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½ Fraction Calculator

Add, subtract, multiply and divide fractions and mixed numbers.

About the Fraction Calculator

Fractions appear everywhere — in recipes, construction measurements, financial ratios, music timing, and school math. Our Fraction Calculator performs all four arithmetic operations on fractions and mixed numbers, shows the step-by-step process, and automatically simplifies the result to its lowest terms.

Whether you're helping a child with homework, scaling a recipe, calculating a material cut, or checking your algebra work, this tool gives you the complete answer with the work shown — so you understand the process, not just the result.

How It Works

Enter two fractions (or mixed numbers). Select the operation: add, subtract, multiply, or divide. The calculator finds the least common denominator for addition and subtraction, applies the appropriate formula, and simplifies the result using the greatest common divisor (GCD).

Formula / Key Reference

Addition: a/b + c/d = (a×d + c×b) / (b×d), then simplify
Subtraction: a/b − c/d = (a×d − c×b) / (b×d), then simplify
Multiplication: a/b × c/d = (a×c) / (b×d), then simplify
Division: a/b ÷ c/d = (a×d) / (b×c), then simplify

Simplification: Divide numerator and denominator by GCD

Real-World Example

Scenario: A recipe calls for 2/3 cup of butter and 3/4 cup of milk. You want to make 1.5 batches and need to know the total combined liquid.

Step 1 — Scale each by 1.5 (or 3/2):

2/3 × 3/2 = 6/6 = 1 cup butter
3/4 × 3/2 = 9/8 = 1 1/8 cup milk

Step 2 — Add them:

1 + 9/8 = 8/8 + 9/8 = 17/8 = 2 1/8 cups total

Answer: You need 2 and 1/8 cups of combined liquid ingredients. The step-by-step view in the calculator shows every GCD simplification so you can follow along.

Common Uses

  • Elementary and middle school math homework
  • Scaling cooking or baking recipes up or down
  • Construction: adding fractional measurements (3/4" + 1 1/8")
  • Financial calculations involving fractional shares or interests
  • Checking calculator or algebra work in school or tutoring

Frequently Asked Questions

How do I add fractions with different denominators? ▼
Find the least common denominator (LCD) of both fractions, convert each fraction to an equivalent fraction with the LCD, then add the numerators. For example: 1/3 + 1/4 — LCD is 12, so it becomes 4/12 + 3/12 = 7/12.
How do I convert a mixed number to a fraction? ▼
Multiply the whole number by the denominator, then add the numerator. For 2 3/4: (2 × 4) + 3 = 11, so it equals 11/4. The calculator accepts mixed numbers directly.
What is a simplified fraction? ▼
A fraction is fully simplified (in lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, divide both by their greatest common divisor (GCD). For 12/18: GCD is 6, so 12/18 = 2/3.
Why do you flip the second fraction when dividing? ▼
Dividing by a fraction is the same as multiplying by its reciprocal. So a/b ÷ c/d = a/b × d/c. The mathematical proof: (a/b) / (c/d) = (a/b) × (d/c) = ad/bc. This is the 'keep, change, flip' rule taught in school.
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