Fraction Calculator — Step-by-Step Solutions

The Fraction Calculator lets you add, subtract, multiply, and divide fractions with ease. It automatically simplifies results to their lowest terms and can convert between improper fractions and mixed numbers.

Enter two fractions, choose an operation, and get your answer instantly. The calculator handles whole numbers, proper fractions, improper fractions, and mixed numbers.

Numerator 1

Denominator 1

Numerator 2

Denominator 2

Result

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Your calculations will appear here

How to Use the Fraction Calculator

Select the operation you need: Add, Subtract, Multiply, Divide, or Simplify. The calculator adjusts its inputs to match your chosen mode.
For Add, Subtract, Multiply, and Divide, enter the numerator and denominator for both fractions. For Simplify, enter a single fraction.
The result appears instantly in its simplest form. Review the step-by-step breakdown to see how the answer was reached, including LCD calculation and simplification.
Use the visual bar and donut chart to see the fraction represented graphically. Toggle between fraction, decimal, and percentage formats below the result.
Share your calculation using the generated URL, which encodes all inputs and the selected mode.

Formula and Theory

A fraction represents a part of a whole, written as a numerator (top number) over a 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.

To add or subtract fractions, they must share a common denominator. The least common denominator (LCD) is the smallest number that both denominators divide into evenly. Once converted, you simply add or subtract the numerators and keep the denominator.

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Dividing by a fraction is equivalent to multiplying by its reciprocal (flipping the second fraction upside down).

Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). A fraction is fully simplified when the GCD of the numerator and denominator is 1.

Worked Examples

Example 1: Adding two fractions

Problem: Calculate 1/4 + 2/3

Solution: The LCD of 4 and 3 is 12. Convert: 1/4 = 3/12 and 2/3 = 8/12. Add the numerators: 3 + 8 = 11. The result is 11/12.

Answer: 11/12

Example 2: Subtracting fractions

Problem: Calculate 5/6 - 1/3

Solution: The LCD of 6 and 3 is 6. Convert: 5/6 stays as 5/6 and 1/3 = 2/6. Subtract: 5 - 2 = 3. The result is 3/6, which simplifies to 1/2.

Answer: 1/2

Example 3: Multiplying fractions

Problem: Calculate 3/5 x 2/7

Solution: Multiply numerators: 3 x 2 = 6. Multiply denominators: 5 x 7 = 35. The result is 6/35, which is already in its simplest form.

Answer: 6/35

Example 4: Dividing fractions

Problem: Calculate 4/9 divided by 2/3

Solution: Flip the second fraction to get 3/2. Multiply: 4/9 x 3/2 = 12/18. Simplify by dividing both by the GCD (6): 12/6 = 2, 18/6 = 3.

Answer: 2/3

Example 5: Simplifying a fraction

Problem: Simplify 24/36

Solution: Find the GCD of 24 and 36, which is 12. Divide both: 24/12 = 2 and 36/12 = 3. The simplified fraction is 2/3.

Answer: 2/3

Frequently Asked Questions

Why do fractions need a common denominator for addition and subtraction?

Fractions must have the same denominator so that each fraction represents parts of the same size. You cannot directly add thirds and quarters because the pieces are different sizes. Converting to a common denominator makes the parts equal, allowing you to add or subtract the numerators.

What is the difference between GCD and LCD?

The greatest common divisor (GCD) is the largest number that divides evenly into two numbers. It is used to simplify fractions. The least common denominator (LCD) is the smallest number that both denominators divide into, and it is used when adding or subtracting fractions.

Why do you flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. If you divide by 2/3, you are asking "how many groups of 2/3 fit in here?" which is mathematically equivalent to multiplying by 3/2.

Can the numerator be larger than the denominator?

Yes. When the numerator is larger than the denominator, the fraction is called an improper fraction and its value is greater than 1. For example, 7/4 equals 1 and 3/4. Improper fractions are perfectly valid and often easier to work with in calculations.

What happens if the denominator is zero?

Division by zero is undefined in mathematics, so a fraction with a denominator of zero has no value. The calculator will display an error message if you enter zero as a denominator.