How to Simplify Fractions: Complete Guide
Simplifying fractions means reducing them to their lowest terms—making the numerator and denominator as small as possible while keeping the same value. Whether you're doing homework, cooking, or working with measurements, knowing how to simplify fractions is essential.
What Does "Simplifying" Mean?
A fraction is simplified (or in lowest terms) when the numerator and denominator have no common factors except 1.
12/18 is NOT simplified (12 and 18 share common factors)
2/3 IS simplified (2 and 3 share no common factors)
Both fractions equal the same value!
Method 1: Divide by GCD (Greatest Common Divisor)
This is the fastest and most reliable method.
Steps:
- Find the GCD of numerator and denominator
- Divide both by the GCD
- The result is the simplified fraction
Step 1: Find GCD(24, 36)
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCD = 12
Step 2: Divide both by 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Answer: 2/3
Method 2: Divide by Small Numbers
If you can't find the GCD quickly, divide by small numbers (2, 3, 5) repeatedly.
Both even, divide by 2: 48/72 = 24/36
Still both even, divide by 2 again: 24/36 = 12/18
Still both even, divide by 2 again: 12/18 = 6/9
Both divisible by 3: 6/9 = 2/3
Method 3: Prime Factorization
Break down numerator and denominator into prime factors, then cancel common ones.
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Cancel common factors (2², 3):
= 5/7
Answer: 5/7
Simplify Fractions Instantly
Free Fraction Calculator →Converting Between Fraction Types
Improper Fraction to Mixed Number
If numerator > denominator, convert to mixed number:
22 ÷ 7 = 3 remainder 1
Answer: 3 1/7
Mixed Number to Improper Fraction
(Whole × Denominator + Numerator) / Denominator
(3 × 7 + 1) / 7 = 22/7
Answer: 22/7
Fraction to Decimal
Simply divide numerator by denominator:
3 ÷ 4 = 0.75
Common Fractions & Their Simplified Forms
| Original | Simplified | Decimal |
|---|---|---|
| 2/4 | 1/2 | 0.5 |
| 3/6 | 1/2 | 0.5 |
| 4/8 | 1/2 | 0.5 |
| 6/9 | 2/3 | 0.667 |
| 9/12 | 3/4 | 0.75 |
| 15/20 | 3/4 | 0.75 |
| 12/16 | 3/4 | 0.75 |
| 10/15 | 2/3 | 0.667 |
Real-World Applications
1. Cooking & Recipes
Problem: Recipe calls for 6/8 cup of flour.
Simplified: 3/4 cup (easier to measure!)
2. Measurements
Problem: Board is 18/24 of a meter long.
Simplified: 3/4 meter
3. Test Scores
Problem: You got 45/60 questions correct.
Simplified: 3/4 = 75%
4. Splitting Bills
Problem: You paid 8/12 of the bill.
Simplified: 2/3 of the bill
Common Mistakes to Avoid
Mistake 1: Only Dividing One Part
Wrong: 12/18 → divide only top by 2 = 6/18
Right: Divide BOTH by GCD: 12/18 = 2/3
Mistake 2: Stopping Too Early
Wrong: 24/36 → divide by 2 = 12/18 (STOP)
Right: Keep going! 12/18 = 6/9 = 2/3
Mistake 3: Confusing Addition/Subtraction with Simplification
You CANNOT simplify before adding: 1/4 + 1/6 ≠ 2/10
Correct: Find common denominator first (12), then add: 3/12 + 2/12 = 5/12
When Fractions Can't Be Simplified
If the numerator and denominator share no common factors, the fraction is already in lowest terms:
- 3/7 (GCD = 1, already simplified)
- 5/8 (GCD = 1, already simplified)
- 11/13 (GCD = 1, already simplified)
Practice Problems
- Simplify 16/24
- Simplify 45/60
- Convert 17/5 to a mixed number
- Convert 2 3/8 to an improper fraction
- Simplify 100/150
Answers: 1) 2/3, 2) 3/4, 3) 3 2/5, 4) 19/8, 5) 2/3
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