Comparing Fractions Calculator
Compare two fractions to see which is greater
How to Compare Fractions
Find Common Denominator
Find the Least Common Denominator (LCD) of both fractions.
Convert Both Fractions
Convert both fractions to equivalent fractions with the common denominator.
Compare Numerators
With the same denominator, the fraction with the larger numerator is greater.
Examples
Example 1: Compare 2/3 and 3/4
LCD of 3 and 4 = 12
2/3 = 8/12
3/4 = 9/12
Since 8 < 9, therefore 2/3 < 3/4
Answer: 2/3 is less than 3/4
Example 2: Compare 5/6 and 10/12
LCD of 6 and 12 = 12
5/6 = 10/12
10/12 = 10/12
Since 10 = 10, therefore 5/6 = 10/12
Answer: The fractions are equal
Example 3: Compare 7/8 and 3/4
LCD of 8 and 4 = 8
7/8 = 7/8
3/4 = 6/8
Since 7 > 6, therefore 7/8 > 3/4
Answer: 7/8 is greater than 3/4
About Comparing Fractions
Comparing fractions means determining which fraction represents a larger (or smaller) quantity, or if they represent the same amount. This skill is essential in math, cooking, construction, and everyday decision-making.
Methods to Compare Fractions
- Common Denominator Method: Convert to same denominator, compare numerators
- Cross Multiplication: For a/b vs c/d, compare a×d with b×c
- Decimal Conversion: Convert both to decimals and compare
- Benchmark Comparison: Compare both to common benchmarks like 1/2 or 1
Special Cases
- Same Denominator: Just compare numerators directly
- Same Numerator: Smaller denominator = larger fraction
- One is Whole Number: Convert to fraction with denominator 1
- Negative Fractions: More negative = smaller value
Real-World Applications
Cooking: Which is more: 2/3 cup or 3/4 cup of flour?
Shopping: Which discount is better: 1/4 off or 30/100 off?
Construction: Which board is thicker: 5/8 inch or 11/16 inch?
Sports: Who ran farther: 3/4 mile or 7/10 mile?
Quick Comparison Tips
- If both fractions are less than 1/2, the one closer to 1/2 is larger
- A fraction greater than 1 is always larger than one less than 1
- With same numerator, smaller denominator means larger fraction (2/3 > 2/5)
- With same denominator, larger numerator means larger fraction (3/4 > 2/4)
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
Method 1: Common Denominator - Convert both to same denominator, compare numerators
Method 2: Cross Multiplication - For a/b vs c/d, compare a×d with b×c
Method 3: Decimal Conversion - Convert to decimals and compare
Example: Compare 2/3 and 3/4
Method 1: LCD = 12, so 2/3 = 8/12, 3/4 = 9/12. Since 8 < 9, therefore 2/3 < 3/4
Method 2: Cross multiply: 2×4 = 8, 3×3 = 9. Since 8 < 9, therefore 2/3 < 3/4
Method 3: Decimals: 2/3 = 0.666..., 3/4 = 0.75. Since 0.666... < 0.75, therefore 2/3 < 3/4
About Comparing Fractions Calculator
The Comparing Fractions Calculator compares two fractions to determine which is greater, less, or if they are equal. It uses common denominator method, cross multiplication, and decimal conversion to show the comparison clearly.
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
Why does a smaller denominator mean a bigger fraction?
Think of pizza slices. 1/2 of a pizza (2 slices) is more than 1/8 of a pizza (8 slices). Fewer, larger pieces means more pizza than many tiny pieces.
Can I just convert to decimals to compare?
Yes! Converting to decimals is a quick and accurate method. Divide the numerator by denominator for each fraction, then compare the decimal values.
What is cross multiplication?
For fractions a/b and c/d, multiply a×d and b×c. If a×d > b×c, then a/b > c/d. This avoids finding the LCD.
How do I compare more than two fractions?
Find the LCD of all denominators, convert all fractions, then compare their numerators to order them from least to greatest.
What about negative fractions?
Compare their absolute values first, then remember that the "larger" negative number is actually smaller. For example, -1/2 > -3/4 because -1/2 is closer to zero.