How do I add fractions?

Adding fractions: Same denominator: Add numerators, keep denominator. 1/4 + 2/4 = 3/4. Different denominators: Find LCM (Least Common Multiple). Convert both fractions. Add numerators. Example: 1/2 + 1/3. LCM(2,3) = 6. Convert: 1/2 = 3/6, 1/3 = 2/6. Add: 3/6 + 2/6 = 5/6. Simplify if needed: 2/4 + 1/4 = 3/4 (already simplified). 4/6 + 2/6 = 6/6 = 1 (simplifies to 1). More examples: 1/4 + 1/8: LCM(4,8)=8, 2/8 + 1/8 = 3/8. 2/3 + 1/6: LCM(3,6)=6, 4/6 + 1/6 = 5/6.

How do I multiply fractions?

Multiplying fractions: Simple rule: Multiply numerators, multiply denominators. No common denominator needed. Example: 1/2 × 1/3 = (1×1)/(2×3) = 1/6. More examples: 2/3 × 3/4 = 6/12 = 1/2 (simplify). 1/2 × 2/1 = 2/2 = 1. 3/4 × 4/5 = 12/20 = 3/5 (simplify). Simplify before or after: Before: Cancel common factors first. 2/3 × 3/4: Cancel 3s → 2/1 × 1/4 = 2/4 = 1/2. After: Multiply then simplify. 2/3 × 3/4 = 6/12, simplify = 1/2. With whole numbers: Convert to fraction (5 = 5/1). 5 × 1/2 = 5/1 × 1/2 = 5/2 = 2 1/2.

How do I divide fractions?

Dividing fractions: Rule: Multiply by reciprocal (flip second fraction). Keep-Change-Flip method: Keep first fraction. Change ÷ to ×. Flip second fraction. Example: 1/2 ÷ 1/4. Keep: 1/2. Change: ÷ to ×. Flip: 1/4 becomes 4/1. Multiply: 1/2 × 4/1 = 4/2 = 2. More examples: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2. 2/3 ÷ 2/3 = 2/3 × 3/2 = 6/6 = 1 (anything divided by itself = 1). 1/2 ÷ 3 = 1/2 ÷ 3/1 = 1/2 × 1/3 = 1/6. Why flip: Division is opposite of multiplication. 6 ÷ 2 = 3 because 3 × 2 = 6. 1/2 ÷ 1/4 = ? asks "how many 1/4s in 1/2?" = 2 (because 2 × 1/4 = 1/2).

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Fraction Calculator

Add, subtract, multiply, and divide fractions with detailed step-by-step solutions showing all work and simplification processes. Features support for proper fractions, improper fractions, mixed numbers, whole numbers, and automatic simplification to lowest terms. Perfect for students learning fraction operations, teachers creating examples, cooks adjusting recipes, and anyone needing accurate fraction math with visual explanations.

How to Use the Fraction Calculator

Use the Fraction Calculator to add, subtract, multiply, and divide fractions with detailed step-by-step solutions showing all work and simplification processes. Features support for proper fractions, improper fractions, mixed numbers, whole numbers, and automatic simplification to lowest terms. Perfect for students learning fraction operations, teachers creating examples, cooks adjusting recipes, and anyone needing accurate fraction math with visual explanations.. Enter your values to get accurate, instant results tailored to your situation.

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Fraction Operations Guide

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Expert Tips

Adding Fractions: Find Common Denominator: 1/4 + 1/6 → LCD = 12 → 3/12 + 2/12 = 5/12. Multiply numerator and denominator to convert: 1/4 × 3/3 = 3/12. Can't add unlike denominators directly.
Multiplying Fractions: Multiply Straight Across: 2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5 (simplified). No common denominator needed. Simplify before or after—before is easier: 2/3 × 3/5 → cancel 3s → 2/5 directly.
Dividing Fractions: Multiply by Reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. "Keep-Change-Flip": Keep first fraction, change ÷ to ×, flip second fraction. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
Simplify by Dividing by GCD: 12/18 → GCD = 6 → 12÷6 / 18÷6 = 2/3. Quick GCD: Factor both, find common factors. 24/36 = (2×2×2×3)/(2×2×3×3) = cancel 2×2×3 = 2/3. Always reduce to lowest terms.

