Mixed Fraction Calculator - Add, Subtract, Multiply & Divide Mixed Numbers

What Is a Mixed Fraction and How to Calculate It?

A mixed fraction (also called a mixed number) is a whole number combined with a proper fraction. For example, 2 1/2 means two whole units plus one-half. Mixed fractions are commonly used in everyday life — recipes (1 1/2 cups of flour), measurements (2 3/4 inches), construction (1 1/2 feet), and many other practical applications.

Here's the thing: mixed fractions are easier to understand than improper fractions for most people. 7/3 as an improper fraction is harder to visualize than 2 1/3 as a mixed number. That's why this calculator converts between mixed numbers and improper fractions automatically.

How to Convert Improper Fraction to Mixed Number

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.

Example 1: 7/3 = 7 ÷ 3 = 2 remainder 1 → 2 1/3

Example 2: 11/4 = 11 ÷ 4 = 2 remainder 3 → 2 3/4

Example 3: 15/6 = 15 ÷ 6 = 2 remainder 3 → 2 3/6 = 2 1/2 (simplified)

How to Convert Mixed Number to Improper Fraction

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.

Formula: (Whole × Denominator + Numerator) / Denominator

Example 1: 2 1/2 = (2 × 2 + 1)/2 = 5/2

Example 2: 3 3/4 = (3 × 4 + 3)/4 = 15/4

Example 3: 1 2/3 = (1 × 3 + 2)/3 = 5/3

How to Add Mixed Fractions

Method 1 (Convert to Improper Fractions): Convert both mixed numbers to improper fractions, find common denominator, add, simplify, convert back to mixed number.

Example: 2 1/2 + 1 1/3 = 5/2 + 4/3 = (15/6 + 8/6) = 23/6 = 3 5/6

Method 2 (Add Separately): Add whole numbers and fractions separately, then combine.

2 + 1 = 3 (whole numbers). 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Total = 3 5/6

How to Subtract Mixed Fractions

Convert both mixed numbers to improper fractions, find common denominator, subtract, simplify, convert back to mixed number.

Example: 3 1/2 - 1 1/4 = 7/2 - 5/4 = 14/4 - 5/4 = 9/4 = 2 1/4

How to Multiply Mixed Fractions

Convert both mixed numbers to improper fractions, multiply numerators and denominators, simplify, convert back to mixed number.

Example: 2 1/3 × 1 1/2 = 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2

How to Divide Mixed Fractions

Convert both mixed numbers to improper fractions, multiply the first by the reciprocal of the second, simplify, convert back to mixed number.

Example: 3 1/2 ÷ 1 1/4 = 7/2 ÷ 5/4 = 7/2 × 4/5 = 28/10 = 14/5 = 2 4/5

Frequently Asked Questions About Mixed Fractions

Q: What is a mixed fraction?
A: A mixed fraction (mixed number) is a whole number combined with a proper fraction, such as 2 1/2 or 3 3/4.

Q: How to convert improper fraction to mixed number?
A: Divide numerator by denominator. Quotient = whole number, remainder = new numerator, denominator stays same. Example: 7/3 = 2 1/3.

Q: How to convert mixed number to improper fraction?
A: Multiply whole number by denominator, add numerator, keep denominator. Example: 2 1/2 = (2×2+1)/2 = 5/2.

Q: How to add mixed fractions?
A: Convert to improper fractions, find common denominator, add, simplify. Example: 2 1/2 + 1 1/3 = 3 5/6.

Q: How to multiply mixed fractions?
A: Convert to improper fractions, multiply numerators and denominators, simplify. Example: 2 1/3 × 1 1/2 = 3 1/2.

Try the mixed fraction calculator above. Enter your mixed numbers. Get instant results. No signup required.