Easily add, subtract, multiply, or divide two fractions. This calculator handles all four operations and shows clear, simplified results to help you understand each step.
Enter your fractions and choose an operation to get an instant answer.
How to Use the Expanded Form Calculator
Using the calculator is simple:
- Enter the numerator and denominator for the first fraction
- Select the operation: addition (+), subtraction (−), multiplication (×), or division (÷)
- Enter the numerator and denominator for the second fraction
- Click Calculate
- View the simplified result
Important:
- Denominators cannot be 0
- Numerators can be 0 (for example, 0/5)
What Are Fraction Operations?
Fractions can be combined using the four basic operations:
- Addition
- Subtraction
- Multiplication
- Division
Each operation follows its own set of rules, which the calculator applies automatically.
How Each Operation Works
Adding Fractions
To add fractions, you need a common denominator:
- Multiply across to create a common denominator
- Add the numerators
- Simplify the result
Example:
(5/10) + (55/150)
→ (5×150 + 55×10) / (10×150)
→ 1300 / 1500
→ Simplified: 13/15
Subtracting Fractions
Subtraction follows the same process as addition:
- Find a common denominator
- Subtract the numerators
- Simplify
Multiplying Fractions
Multiply straight across:
- Numerators × numerators
- Denominators × denominators
Example:
(2/3) × (4/5) = 8/15
Dividing Fractions
Flip the second fraction and multiply:
- Keep the first fraction
- Invert the second fraction
- Multiply
Example:
(2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6
Simplifying Fractions
After performing any operation, the result is simplified using the greatest common divisor (GCD).
For example:
1300 / 1500
GCD = 100
→ 13 / 15
This ensures your final answer is in its simplest form.
Example Calculation
Let’s walk through a full example:
(5/10) + (55/150)
Step 1: Cross multiply
→ (5×150 + 55×10) / (10×150)
Step 2: Calculate
→ (750 + 550) / 1500
→ 1300 / 1500
Step 3: Simplify
→ Divide by GCD (100)
→ 13 / 15
Frequently Asked Questions
Q1: How do you add fractions with different denominators?
Find a common denominator, then add the numerators.
Q2: Do you always need to simplify the answer?
Yes, results are usually given in simplest form.
Q3: What happens when you divide fractions?
You multiply by the reciprocal of the second fraction.
Q4: Can fractions have zero numerators?
Yes, for example 0/5 = 0.
Q5: Why is division by zero not allowed?
Because it is undefined in mathematics.