Fraction Comparison
Determine which of two fractions is greater, smaller, or equal using cross-multiplication (a×d vs b×c) or LCD conversion.
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Cross-multiplication avoids finding LCD—works for any two fractions. Same numerator: 1/2 > 1/3 because smaller denominator means larger pieces. Unit fractions: 1/2 > 1/3 > 1/4 > ... — smaller denominator, larger value.
Ready to run the numbers?
Why: Comparing fractions is essential for ordering, estimation, and verifying equivalence in recipes, measurements, and finance.
How: Cross-multiply: compare a×d with b×c. If a×d > b×c, then a/b > c/d. Alternatively, convert both to LCD and compare numerators.
Run the calculator when you are ready.
📐 Examples — Click to Load
Fraction 1
Fraction 2
Decimal Values Comparison
Proportion Comparison
📐 Step-by-Step (Cross-Multiplication)
For educational and informational purposes only. Verify with a qualified professional.
🧮 Fascinating Math Facts
Cross multiplication: a×d vs b×c avoids finding LCD—works for any two fractions.
When a×d = b×c, the fractions are equivalent (e.g., 1/4 = 2/8).
1. Key Takeaways
- • Use cross multiplication to compare fractions without finding a common denominator: a/b > c/d iff a×d > b×c.
- • Alternatively, convert both fractions to the same denominator (LCD) and compare numerators.
- • Same numerator: smaller denominator means larger fraction (e.g., 1/2 > 1/3).
- • Same denominator: larger numerator means larger fraction (e.g., 3/5 > 2/5).
- • For negative fractions, compare absolute values first, then reverse the inequality.
2. Did You Know?
Cross Multiplication
a×d vs b×c avoids finding LCD—works for any two fractions.
LCD Method
Convert to LCD, then compare numerators. More intuitive for some.
Decimal Check
Convert to decimals: 1/2=0.5, 1/3≈0.333. Quick verification.
Benchmark 1/2
Compare to 1/2: if num/den > 1/2, fraction > 1/2.
Unit Fractions
1/2 > 1/3 > 1/4 > ... — smaller denominator, larger value.
Negative Reversal
-1/3 > -1/2 because -0.333 > -0.5 on the number line.
3. How It Works
Fraction comparison determines which of two fractions is greater, smaller, or if they are equal. The cross-multiplication method multiplies the numerator of each fraction by the denominator of the other. If a×d > b×c, then a/b > c/d. The LCD method converts both fractions to equivalent forms with the same denominator, then compares numerators.
Inputs
Two fractions: numerator1/denominator1 and numerator2/denominator2
Outputs
Comparison result (>, <, =), difference, cross-multiplication proof, LCD conversion
4. Expert Tips
Cross multiply first
For quick comparison, compute a×d and b×c. No LCD needed.
Same numerator rule
If numerators equal, smaller denominator = larger fraction (1/2 > 1/3).
Same denominator rule
If denominators equal, larger numerator = larger fraction (3/5 > 2/5).
Decimal sanity check
Divide num by den for each—verify your comparison makes sense.
5. Comparison Table
| Method | When to Use | Example |
|---|---|---|
| Cross multiplication | Any two fractions | 2/3 vs 3/5: 2×5=10, 3×3=9 → 2/3 > 3/5 |
| LCD conversion | Need common denominator for addition | 1/2 vs 1/3 → 3/6 vs 2/6 |
| Decimal conversion | Quick check | 1/2=0.5, 1/3≈0.333 → 1/2 > 1/3 |
| Benchmark 1/2 | Estimation | 3/7 < 1/2? 3/7≈0.43 < 0.5, yes |
6. FAQ
Use cross multiplication: for a/b and c/d, compare a×d with b×c. If a×d > b×c, then a/b > c/d. If equal, the fractions are equivalent.
Multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first by the numerator of the second. Compare the two products.
When a×d = b×c (cross products equal). For example, 1/4 = 2/8 because 1×8 = 4×2 = 8.
Compare absolute values first. The fraction with the larger absolute value is "more negative" (smaller). E.g., -1/2 < -1/3.
Simply compare the numerators. The fraction with the larger numerator is greater (e.g., 3/5 > 2/5).
The fraction with the smaller denominator is greater (e.g., 1/2 > 1/3). Smaller denominator = larger pieces.
Find the Least Common Denominator (LCM of denominators), convert both fractions to equivalents with that denominator, then compare numerators.
Yes. Divide numerator by denominator for each fraction. Compare the decimals. Useful for verification.
7. Quick Stats
a×d vs b×c
Cross product
LCD
Common denominator
|a/b − c/d|
Difference
> < =
Result symbols
8. Sources
9. Disclaimer
⚠️ Warning: This calculator is for educational purposes. Fraction comparison uses standard mathematical definitions. For critical applications, verify with authoritative sources.
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