Fraction Calculator — Add, Subtract, Multiply & Divide
Add, subtract, multiply, and divide fractions with step-by-step solutions. Simplify fractions, compare them, convert between fractions and decimals, find fractions of numbers, and discover equivalent fractions — all with interactive visual pie charts.
What is a Fraction?
A fraction represents a part of a whole. Every fraction has a numerator (top number) and denominator (bottom number). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.
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.
Proper Fractions
Numerator < denominator (e.g., 1/2, 3/8). Represents less than one whole.
Improper Fractions
Numerator ≥ denominator (e.g., 5/3, 7/4). Can be converted to mixed numbers.
Mixed Numbers
Whole number + proper fraction (e.g., 2 1/3). Convert: multiply whole number by denominator, add numerator.
How to Add Fractions
Same Denominator
2/7 + 3/7 = 5/7
Add numerators, keep denominator.
Different Denominators
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Find LCD, convert, then add numerators.
How to Subtract Fractions
Find a common denominator, then subtract numerators. Never subtract denominators!
5/8 − 3/8 = 2/8 = 1/4
3/4 − 1/3 = 9/12 − 4/12 = 5/12
How to Multiply Fractions
Multiply numerators together and denominators together. Pro tip: Cancel common factors before multiplying to simplify the math.
2/3 × 3/4 = 6/12 = 1/2
Cross-cancel: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2
How to Divide Fractions
Flip the second fraction and multiply. Remember: "Keep, Change, Flip" — keep the first fraction, change division to multiplication, flip the second fraction.
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 (Greatest Common Divisor) of numerator and denominator, then divide both by it.
8/12 → GCD = 4 → 8÷4 / 12÷4 = 2/3
12/18 → GCD = 6 → 12÷6 / 18÷6 = 2/3
Converting Between Fractions, Decimals & Percentages
Converting between formats is essential for everyday math. Here are the three most common conversions:
Fraction → Decimal
3/4 = 3 ÷ 4 = 0.75
Divide numerator by denominator.
Decimal → Fraction
0.75 = 75/100 = 3/4
Count decimal places, put over power of 10, simplify.
Fraction → Percentage
3/4 × 100 = 75%
Multiply by 100.
Real-World Fraction Examples
Fractions appear everywhere — from your kitchen to job sites to bank statements. Here are practical examples that show how fraction math works in daily life.
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 = 30%.
Common Mistakes to Avoid
Adding Denominators
1/3 + 1/4 ≠ 2/7. You must find a common denominator first!
Not Simplifying
4/8 should always be simplified to 1/2.
Flipping the Wrong Fraction
When dividing, only flip the second fraction, not the first.
Forgetting Mixed Numbers
Convert mixed numbers to improper fractions before multiplying or dividing.
Cross-Multiplying at the Wrong Time
Cross-multiplication is for comparing fractions or solving proportions — not for adding or subtracting.
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.
- Compare fractions: Convert to a common denominator or decimal to see which is larger.
- Practice: Use our free Fraction Calculator to check your work and see step-by-step solutions.
Common Fraction, Decimal & Percentage Conversions
Quick reference for the most commonly used fractions. Bookmark this page for easy access.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/10 | 0.10 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.20 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333 | 33.33% |
| 3/8 | 0.375 | 37.5% |
| 2/5 | 0.40 | 40% |
| 1/2 | 0.50 | 50% |
| 3/5 | 0.60 | 60% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.6667 | 66.67% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.80 | 80% |
| 5/6 | 0.8333 | 83.33% |
| 7/8 | 0.875 | 87.5% |
| 1/1 | 1.00 | 100% |
Fraction Operation Quick Reference
A summary of every fraction operation at a glance.
| Operation | Rule | Example |
|---|---|---|
| Add | Find common denominator, add numerators | 1/3 + 1/4 = 4/12 + 3/12 = 7/12 |
| Subtract | Find common denominator, subtract numerators | 3/4 − 1/3 = 9/12 − 4/12 = 5/12 |
| Multiply | Multiply numerators, multiply denominators | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Flip second fraction, then multiply | 1/2 ÷ 1/4 = 1/2 × 4/1 = 2 |
| Simplify | Divide numerator and denominator by GCD | 8/12 → GCD=4 → 2/3 |
Frequently Asked Questions About Fractions
What is a fraction?
A fraction represents a part of a whole. Every fraction has a numerator (top) and denominator (bottom). Types: Proper (numerator < denominator, like 1/2), Improper (numerator ≥ denominator, like 5/3), Mixed number (whole number + fraction, like 2 1/3).
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.
How do you subtract fractions?
Find a common denominator, then subtract numerators. Never subtract denominators! Example: 5/8 − 3/8 = 2/8 = 1/4. For different denominators: 3/4 − 1/3 = 9/12 − 4/12 = 5/12.
How do you 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 do you divide fractions?
To divide fractions, flip the second fraction and multiply. Remember: Keep, Change, Flip — keep the first fraction, change division to multiplication, flip the second fraction. Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
How do you simplify a fraction?
Find the GCD (Greatest Common Divisor) of the numerator and denominator, then divide both by it. Example: 8/12 → GCD=4 → 8÷4/12÷4 = 2/3.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals (like 1/3 = 0.333...).
How do you convert a decimal to a fraction?
Count the decimal places, put the digits over the appropriate power of 10, then simplify. Example: 0.75 = 75/100 = 3/4.
How do you convert a fraction to a percentage?
Multiply the fraction by 100. Example: 3/4 × 100 = 75%. You can also convert to decimal first (0.75) then multiply by 100.
What is an equivalent fraction?
Equivalent fractions represent the same value but have different numerators and denominators. Example: 1/2, 2/4, 3/6, and 4/8 are all equivalent.
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.
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.
Reviewed by Shahid
Content Reviewer & Calculator SpecialistContent reviewer specializing in marketing, finance, health, and math calculators on GM Calculator.