Math

Mixed Number Calculator

Add, subtract, multiply, and divide mixed numbers. Shows improper fraction conversion and step-by-step work.

Quick Answer

Convert mixed numbers to improper fractions, find a common denominator (for +/−), perform the operation, then simplify. 2 1/3 + 1 2/5 = 7/3 + 7/5 = 35/15 + 21/15 = 56/15 = 3 11/15.

Enter Mixed Numbers

Format: Whole Numerator / Denominator. Leave whole number as 0 for proper fractions.

Results

3 11/15

Mixed Number

56/15

Improper Fraction

Step-by-Step

Convert to improper fractions: 7/3 and 7/5

Common denominator: 15

Adjusted: 35/15 + 21/15

Simplify: 56/15

Result: 3 11/15

About This Tool

The Mixed Number Calculator performs addition, subtraction, multiplication, and division on mixed numbers and fractions. It converts mixed numbers to improper fractions, performs the chosen operation, simplifies the result, and converts back to a mixed number — showing every step.

How Mixed Number Arithmetic Works

The first step is always converting mixed numbers to improper fractions. Multiply the whole number by the denominator and add the numerator. For 2 1/3: (2 × 3) + 1 = 7, so 2 1/3 = 7/3. Then perform the operation using standard fraction arithmetic.

Addition and Subtraction

After converting to improper fractions, find the least common denominator (LCD). Adjust both fractions to have this denominator, then add or subtract the numerators. Simplify the result and convert back to a mixed number if needed.

Multiplication and Division

Multiplication is simpler: multiply numerators together and denominators together, then simplify. For division, multiply by the reciprocal of the second fraction. 2 1/3 ÷ 1 2/5 = 7/3 × 5/7 = 35/21 = 5/3 = 1 2/3.

Simplification

The calculator always returns the result in its simplest form by dividing both numerator and denominator by their greatest common factor. This ensures you get the cleanest possible answer.

Frequently Asked Questions

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. 3 2/5 becomes (3×5+2)/5 = 17/5.

How do I add mixed numbers?

Convert to improper fractions, find a common denominator, add the numerators, simplify, and convert back. Or add the whole numbers and fractions separately.

How do I multiply mixed numbers?

Convert to improper fractions, multiply numerators together and denominators together, then simplify. 1 1/2 × 2 1/3 = 3/2 × 7/3 = 21/6 = 7/2 = 3 1/2.

What is an improper fraction?

A fraction where the numerator is greater than or equal to the denominator, like 7/3. It can be converted to a mixed number: 7/3 = 2 1/3.

How do I divide mixed numbers?

Convert to improper fractions, flip the second fraction (reciprocal), then multiply. 2 1/4 ÷ 1 1/2 = 9/4 × 2/3 = 18/12 = 3/2 = 1 1/2.

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