Fraction Calculator

Fraction Calculator

Add, subtract, multiply, divide fractions with mixed numbers. Shows simplified result with step-by-step working.

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What is a Fraction Calculator?

A Fraction Calculator performs the four basic arithmetic operations (add, subtract, multiply, divide) on fractions, automatically simplifying the result. Essential for: middle/high school math homework, cooking recipe adjustments (half of 3/4 cup), construction measurements (board lengths in feet/inches), music theory (note durations), probability calculations, engineering ratios. The tool handles improper fractions (5/3), mixed numbers (1 2/3), and reduces results using greatest common divisor (GCD). Both fraction form and decimal equivalent displayed.

How to use this tool

  1. Enter Fraction A — Numerator and denominator as separate fields.
  2. Choose operation — +, -, ×, ÷
  3. Enter Fraction B — Same format.
  4. Click Calculate — Result shown as simplified fraction + decimal.

Fraction operations

Add/Subtract: a/b ± c/d = (a×d ± c×b) / (b×d)

Multiply: (a/b) × (c/d) = (a×c) / (b×d)

Divide: (a/b) ÷ (c/d) = (a×d) / (b×c)

Simplify: Divide both numerator and denominator by their GCD (Greatest Common Divisor).

Example: 1/2 + 1/3
= (1*3 + 1*2) / (2*3)
= 5/6 (already simplified, GCD = 1)

Examples

  • Recipe halving: 3/4 cup ÷ 2 = 3/8 cup
  • Combining ingredients: 1/4 + 1/3 = 7/12
  • Pizza fractions: 1/2 pizza × 3 people = 3/2 = 1.5 pizzas
  • Music timing: 1/4 note + 1/8 note = 3/8 note
  • Test problem: 2/3 ÷ 4/5 = 10/12 = 5/6

Tips & best practices

  • Negative fractions work — sign on numerator
  • Divide by zero gives error — check denominators
  • Result shows as mixed number if numerator > denominator
  • Decimal equivalent always shown alongside
  • For three+ fractions: chain operations (result × next fraction)

Frequently Asked Questions

What does 1 1/2 mean in fractions?

Mixed number: 1 whole + 1/2 = 3/2 improper fraction. To convert: (whole × denominator + numerator) / denominator.

Why is 6/8 simplified to 3/4?

GCD of 6 and 8 is 2. Divide both: 6/2 = 3, 8/2 = 4. So 6/8 = 3/4 (simpler representation, same value).

How do I add three fractions?

Add two first, then add the result to the third. Or find common denominator for all three at once.

Can I do fractions with variables?

Not this tool — numerical only. For algebraic fractions (x/2 + 1/x), use Wolfram Alpha or symbolic math software.

What if both denominators are huge?

Common denominator becomes very large but tool handles standard integer sizes. For huge fractions, BigInt support would be needed.

Related tools

Decimal to Fraction · GCD & LCM Calculator · Percentage Calculator

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