Compare Fractions
Compare two fractions to find which is larger, smaller, or equal — with step-by-step explanation.
Three Methods for Comparing Fractions
Method 1: Cross-Multiplication (Fastest)
To compare a/b and c/d, multiply diagonally and compare the products:
If a×d < b×c, then a/b < c/d
If a×d = b×c, then a/b = c/d
Example: Compare 3/5 vs 4/7
3×7 = 21 vs 5×4 = 20 → 21 > 20 → 3/5 > 4/7
Method 2: Common Denominator
Convert both fractions to the same denominator (LCD), then compare numerators.
Example: Compare 2/3 vs 3/5
- LCD(3, 5) = 15
- 2/3 = 10/15 and 3/5 = 9/15
- 10 > 9 → 2/3 > 3/5
Method 3: Decimal Conversion
Divide each fraction to get a decimal, then compare:
Example: Compare 5/8 vs 7/11
5 ÷ 8 = 0.625 vs 7 ÷ 11 ≈ 0.636 → 5/8 < 7/11
Comparing Fractions with the Same Denominator
When denominators are equal, the fraction with the larger numerator is greater:
Example: 7/12 > 5/12 because 7 > 5.
Comparing Fractions with the Same Numerator
When numerators are equal, the fraction with the smaller denominator is greater (the pieces are larger):
Example: 3/5 > 3/8 because fifths are larger than eighths.
Real-World Applications
- Cooking: Is 2/3 cup more or less than 3/4 cup? (3/4 > 2/3, so 3/4 cup is more.)
- Finance: Which is the better return: 3/8 or 5/13? Cross-multiply: 3×13=39 vs 8×5=40, so 5/13 is slightly better.
- Sports: Comparing batting averages expressed as fractions.
- Maps and scale: Comparing fractional scales like 1/50,000 vs 1/25,000.
Common Mistakes to Avoid
- Comparing numerators without matching denominators: 3/8 is NOT greater than 2/5 just because 3 > 2. (2/5 = 0.4 > 3/8 = 0.375.)
- Forgetting negative fractions: -1/3 > -1/2 even though 1/3 < 1/2 (on the number line, -1/3 is closer to zero).
Frequently Asked Questions
How do you compare two fractions?
Use cross-multiplication (compare a×d vs b×c for a/b and c/d), find a common denominator, or convert both to decimals. All three methods give the same result.
How does cross-multiplication work for comparing fractions?
For a/b vs c/d: compute a×d and b×c. The larger product indicates the larger fraction. Example: 3/4 vs 5/7 → 3×7=21 > 4×5=20, so 3/4 > 5/7.
Which is bigger: 2/3 or 3/4?
3/4 is bigger. Cross-multiplication: 2×4=8 < 3×3=9, so 2/3 < 3/4. As decimals: 0.667 < 0.75.
How do you compare fractions with the same denominator?
Simply compare the numerators. The larger numerator means the larger fraction. Example: 5/8 > 3/8 because 5 > 3.
Is the Compare Fractions tool free?
Yes, completely free. No registration, no limits, no hidden fees.