Simplify Fractions Calculator
Reduce fractions to their lowest terms using GCD and prime factorization
Simplify Fractions
Simplified Result
Example Calculations
Simplifying 12/18
Step 1: Find GCD of 12 and 18
Step 2: Prime factors of 12: 2 × 2 × 3
Step 3: Prime factors of 18: 2 × 3 × 3
Step 4: GCD = 2 × 3 = 6
Step 5: 12 ÷ 6 = 2, 18 ÷ 6 = 3
Answer: 2/3
Mixed Number: 2 3/6
Step 1: Convert to improper: (2 × 6 + 3)/6 = 15/6
Step 2: Find GCD(15, 6) = 3
Step 3: 15 ÷ 3 = 5, 6 ÷ 3 = 2
Answer: 5/2 or 2 1/2
Types of Fractions
Proper Fractions
Numerator < Denominator
Example: 3/4, 5/8
Improper Fractions
Numerator ≥ Denominator
Example: 7/4, 9/3
Mixed Numbers
Whole number + proper fraction
Example: 2 1/3, 5 3/4
Simplification Tips
Find the GCD to reduce to lowest terms
Negative signs go in the numerator
Improper fractions can become mixed numbers
Denominator cannot be zero
Understanding Fraction Simplification
What is Simplifying Fractions?
Simplifying fractions means reducing them to their lowest terms by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). This makes fractions easier to work with and understand.
The GCD Method
The most efficient way to simplify fractions is to find the GCD of the numerator and denominator using the Euclidean algorithm, then divide both by this value.
Why Simplify Fractions?
- •Easier to compare and understand
- •Simpler arithmetic operations
- •Standard mathematical convention
- •Required in many mathematical contexts
Step-by-Step Process
Step 1: Find the GCD
Use prime factorization or the Euclidean algorithm
Step 2: Divide Both Terms
Divide numerator and denominator by the GCD
Step 3: Check Result
Verify the fraction is in lowest terms (GCD = 1)
Special Cases
- • Negative fractions: Keep the negative in the numerator
- • Improper fractions: Can be converted to mixed numbers
- • Zero numerator: Result is always 0
- • Equal terms: Result is always 1