Fraction Calculator
Enter the numerator (top number) and denominator (bottom number) for each fraction, select an operation, and click Calculate.
How to Use
- Enter the first fraction's numerator and denominator
- Select the operation (+, −, ×, ÷)
- Enter the second fraction's numerator and denominator
- Click "Calculate" to see the result
The calculator automatically simplifies the result and shows it as a fraction, mixed number, and decimal.
Understanding Fractions
A fraction represents a part of a whole. It consists of two numbers: the numerator (top) tells how many parts you have, and the denominator (bottom) tells how many equal parts the whole is divided into.
Adding and Subtracting Fractions
To add or subtract fractions, they must have the same denominator (common denominator):
a/b + c/d = (ad + bc) / bd
a/b - c/d = (ad - bc) / bd
Example: 1/4 + 1/3
- Find common denominator: 4 × 3 = 12
- Convert: 1/4 = 3/12 and 1/3 = 4/12
- Add: 3/12 + 4/12 = 7/12
Multiplying Fractions
To multiply fractions, multiply the numerators together and the denominators together:
a/b × c/d = (a × c) / (b × d)
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing Fractions
To divide fractions, multiply by the reciprocal (flip the second fraction):
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Simplifying Fractions
A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify, divide both by their greatest common factor (GCF):
Example: Simplify 8/12
- Find GCF of 8 and 12: GCF = 4
- Divide both by 4: 8÷4 = 2, 12÷4 = 3
- Simplified: 2/3
Mixed Numbers
A mixed number combines a whole number with a fraction (e.g., 2 1/3). When the numerator is larger than the denominator, the fraction is "improper" and can be converted to a mixed number:
Example: Convert 7/3 to a mixed number
- Divide: 7 ÷ 3 = 2 remainder 1
- Mixed number: 2 1/3
Related Calculators
Frequently Asked Questions
How do you add fractions with different denominators?
Find a common denominator (usually by multiplying the two denominators), convert each fraction to equivalent fractions with that denominator, then add the numerators. For example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
Why do you flip the second fraction when dividing?
Dividing by a fraction is the same as multiplying by its reciprocal. When you divide by 1/2, you're asking 'how many halves fit into this number?' which is the same as multiplying by 2. So a/b ÷ c/d = a/b × d/c.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator. For example: 7/3 = 7÷3 = 2 remainder 1, so 7/3 = 2 1/3.
What is the easiest way to simplify a fraction?
Find the GCF (Greatest Common Factor) of the numerator and denominator, then divide both by it. For 24/36: GCF of 24 and 36 is 12, so 24/36 = (24÷12)/(36÷12) = 2/3. You can also simplify step by step using small common factors.