Fraction Calculator
Calculate fractions instantly with our free online fraction calculator. Add, subtract, multiply, and divide fractions with ease. Simplify fractions to lowest terms, convert to decimals and percentages, and work with mixed numbers. Get step-by-step solutions perfect for homework, cooking, woodworking, and more. Trusted by over 40 million students and teachers worldwide.
How to Calculate Fractions
To calculate with fractions, you need to understand the basic operations:
- Adding/Subtracting: Find a common denominator, then add or subtract the numerators
- Multiplying: Multiply numerators together and denominators together
- Dividing: Multiply by the reciprocal (flip the second fraction)
- Simplifying: Divide numerator and denominator by their GCF
Example: 2/3 × 3/5 = 6/15 = 2/5
🔍 Quick Answers to Common Fraction Questions
How do I add fractions with different denominators?
To add fractions with different denominators, find the least common denominator (LCD), convert each fraction, then add the numerators. Example: 1/4 + 1/3 → LCD is 12 → 3/12 + 4/12 = 7/12.
How do I multiply fractions?
To multiply fractions, multiply the numerators together and denominators together. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. Tip: Simplify before multiplying for easier math!
How do I divide fractions?
To divide fractions, multiply by the reciprocal (flip the second fraction). Remember: "Keep, Change, Flip" — 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
How do I simplify a fraction?
To simplify, divide both numerator and denominator by their greatest common factor (GCF). Example: 12/18 → GCF is 6 → 12÷6 / 18÷6 = 2/3.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions create repeating decimals: 1/3 = 0.333...
What's the difference between a proper and improper fraction?
A proper fraction has a numerator smaller than its denominator (like 3/4). An improper fraction has a numerator ≥ denominator (like 7/4), which can be written as a mixed number (1¾).
📋 Fraction Cheat Sheet (Common Equivalents)
Memorize these common fraction-decimal-percentage conversions for quick mental math:
🌍 Where Fractions Are Used in Real Life
Cooking & Recipes
💡 Double a recipe: 3/4 cup × 2 = 1½ cups
Woodworking & Construction
💡 5/8" + 3/16" = 13/16"
Music & Time Signatures
💡 3/4 time = waltz rhythm
Finance & Stocks
💡 1/4 of $1000 = $250
📚 Complete Guide to Fraction Operations
Adding and Subtracting Fractions
The key to adding or subtracting fractions is having a common denominator. Once you have the same denominator, simply add or subtract the numerators.
Different Denominators: a/b + c/d = (ad + bc)/bd
✓ Example: Add 2/3 + 1/4
Step 1: Find LCD of 3 and 4 = 12
Step 2: Convert: 2/3 = 8/12 and 1/4 = 3/12
Step 3: Add numerators: 8/12 + 3/12 = 11/12
Multiplying Fractions
Multiplying fractions is straightforward: multiply straight across. Numerator × Numerator and Denominator × Denominator.
✓ Example: Multiply 3/4 × 2/5
3 × 2 = 6 (numerator)
4 × 5 = 20 (denominator)
Result: 6/20 = 3/10 (simplified)
Dividing Fractions
To divide fractions, remember "Keep, Change, Flip": Keep the first fraction, change division to multiplication, and flip the second fraction.
✓ Example: Divide 1/2 ÷ 3/4
Keep: 1/2
Change: ÷ becomes ×
Flip: 3/4 becomes 4/3
Calculate: 1/2 × 4/3 = 4/6 = 2/3
❓ Frequently Asked Questions
The LCD is the smallest number that both denominators divide into evenly. To find it: 1) List the multiples of each denominator, 2) Find the smallest number that appears in both lists. For example, for 1/4 and 1/6, the LCD is 12 (multiples of 4: 4, 8, 12... multiples of 6: 6, 12...). Alternatively, multiply the denominators and simplify if needed.
Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator. Example: 11/4 → 11 ÷ 4 = 2 remainder 3 → 2¾.
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. Example: 2¾ → (2 × 4) + 3 = 11, so the answer is 11/4.
Equivalent fractions represent the same value but have different numerators and denominators. You create them by multiplying or dividing both parts by the same number. Example: 1/2 = 2/4 = 3/6 = 4/8 = 50/100. They all equal 0.5 or 50%.
Write the decimal over 1, then multiply both by 10 for each decimal place. Finally, simplify. Example: 0.625 → 625/1000 → divide both by 125 → 5/8. For repeating decimals like 0.333..., the fraction is 1/3.
Yes! A negative fraction has a negative value. You can write it as -1/2, or (-1)/2, or 1/(-2) — they all equal the same thing: -0.5. When multiplying or dividing, the same rules apply: negative × positive = negative, negative × negative = positive.
There are two easy methods: 1) Convert both to decimals and compare, or 2) Cross-multiply: for a/b vs c/d, compare a×d with b×c. If a×d > b×c, then a/b is larger. Example: 2/3 vs 3/5 → 2×5=10 vs 3×3=9 → 10>9 → 2/3 > 3/5.
Yes! This fraction calculator is 100% free with no signup required. Use it unlimited times on any device — desktop, tablet, or mobile. All calculations happen instantly in your browser with no data stored on our servers. Perfect for students, teachers, cooks, carpenters, and anyone working with fractions!
This calculator and content has been reviewed for mathematical accuracy by our team of educators and math specialists.
Last reviewed and updated: February 15, 2026
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