Simplify Fractions Calculator
Reduce fractions to their lowest terms
How to Simplify Fractions
Find the GCD
Find the Greatest Common Divisor (GCD) of the numerator and denominator.
Divide Both Numbers
Divide both the numerator and denominator by the GCD.
Check Result
If GCD = 1, the fraction is already in simplest form.
Examples
Example 1: Simplify 12/16
GCD of 12 and 16 = 4
12 ÷ 4 = 3
16 ÷ 4 = 4
Answer: 3/4
Example 2: Simplify 24/36
GCD of 24 and 36 = 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Answer: 2/3
Example 3: Simplify 15/20
GCD of 15 and 20 = 5
15 ÷ 5 = 3
20 ÷ 5 = 4
Answer: 3/4
Example 4: Simplify 7/13
GCD of 7 and 13 = 1
Answer: 7/13 (already in simplest form)
About Simplifying Fractions
Simplifying (or reducing) a fraction means expressing it in its lowest terms by dividing both the numerator and denominator by their greatest common divisor. This makes fractions easier to understand and work with.
What is Simplest Form?
A fraction is in simplest form (or lowest terms) when the numerator and denominator have no common factors other than 1. For example, 2/3 is in simplest form, but 4/6 is not (it can be reduced to 2/3).
Why Simplify Fractions?
- Easier to understand: 1/2 is clearer than 50/100
- Easier to compare: Comparing simplified fractions is simpler
- Standard form: Most math problems require answers in simplest form
- Cleaner calculations: Working with smaller numbers is easier
Finding the GCD
There are several methods to find the GCD:
- Listing factors: List all factors of both numbers and find the greatest common one
- Prime factorization: Break down into prime factors and multiply common ones
- Euclidean algorithm: Repeatedly divide and find remainders (used by this calculator)
Real-World Applications
Cooking: A recipe using 6/8 cup is clearer as 3/4 cup.
Money: 25/100 dollars is better expressed as 1/4 dollar (or 25 cents).
Measurements: 8/12 inch is simpler as 2/3 inch.
Common Simplifications
- 2/4 = 1/2
- 3/6 = 1/2
- 4/8 = 1/2
- 6/9 = 2/3
- 9/12 = 3/4
- 10/15 = 2/3
- 12/16 = 3/4
How to Use This Calculator
Enter Your Values
Input the required values in the calculator fields above. Make sure all inputs are valid numbers.
Click Calculate
Press the "Calculate" button to perform the calculation and see your results.
Review Results
Review the calculated results displayed below. Use these values for your needs.
Formula
Simplified Fraction = (Numerator ÷ GCD) / (Denominator ÷ GCD)
where GCD is the Greatest Common Divisor
Example: Simplify 12/18
Step 1: Find GCD(12, 18) = 6
Step 2: 12 ÷ 6 = 2, 18 ÷ 6 = 3
Step 3: Simplified fraction = 2/3
About Simplify Fractions Calculator
The Simplify Fractions Calculator reduces fractions to their lowest terms (simplest form) by finding the GCD and dividing both numerator and denominator. It shows the simplified fraction, GCD, decimal form, percentage, and mixed number representation.
When to Use This Calculator
- Quick Calculations: Get instant results without manual computation
- Accuracy: Ensure precise calculations every time
- Planning: Use for project planning and estimation
- Verification: Double-check your manual calculations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate calculations immediately
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works on all devices
- ✅ Accurate: Precise mathematical calculations
Tips for Best Results
- Double-Check Inputs: Verify all values before calculating
- Use Valid Numbers: Ensure inputs are valid numbers
- Review Results: Check results for reasonableness
- Clear and Retry: Clear inputs if you need to recalculate
Frequently Asked Questions
What is the GCD?
The GCD (Greatest Common Divisor) is the largest number that divides evenly into both the numerator and denominator. It is also called the GCF (Greatest Common Factor).
How do I know if a fraction is fully simplified?
A fraction is fully simplified when the GCD of the numerator and denominator is 1. This means they share no common factors other than 1.
Can all fractions be simplified?
No. If the numerator and denominator are coprime (share no common factors), the fraction is already in simplest form. For example, 3/7 and 5/11 cannot be simplified further.
Does simplifying change the value of the fraction?
No! Simplifying only changes how the fraction looks, not its value. 2/4, 3/6, and 1/2 all represent the same amount - they are equivalent fractions.
What if the numerator is larger than the denominator?
Simplify the same way! The result will be an improper fraction (or can be converted to a mixed number). For example, 12/8 simplifies to 3/2 or 1 1/2.