Lowest Term Calculator
Simplify fractions to their lowest terms with step-by-step solutions
Enter Your Fraction
Results
Decimal Form
Calculation Details
Solution Summary
Common Examples
Example 1
Example 2
Example 3
Example 4
Key Concepts
Lowest Terms
The simplified form where GCD of numerator and denominator is 1
GCD Method
Divide both numerator and denominator by their greatest common divisor
Equivalent Fractions
Different fractions that represent the same value
Proper vs Improper
Proper fractions are less than 1, improper fractions are ≥ 1
How to Simplify
Find Factors
List all factors of numerator and denominator
Find GCD
Identify the greatest common divisor
Divide Both
Divide numerator and denominator by GCD
Check Result
Verify GCD of result equals 1
Tips & Applications
Simplified fractions are easier to understand and compare
Essential for cooking, construction, and measurements
Foundation for fraction arithmetic operations
Supports both standard and mixed number forms
Automatically detects if fraction is already simplified
Understanding Lowest Terms
What are Lowest Terms?
A fraction is in its lowest terms (or simplest form) when the greatest common divisor (GCD) of the numerator and denominator equals 1. This means the fraction cannot be reduced further.
Why Simplify Fractions?
- • Easier to understand: 1/2 is clearer than 8/16
- • Easier to compare: Which is larger, 3/4 or 6/8?
- • Simpler calculations: Adding 1/4 + 1/2 vs 3/12 + 6/12
- • Standard form: Mathematical convention for final answers
Finding the GCD
Method 1: List all factors and find the largest common one
Method 2: Use the Euclidean algorithm
Method 3: Prime factorization method
Worked Example
Simplify 18/24
Step 1: Find factors
• Factors of 18: 1, 2, 3, 6, 9, 18
• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Common factors: 1, 2, 3, 6
Step 3: GCD = 6
Step 4: 18÷6 = 3, 24÷6 = 4
Result: 18/24 = 3/4
Quick Check
To verify a fraction is in lowest terms:
• Find GCD of numerator and denominator
• If GCD = 1, it's already simplified
• If GCD > 1, divide both by the GCD
Common Mistakes to Avoid
❌ Incorrect
• Only dividing by small numbers like 2 or 3
• Stopping before reaching lowest terms
• Forgetting to check if already simplified
• Dividing numerator and denominator by different numbers
✅ Correct
• Find the GCD first, then divide
• Continue until GCD equals 1
• Check if fraction is already in lowest terms
• Always divide both parts by the same number
Real-World Applications
🍕 Cooking
Recipe measurements: 6/8 cup = 3/4 cup is easier to measure
🏗️ Construction
Material measurements: 16/32 inch = 1/2 inch bolts
📊 Statistics
Survey results: 12/16 responses = 3/4 or 75%