Fraction Calculator - Add, Subtract, Multiply & Divide Fractions

What is a Fraction Calculator?

A fraction calculator is a free online tool that performs mathematical operations on fractions including addition, subtraction, multiplication, and division. Whether you're a student working on math homework, a cook adjusting recipe measurements, a contractor calculating materials, or anyone needing to work with fractions, our calculator provides instant, accurate results with step-by-step solutions. It simplifies fractions, converts between mixed numbers and improper fractions, and shows the complete working process.

How to Use the Fraction Calculator

Calculating with fractions is simple:

1. Enter First Fraction: Input the numerator and denominator (e.g., 3/4)
2. Select Operation: Choose add (+), subtract (−), multiply (×), or divide (÷)
3. Enter Second Fraction: Input the second fraction's numerator and denominator
4. Include Mixed Numbers (Optional): Enter whole numbers for mixed fractions (e.g., 2 1/3)
5. Calculate: Click the button to compute the result
6. View Answer: See the result as a simplified fraction
7. Review Steps: Check the step-by-step solution to understand the process
8. Convert Format: Switch between improper fractions and mixed numbers

Understanding Fraction Basics

Parts of a Fraction

Numerator: The top number (how many parts you have)

Denominator: The bottom number (total parts the whole is divided into)

Example: In 3/4, the numerator is 3 and denominator is 4

Types of Fractions

Proper Fractions

Definition: Numerator is less than denominator

Examples: 1/2, 3/4, 5/8, 7/10

Value: Always less than 1

Improper Fractions

Definition: Numerator is greater than or equal to denominator

Examples: 5/4, 7/3, 9/5, 11/8

Value: Equal to or greater than 1

Mixed Numbers

Definition: Combination of whole number and proper fraction

Examples: 1 1/2, 2 3/4, 3 2/5, 5 1/8

Value: Always greater than 1

Conversion: 1 1/2 = 3/2 (improper fraction)

Equivalent Fractions

Definition: Different fractions representing the same value

Examples: 1/2 = 2/4 = 3/6 = 4/8 = 5/10

Use: Simplifying and comparing fractions

Simplifying Fractions

Reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Example: 8/12 ÷ 4/4 = 2/3 (simplified)

Fraction Operations Explained

Adding Fractions

Same Denominator (Easy!)

Add the numerators, keep the denominator the same.

Example: 1/5 + 2/5 = 3/5

Different Denominators (Need Common Denominator)

Find the least common denominator (LCD), convert both fractions, then add.

Subtracting Fractions

Same Denominator

Subtract the numerators, keep the denominator.

Example: 4/7 − 2/7 = 2/7

Different Denominators

Find LCD, convert, then subtract.

Multiplying Fractions

Simple Rule

Multiply numerators together, multiply denominators together, then simplify.

Example: 2/3 × 3/4 = 6/12 = 1/2 (simplified)

Shortcut: Cross-Canceling

Cancel common factors before multiplying to get simplified answer immediately.

Example: 2/3 × 3/4 → Cancel the 3s → 2/4 = 1/2

Dividing Fractions

Flip and Multiply Rule

Flip the second fraction (reciprocal), then multiply.

Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

Why It Works

Dividing by a fraction is the same as multiplying by its reciprocal.

Why Use a Fraction Calculator?

Homework Help

Get accurate answers quickly and learn the steps to solve fraction problems correctly on future assignments.

Avoid Common Errors

Eliminate mistakes from finding wrong common denominators, incorrect simplification, or arithmetic errors.

Save Time

Calculate complex fractions in seconds instead of spending minutes on manual calculations.

Learn the Process

Step-by-step solutions help you understand the method, not just get the answer, improving your math skills.

Recipe Adjustments

Double or halve recipe measurements accurately when cooking or baking for different serving sizes.

Construction & DIY

Calculate precise material measurements when working with lumber, tiles, fabric, or other materials measured in fractions.

Verify Your Work

Double-check manual calculations to ensure accuracy on homework, tests, or professional work.

Handle Mixed Numbers Easily

Convert between mixed numbers and improper fractions effortlessly for easier computation.

Frequently Asked Questions (FAQs)

How do you add fractions with different denominators?

Find the least common denominator (LCD), convert both fractions to equivalent fractions with that denominator, then add the numerators. Example: 1/3 + 1/4 → LCD is 12 → 4/12 + 3/12 = 7/12.

What is the easiest way to multiply fractions?

Multiply the numerators together and denominators together, then simplify. Even easier: cross-cancel common factors before multiplying. Example: 2/3 × 3/5 → Cancel the 3s → 2/5.

How do you divide fractions?

Flip the second fraction (find its reciprocal) and multiply. Example: 1/2 ÷ 3/4 becomes 1/2 × 4/3 = 4/6 = 2/3 simplified.

