numbers
Operating directly on mixed numbers is prone to errors. The safest mathematical approach involves these three stages:
1. Convert to Improper Fractions
Multiply the whole number by the denominator, then add the numerator to get the new numerator:
Improper Numerator = (Whole × Denominator) + Numerator
2. Perform the Fraction Arithmetic
- Addition/Subtraction: Cross-multiply to find a common denominator, then add/subtract numerators.
- Multiplication: Multiply the numerators together and denominators together.
- Division: Invert the second fraction (the reciprocal) and multiply.
3. Simplify and Reconvert
Reduce the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD). If the numerator is larger than the denominator, convert it back into a mixed number.
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Frequently asked questions
A mixed fraction (or mixed number) is a combination of a whole number and a proper fraction, such as 1 1/2. It represents the sum of the whole number and the fraction.
To add mixed fractions, first convert each mixed fraction into an improper fraction. Find a common denominator, add the numerators, and then convert the resulting improper fraction back into a mixed fraction if necessary.
Convert both mixed numbers to improper fractions, then multiply the numerators together and the denominators together. Simplify the resulting fraction and convert it back to a mixed number.
No, division requires converting them to improper fractions first. After converting, multiply the first fraction by the reciprocal (the inverted version) of the second fraction.
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