Fraction Calculator

Perform any operation on fractions - add, subtract, multiply, divide, and simplify.

What is a Fraction?

A fraction represents a part of a whole. It consists of two integers: the numerator (top number) which tells you how many parts you have, and the denominator (bottom number) which tells you how many equal parts the whole is divided into. For example, 3/4 means you have 3 out of 4 equal parts.

Fractions are one of the most fundamental concepts in mathematics and appear in everyday life constantly - from cooking recipes (1/2 cup of flour) to financial calculations (3/8 of a portfolio in equities) to engineering measurements. Understanding how to perform arithmetic operations on fractions is an essential skill.

A proper fraction has a numerator smaller than the denominator (e.g., 2/5). An improper fraction has a numerator equal to or greater than the denominator (e.g., 7/3). A mixed number combines a whole number with a proper fraction (e.g., 2 1/3). This calculator works with all types and automatically converts improper fractions to mixed numbers for readability.

Simplification is the process of reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). For instance, 8/12 simplifies to 2/3 because GCD(8,12) = 4, and dividing both by 4 gives 2/3. A fully simplified fraction has no common factor between numerator and denominator other than 1 - it is in its lowest terms.

This calculator handles all four arithmetic operations - addition, subtraction, multiplication, and division - and automatically simplifies results to lowest terms, shows the mixed number form, and displays the decimal equivalent.

Fraction Formulas

Addition: a/b + c/d = (a×d + c×b) / (b×d)

Example: 1/3 + 1/4 = (1×4 + 1×3) / (3×4) = 7/12

Subtraction: a/b − c/d = (a×d − c×b) / (b×d)

Example: 3/4 − 1/3 = (3×3 − 1×4) / (4×3) = 5/12

Multiplication: a/b × c/d = (a×c) / (b×d)

Example: 2/3 × 3/4 = 6/12 = 1/2

Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8

GCD simplification: Simplified fraction = original / GCD(numerator, denominator)

How to Use This Calculator

Steps to Calculate with Fractions

Select an operation using the tabs at the top: Add, Subtract, Multiply, or Divide.

Enter the first fraction by typing the numerator and denominator in the first set of fields.

Enter the second fraction in the second set of fields. Use negative values for negative fractions.

Click Calculate to see the simplified result, mixed number form, decimal value, and step-by-step working.

Example Calculations

Example 1 - Adding Fractions

What is 2/3 + 3/8?

Cross multiply: numerator = 2×8 + 3×3 = 16 + 9 = 25

Multiply denominators: 3×8 = 24

Result: 25/24. GCD(25,24) = 1, so already simplified.

2/3 + 3/8 = 25/24 = 1 1/24 ≈ 1.041667

Try this example →

Example 2 - Dividing Fractions

What is 5/6 ÷ 2/3?

Flip the second fraction (reciprocal): 2/3 becomes 3/2

Multiply: 5/6 × 3/2 = (5×3)/(6×2) = 15/12

Simplify: GCD(15,12) = 3, so 15/12 = 5/4

5/6 ÷ 2/3 = 5/4 = 1 1/4 = 1.25

Try this example →

Example 3 - Multiplying Fractions

What is 7/8 × 4/5?

Multiply numerators: 7×4 = 28

Multiply denominators: 8×5 = 40

Simplify 28/40: GCD(28,40) = 4, so 28/40 = 7/10

7/8 × 4/5 = 7/10 = 0.7

Try this example →

Frequently Asked Questions

How do you add fractions with different denominators?+

Find the least common denominator (LCD) of both fractions, convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, 1/3 + 1/4: the LCD is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12. Adding gives 7/12.

How do you multiply fractions?+

Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-simplify before multiplying to keep numbers smaller.

How do you divide fractions?+

To divide by a fraction, multiply by its reciprocal (flip numerator and denominator). For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which as a mixed number is 1 7/8.

What is a mixed number?+

A mixed number combines a whole number and a proper fraction, such as 2 3/4. To convert an improper fraction to a mixed number, divide the numerator by the denominator - the quotient is the whole number and the remainder is the new numerator.

How do you simplify a fraction?+

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD. For example, 12/18: GCD(12,18) = 6, so 12/18 = 2/3. A fraction is fully simplified when the GCD of numerator and denominator is 1.

How do you subtract fractions with different denominators?+

Subtracting fractions with different denominators follows the same steps as addition: (1) Find the Least Common Denominator (LCD). (2) Convert both fractions to equivalent fractions with the LCD. (3) Subtract the numerators and keep the denominator. (4) Simplify if possible. Example: 3/4 − 1/6. LCD = 12. Convert: 9/12 − 2/12 = 7/12. If the result is negative (e.g. 1/4 − 1/2 = −1/4), that is a valid answer.

What is the difference between a proper fraction and an improper fraction?+

A proper fraction has a numerator smaller than the denominator (e.g. 3/4, 7/8) - its value is less than 1. An improper fraction has a numerator greater than or equal to the denominator (e.g. 5/3, 11/4) - its value is 1 or more. Improper fractions can be expressed as mixed numbers (e.g. 5/3 = 1 and 2/3). In arithmetic operations, it is usually easier to work with improper fractions than mixed numbers - convert mixed numbers to improper fractions before multiplying or dividing.

How do you convert an improper fraction to a mixed number?+

To convert an improper fraction (where numerator is greater than denominator) to a mixed number: divide the numerator by the denominator. The quotient is the whole number part; the remainder becomes the new numerator over the original denominator. Example: 17/5. 17 divided by 5 = 3 remainder 2. So 17/5 = 3 and 2/5.

What is a proper fraction vs an improper fraction?+

A proper fraction has a numerator smaller than the denominator (e.g. 3/4, value less than 1). An improper fraction has a numerator equal to or greater than the denominator (e.g. 7/4, value 1 or more). Improper fractions are mathematically valid and are often easier to work with in calculations. Mixed numbers (1 and 3/4) are just improper fractions written differently.

How do you subtract fractions with different denominators?+

Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction with the LCD. Then subtract the numerators and keep the denominator. Example: 3/4 minus 1/6. LCD = 12. Convert: 9/12 minus 2/12 = 7/12. Always simplify the result to lowest terms.

Fraction Calculator

What is a Fraction?

Fraction Formulas

How to Use This Calculator

Steps to Calculate with Fractions

Example Calculations

Example 1 - Adding Fractions

What is 2/3 + 3/8?

Example 2 - Dividing Fractions

What is 5/6 ÷ 2/3?

Example 3 - Multiplying Fractions

What is 7/8 × 4/5?

Frequently Asked Questions

🔗 Related Calculators

📌 Quick Tips