Mixed Fraction Calculator
Add, subtract, multiply, or divide two mixed fractions. Results shown as simplified mixed number, improper fraction, and decimal.
Reviewed & updated for 2026 · How we calculate
Working with mixed fractions step-by-step
Mixed fractions are everywhere in everyday measurements: cooking (2 ¾ cups), construction (5 ⅛ inches), and tools (1 ½ wrench). To do math with them, convert to improper fractions first, perform the operation, then convert back.
Converting mixed to improper fractions
Formula: improper numerator = (whole × denominator) + original numerator. Same denominator.
Example: 2 ⅓ → (2 × 3) + 1 = 7, denominator stays 3 → 7/3.
The four operations on fractions
- Addition / subtraction: Find a common denominator first. To add 1 ½ + 2 ⅓: convert to 3/2 + 7/3 → common denominator 6 → 9/6 + 14/6 = 23/6 = 3 ⅚.
- Multiplication: Convert to improper, then multiply numerators and denominators straight across. 2 ⅓ × 1 ½ = 7/3 × 3/2 = 21/6 = 7/2 = 3 ½. No common denominator needed.
- Division: Multiply by reciprocal. 2 ⅓ ÷ 1 ½ = 7/3 × 2/3 = 14/9 = 1 5/9. (Flip the second fraction, then multiply.)
Simplifying fractions
Always reduce to lowest terms. Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it.
Example: 18/24 → GCD(18, 24) = 6 → 18/6 = 3, 24/6 = 4 → 3/4. The calculator does this automatically.
Common applications
- Cooking: Doubling a recipe that calls for 1 ¾ cups flour: 1 ¾ × 2 = 3 ½ cups. Halving 2 ⅔ cup sugar: 2 ⅔ × ½ = 1 ⅓ cups.
- Carpentry: Stair tread depth 11 ¼" minus tread thickness ¾" = 10 ½" remaining. Cutting board lengths.
- Sewing: Pattern adjustments. Need 2 ⅜ yards of fabric for one curtain × 4 curtains = 9 ½ yards.
- Tools: Socket wrenches sized in fractions. 11/16" needs to grip a 5/8" + 1/16" bolt.
FAQs
What is a mixed fraction?
A mixed fraction (or mixed number) combines a whole number with a fraction. Example: 2 1/3, 5 7/8. Mathematically, 2 1/3 = 2 + 1/3 = 7/3 (as an improper fraction).
How do I add mixed fractions?
Two methods. Method 1: Convert both to improper fractions, find common denominator, add, simplify. Method 2: Add whole parts, add fractional parts separately, combine. Example: 2 1/4 + 1 1/3 = (2+1) + (1/4+1/3) = 3 + 7/12 = 3 7/12.
How do I convert improper fraction to mixed?
Divide numerator by denominator. The quotient is the whole part; the remainder over the original denominator is the fractional part. Example: 17/5 → 17÷5 = 3 remainder 2 → 3 2/5.
How do I simplify a fraction?
Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. Example: 12/16 → GCD is 4 → 12÷4 / 16÷4 = 3/4.