Essential Fundamentals — Fraction rules

Operations

Addition/Subtraction: Requires common denominator. Find LCD (least common multiple of denominators). 1/3 + 1/4 → LCD 12 → 4/12 + 3/12 = 7/12. Subtraction same: 1/2 - 1/3 → 3/6 - 2/6 = 1/6.
Multiplication/Division: Multiply: Straight across (a/b × c/d = ac/bd). Divide: Multiply by reciprocal (a/b ÷ c/d = a/b × d/c). Simplify first to avoid large numbers: 4/9 × 3/8 → cancel 4 and 8 (÷4) → 1/9 × 3/2 → 3/18 → 1/6.

Advanced Strategies — Complex fraction operations

Efficiency Techniques

Cross-Cancellation: Simplify before multiplying. 15/28 × 14/45 → cancel 15 and 45 (÷15), cancel 14 and 28 (÷14) → 1/2 × 1/3 = 1/6. Avoids large intermediate numbers.
Complex Fractions: Fraction divided by fraction: (3/4)/(5/6) = 3/4 × 6/5 = 18/20 = 9/10. Multiply by reciprocal of denominator. Simplify step-by-step for clarity.

Frequently Asked Questions

How do I add fractions?: Adding fractions: Same denominator: Add numerators, keep denominator. 1/4 + 2/4 = 3/4. Different denominators: Find LCM (Least Common Multiple). Convert both fractions. Add numerators. Example: 1/2 + 1/3. LCM(2,3) = 6. Convert: 1/2 = 3/6, 1/3 = 2/6. Add: 3/6 + 2/6 = 5/6. Simplify if needed: 2/4 + 1/4 = 3/4 (already simplified). 4/6 + 2/6 = 6/6 = 1 (simplifies to 1). More examples: 1/4 + 1/8: LCM(4,8)=8, 2/8 + 1/8 = 3/8. 2/3 + 1/6: LCM(3,6)=6, 4/6 + 1/6 = 5/6.
How do I multiply fractions?: Multiplying fractions: Simple rule: Multiply numerators, multiply denominators. No common denominator needed. Example: 1/2 × 1/3 = (1×1)/(2×3) = 1/6. More examples: 2/3 × 3/4 = 6/12 = 1/2 (simplify). 1/2 × 2/1 = 2/2 = 1. 3/4 × 4/5 = 12/20 = 3/5 (simplify). Simplify before or after: Before: Cancel common factors first. 2/3 × 3/4: Cancel 3s → 2/1 × 1/4 = 2/4 = 1/2. After: Multiply then simplify. 2/3 × 3/4 = 6/12, simplify = 1/2. With whole numbers: Convert to fraction (5 = 5/1). 5 × 1/2 = 5/1 × 1/2 = 5/2 = 2 1/2.
How do I divide fractions?: Dividing fractions: Rule: Multiply by reciprocal (flip second fraction). Keep-Change-Flip method: Keep first fraction. Change ÷ to ×. Flip second fraction. Example: 1/2 ÷ 1/4. Keep: 1/2. Change: ÷ to ×. Flip: 1/4 becomes 4/1. Multiply: 1/2 × 4/1 = 4/2 = 2. More examples: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 = 1 1/2. 2/3 ÷ 2/3 = 2/3 × 3/2 = 6/6 = 1 (anything divided by itself = 1). 1/2 ÷ 3 = 1/2 ÷ 3/1 = 1/2 × 1/3 = 1/6. Why flip: Division is opposite of multiplication. 6 ÷ 2 = 3 because 3 × 2 = 6. 1/2 ÷ 1/4 = ? asks "how many 1/4s in 1/2?" = 2 (because 2 × 1/4 = 1/2).