Fraction Calculator

Add, subtract, multiply and divide fractions with steps shown.

Overview

Performs addition, subtraction, multiplication, and division on fractions, mixed numbers, and improper fractions with step-by-step simplification.

Formula & Calculation Method

Addition: a/b + c/d = (ad + bc) / bd | Multiplication: a/b × c/d = ac / bd | Division: a/b ÷ c/d = ad / bc

Converts mixed numbers to improper fractions, finds common denominators, and reduces results to lowest terms via GCD.

Worked Example: Adding 2/3 + 3/4

Inputs: Fraction 1 = 2/3 | Operation = Addition (+) | Fraction 2 = 3/4

  • Find common denominator for 3 and 4: LCM(3, 4) = 12
  • Convert numerators: (2 × 4) / 12 = 8/12 and (3 × 3) / 12 = 9/12
  • Add numerators: (8 + 9) / 12 = 17/12
  • Convert to mixed fraction: 1 and 5/12 (Decimal: 1.4167)

Summary: 2/3 + 3/4 = 17/12 | Mixed Number = 1 5/12 | Decimal = 1.4167

Common Use Cases

  • Carpentry & Woodworking: Calculate fractional imperial lumber measurements (e.g. 3/8" + 5/16").
  • Cooking & Baking: Halve or double recipe ingredient quantities with fractional cup measurements.
  • Algebra Homework: Verify manual fraction operations with complete step-by-step simplification breakdowns.

Frequently Asked Questions

What is an improper fraction?

A fraction where the numerator is greater than or equal to the denominator (e.g. 7/4), which converts to the mixed number 1 3/4.

Why can't you add fractions with different denominators directly?

Because the denominator defines the size of the fractional pieces; you must convert them to equal-sized pieces before adding.

What is the reciprocal of a fraction?

The reciprocal of a/b is b/a; multiplying a fraction by its reciprocal always equals 1.

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