How do you simplify fractions?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, like 2 3/4 (two and three-quarters). It represents a value greater than one but is often easier to visualize than improper fractions.

How do you convert mixed numbers to improper fractions?

Multiply the whole number by the denominator, add the numerator, and place over the original denominator. Example: 2 3/4 → (2×4)+3 / 4 = 11/4.

How do you convert improper fractions to mixed numbers?

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator. Example: 11/4 → 11÷4 = 2 remainder 3 → 2 3/4.

Can fractions have negative numbers?

Yes! Negative fractions work the same way as positive ones. The negative sign can go on the numerator, denominator, or in front of the fraction. Example: -1/2 = 1/(-2) = -(1/2).

What is the least common denominator (LCD)?

The smallest number that is a multiple of all denominators in your problem. It's used to convert fractions to equivalent fractions for addition and subtraction. Example: LCD of 4 and 6 is 12.

Why can't the denominator be zero?

Division by zero is undefined in mathematics. A denominator of zero would mean dividing something into zero parts, which is impossible. Fractions with zero denominators don't exist.

How do you compare fractions?

Convert them to have the same denominator, then compare numerators. Or convert to decimals. Example: Which is bigger, 2/3 or 3/5? → 10/15 vs 9/15 → 2/3 is larger.

What's the difference between proper and improper fractions?

Proper fractions are less than 1 (numerator < denominator, like 3/4). Improper fractions are 1 or greater (numerator ≥ denominator, like 5/4). Both are mathematically valid.

How do you add mixed numbers?

Method 1: Convert to improper fractions, add, then convert back. Method 2: Add whole numbers and fractions separately, then combine. Example: 1 1/2 + 2 1/3 = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6.

Can you simplify before multiplying fractions?

Yes! This is called cross-canceling. If any numerator and any denominator share a common factor, divide both by that factor before multiplying. This gives you the simplified answer immediately.

What are equivalent fractions?

Fractions that represent the same value but have different numerators and denominators. Created by multiplying or dividing both parts by the same number. Example: 1/2 = 2/4 = 3/6 = 4/8.

Step-by-Step Examples

Example 1: Adding Fractions with Different Denominators

Example 2: Subtracting Mixed Numbers

Example 3: Multiplying Fractions with Simplification

Example 4: Dividing Fractions

Tips for Working with Fractions

1. Memorize Common Equivalents

• 1/2 = 0.5
• 1/4 = 0.25, 3/4 = 0.75
• 1/3 ≈ 0.33, 2/3 ≈ 0.67
• 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875

2. Always Simplify Final Answers

Reduce fractions to lowest terms unless specifically told not to. Teachers and applications expect simplified answers.

3. Use Cross-Canceling for Multiplication

Simplifying before multiplying is faster and gives you the simplified answer immediately—no reduction needed afterward.

4. Draw Pictures for Understanding

Visual representations help, especially for beginners. Draw circles or rectangles divided into parts to see what fractions represent.

5. Check Your Work with Decimals

Convert your fraction answer to a decimal and verify it makes sense. 3/4 should equal 0.75, for example.

6. Find LCD Efficiently

For two numbers, multiply them together and divide by their GCD. Or use the listing multiples method for small numbers.

7. Keep Track of Negative Signs

In subtraction, be careful with negative results. In multiplication/division, remember: same signs = positive, different signs = negative.

8. Practice Mental Math

Common fractions like halves, quarters, and thirds appear frequently. Being quick with these saves time.

Fraction to Decimal Conversion

Common Conversions to Memorize

Halves:

• 1/2 = 0.5

Thirds:

• 1/3 = 0.333... (repeating)
• 2/3 = 0.666... (repeating)

Quarters:

• 1/4 = 0.25
• 3/4 = 0.75

Fifths:

• 1/5 = 0.2
• 2/5 = 0.4
• 3/5 = 0.6
• 4/5 = 0.8

Eighths:

• 1/8 = 0.125
• 3/8 = 0.375
• 5/8 = 0.625
• 7/8 = 0.875

Tenths:

Easy! Just move decimal: 3/10 = 0.3, 7/10 = 0.7

How to Convert

Divide the numerator by the denominator.

Example: 3/8 → 3 ÷ 8 = 0.375

Practice Problems (Try These!)

Beginner Level

1. 1/4 + 1/4 = ?
2. 3/5 − 1/5 = ?
3. 2/3 × 3/4 = ?
4. 1/2 ÷ 1/4 = ?

Intermediate Level

5. 1/3 + 1/4 = ?
6. 5/6 − 1/3 = ?
7. 2 1/2 × 3 = ?
8. 3/4 ÷ 2/3 = ?

Advanced Level

9. 2 3/4 + 1 5/6 = ?
10. 4 1/3 − 2 3/4 = ?
11. 1 1/2 × 2 2/3 = ?
12. 3 1/4 ÷ 1 1/2 = ?