Fraction Calculator - Add, Subtract, Multiply & Divide Fractions Online
Solve fraction problems instantly with step-by-step solutions. Add, subtract, multiply, divide fractions and mixed numbers. Free, accurate, no sign up required.
Quick Fraction Operations
Click any example to calculate instantly
How to Use the Fraction Calculator
Follow these simple steps to solve any fraction problem
Enter Your Fractions
Type the numerator (top number) and denominator (bottom number) for each fraction. Add whole numbers for mixed fractions like 2½.
Choose Operation
Select whether you want to add, subtract, multiply, or divide the fractions using the operation buttons at the top.
Get Your Answer
Click calculate to see your result simplified to lowest terms, plus decimal and percentage equivalents with full step-by-step solution.
Fraction Operations Explained
Understanding the four basic operations with fractions
Adding Fractions
Same denominators: Add the numerators and keep the denominator.
Different denominators: Find the common denominator first, then add.
Subtracting Fractions
Same denominators: Subtract the numerators and keep the denominator.
Different denominators: Find the common denominator first, then subtract.
Multiplying Fractions
Simple rule: Multiply numerators together and denominators together.
Tip: Simplify before multiplying to work with smaller numbers.
Dividing Fractions
Keep, Change, Flip: Keep the first fraction, change to multiplication, flip the second.
Remember: Dividing by a fraction is the same as multiplying by its reciprocal.
Common Fractions Reference Chart
Quick reference for fraction, decimal, and percentage conversions
| Fraction | Decimal | Percentage | Fraction | Decimal | Percentage |
|---|---|---|---|---|---|
| ½ | 0.5 | 50% | ⅕ | 0.2 | 20% |
| ⅓ | 0.333... | 33.33% | ⅖ | 0.4 | 40% |
| ¼ | 0.25 | 25% | ⅗ | 0.6 | 60% |
| ⅔ | 0.666... | 66.67% | ⅘ | 0.8 | 80% |
| ¾ | 0.75 | 75% | ⅙ | 0.166... | 16.67% |
| ⅛ | 0.125 | 12.5% | ⅚ | 0.833... | 83.33% |
| ⅜ | 0.375 | 37.5% | ⅐ | 0.142... | 14.29% |
| ⅝ | 0.625 | 62.5% | ⅑ | 0.111... | 11.11% |
| ⅞ | 0.875 | 87.5% | ⅒ | 0.1 | 10% |
Why Use Our Fraction Calculator?
Trusted by students, teachers, and professionals worldwide
Instant Results
Get accurate answers in milliseconds. No waiting, no page reloads. Results appear immediately as you calculate.
Step-by-Step Solutions
Every calculation shows the complete solution process. Perfect for learning and understanding fraction math.
Always Simplified
Results are automatically reduced to lowest terms. No need to simplify manually after calculating.
Multiple Formats
See your answer as a fraction, mixed number, decimal, and percentage all at once for complete understanding.
Works Everywhere
Use on any device with a web browser. Phone, tablet, laptop, desktop. No app download required.
100% Free Forever
No sign up, no subscription, no hidden fees. Use unlimited calculations without any restrictions.
Real World Fraction Applications
Fractions are everywhere in daily life
Cooking & Baking
Scale recipes up or down by multiplying fractions. Combine ingredients measured in cups, tablespoons, and teaspoons.
Construction & DIY
Calculate lumber measurements, tile spacing, and material quantities. Work with inches and feet in fractional form.
Finance & Business
Calculate stock prices, ownership percentages, and financial ratios that are often expressed as fractions.
Music & Rhythm
Understand time signatures, note durations, and rhythm patterns that are based on fractional divisions.
Engineering
Work with precise measurements, gear ratios, and scaling factors that require fractional calculations.
Science & Medicine
Calculate dosages, concentrations, and ratios used in chemistry, biology, and medical applications.
Understanding Fractions: A Complete Guide
Fractions represent parts of a whole and are one of the most fundamental concepts in mathematics. A fraction consists of two numbers separated by a line: the numerator on top tells you how many parts you have, while the denominator on the bottom tells you how many equal parts make up the whole. For example, three quarters means you have 3 parts out of 4 equal parts.
This fraction calculator handles all four basic operations: addition, subtraction, multiplication, and division. It works with proper fractions where the numerator is smaller than the denominator, improper fractions where the numerator is larger, and mixed numbers that combine whole numbers with fractions. Every result is automatically simplified to its lowest terms.
How Fraction Addition and Subtraction Work
Adding and subtracting fractions requires a common denominator. When fractions share the same denominator, you simply add or subtract the numerators while keeping the denominator unchanged. For instance, two fifths plus one fifth equals three fifths because you add 2 plus 1 to get 3, keeping 5 as the denominator.
