How to Add, Subtract, Multiply & Divide Fractions (Step-by-Step Guide)

Fractions don't have to be confusing. Learn each operation with clear formulas, find common denominators easily, simplify your answers, and avoid the mistakes that trip up most people.

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What Is a Fraction?

A fraction represents a part of a whole. Every fraction has a numerator (top) and denominator (bottom). Types: Proper (1/2, 3/8), Improper (5/3, 7/4), Mixed number (2 1/3).

How to Add Fractions

Same denominator: Add numerators, keep denominator. 2/7 + 3/7 = 5/7. Different denominators: Find the LCD, convert, then add. 1/3 + 1/4: LCD = 12, 4/12 + 3/12 = 7/12.

How to Subtract Fractions

Find a common denominator, then subtract numerators. 5/8 - 3/8 = 2/8 = 1/4. 3/4 - 1/3 = 9/12 - 4/12 = 5/12. Never subtract denominators!

How to Multiply Fractions

Multiply numerators together and denominators together. 2/3 × 3/4 = 6/12 = 1/2. Pro tip: Cancel common factors before multiplying to simplify the math.

How to Divide Fractions

Flip the second fraction and multiply. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. 3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10 = 2 1/10.

How to Simplify Fractions

Find the GCD of numerator and denominator, then divide both. 12/18: GCD = 6, so 12÷6 / 18÷6 = 2/3.

Converting Between Fractions, Decimals & Percentages

Fraction → Decimal: Divide numerator by denominator: 3/4 = 0.75. Decimal → Fraction: Count decimal places: 0.75 = 75/100 = 3/4. Fraction → %: Multiply by 100: 3/4 = 75%.

Real-World Fraction Examples

🧁 Cooking: Recipe calls for 3/4 cup flour, make half → 3/4 × 1/2 = 3/8 cup. 🏠 Construction: Board 5 3/8 ft, remove 1 1/2 ft → 43/8 - 12/8 = 31/8 = 3 7/8 ft. 💰 Finance: Own 2/5 of business, sell 1/4 of share → keep 3/10.

Common Mistakes to Avoid

Adding denominators — 1/3 + 1/4 ≠ 2/7
Not simplifying — 4/8 should be 1/2
Flipping the wrong fraction when dividing
Forgetting to convert mixed numbers before multiplying/dividing
Cross-multiplying when you shouldn't

Key Takeaways

Add/Subtract: Find a common denominator first, then add or subtract numerators
Multiply: Multiply numerators together and denominators together
Divide: Flip the second fraction, then multiply
Always simplify your final answer to lowest terms

Ready to practice? Use our free Fraction Calculator to check your work and see step-by-step solutions.

FAQs

How do you add fractions with different denominators?

Find the least common denominator (LCD), convert each fraction so they share it, then add the numerators. For example, 1/3 + 1/4: LCD is 12, so convert to 4/12 + 3/12 = 7/12.

What is the difference between a proper and improper fraction?

A proper fraction has a numerator smaller than the denominator (like 3/4). An improper fraction has a numerator larger than or equal to the denominator (like 5/3). Improper fractions can be converted to mixed numbers.

How do you simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 8/12: GCD is 4, so 8÷4 / 12÷4 = 2/3.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals (like 1/3 = 0.333...).

What is a mixed number?

A mixed number combines a whole number and a proper fraction, like 2 1/3. To convert an improper fraction (7/3) to a mixed number, divide: 7 ÷ 3 = 2 remainder 1, so 2 1/3.