When denominators differ, you must find the least common denominator before proceeding. The LCD is the smallest number that both denominators divide into evenly. Once you convert both fractions to equivalent fractions with this common denominator, addition and subtraction become straightforward. Our calculator handles this conversion automatically and shows you each step.
Multiplying and Dividing Fractions
Multiplication is actually simpler than addition because you do not need a common denominator. To multiply fractions, multiply the numerators together to get the new numerator, then multiply the denominators together to get the new denominator. Two thirds times three quarters equals six twelfths, which simplifies to one half.
Division uses a technique called multiplying by the reciprocal. To divide by a fraction, you flip the second fraction upside down and multiply instead. This works because dividing by a number is the same as multiplying by its inverse. Half divided by one quarter becomes half times four, which equals two. The phrase "keep, change, flip" helps many students remember this process.
Working with Mixed Numbers
Mixed numbers combine whole numbers with fractions, like two and three quarters. To calculate with mixed numbers, you typically convert them to improper fractions first. Multiply the whole number by the denominator, add the numerator, and place that result over the original denominator. Two and three quarters becomes eleven quarters because 2 times 4 plus 3 equals 11.
After completing your calculation, you may want to convert an improper fraction back to a mixed number. Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same. Our calculator performs these conversions automatically and displays results in both formats.
Simplifying Fractions to Lowest Terms
A fraction is in lowest terms when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor of both numbers and divide both by it. Six eighths simplifies to three quarters because both 6 and 8 are divisible by 2.
This calculator uses an efficient algorithm to find the GCD and always presents results in simplified form. Simplified fractions are easier to understand, compare, and use in further calculations. They also help you recognize equivalent fractions and see relationships between different fractional values.
Practical Tips for Fraction Calculations
When working with fractions by hand, simplifying before you multiply can make calculations easier. If you notice that a numerator and denominator in different fractions share a common factor, divide both by that factor first. This cross cancellation technique keeps numbers smaller and reduces the need for simplification afterward.
For addition and subtraction, finding the least common denominator rather than just any common denominator results in smaller numbers. While multiplying the two denominators always gives a common denominator, it may not be the smallest one. The LCD makes arithmetic simpler and results require less simplification.
Frequently Asked Questions
Everything you need to know about fraction calculations
How do I add fractions with different denominators?
To add fractions with different denominators, first find the least common denominator (LCD). Convert each fraction to an equivalent fraction with this LCD by multiplying both numerator and denominator by the necessary factor. Then add the numerators while keeping the common denominator. Finally, simplify if possible. For example, to add 1/3 + 1/4, the LCD is 12. 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 its denominator, representing a value less than 1 (like 3/4). An improper fraction has a numerator equal to or larger than its denominator, representing a value of 1 or greater (like 5/4). Improper fractions can be converted to mixed numbers. For example, 5/4 equals 1 and 1/4.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. Place this result over the original denominator. For example, to convert 2 3/4: multiply 2 × 4 = 8, then add 3 to get 11. The improper fraction is 11/4. Our calculator handles mixed numbers automatically in all operations.
Why do I need to flip the second fraction when dividing?
Dividing by a fraction is the same as multiplying by its reciprocal (flipped version). This is because division asks "how many times does this fit into that?" When you flip and multiply, you are finding how many groups of the divisor fit into the dividend. The rule "keep, change, flip" helps remember: keep the first fraction, change division to multiplication, flip the second fraction.
What does it mean to simplify or reduce a fraction?
Simplifying a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD) until they share no common factors except 1. For example, 6/8 simplifies to 3/4 because both 6 and 8 are divisible by 2. Simplified fractions are easier to work with and understand. Our calculator automatically simplifies all results.
How do I 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... Our calculator shows decimal equivalents for all results, including repeating decimals rounded to a practical number of digits.
How do I convert a fraction to a percentage?
Convert the fraction to a decimal, then multiply by 100. Alternatively, find an equivalent fraction with 100 as the denominator. For example, 3/4 = 0.75 = 75%. Our calculator displays percentage equivalents automatically alongside fraction and decimal results.
Can this calculator handle negative fractions?
Yes, you can enter negative numbers for the numerator, denominator, or whole number. The calculator handles negative fractions correctly in all operations. A negative sign can be placed with either the numerator or denominator; the result will be properly signed.
What is the least common denominator and why does it matter?
The least common denominator (LCD) is the smallest number that all denominators in a problem divide into evenly. Using the LCD rather than just any common denominator keeps numbers smaller and calculations simpler. For 1/4 and 1/6, the LCD is 12 (not 24), making it easier to add: 3/12 + 2/12 = 5/12.
Is this fraction calculator free to use?
Yes, this fraction calculator is completely free with no limitations. You can perform unlimited calculations without signing up or paying anything. It works on all devices with a web browser, including smartphones, tablets, and computers. There are no ads that block functionality or require payment to remove.
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