Comparing Fractions Calculator

Compare any two fractions instantly to determine which is greater, lesser, or if they are equal. See cross-multiplication steps and visual bar chart comparison.

📐 Comparing Fractions Calculator
Result
Visual Diagram
Definition

What is Comparing Fractions Calculator?

A Comparing Fractions Calculator determines the relationship between two fractions — whether one is greater than, less than, or equal to the other. Comparing fractions with different denominators requires converting the fractions to a common denominator or using cross-multiplication.

Fraction comparison is used in cooking (which recipe uses more sugar?), finance (which interest rate is higher?), statistics (which probability is greater?), and engineering (which tolerance is tighter?).

The cross-multiplication method is the fastest way to compare fractions: multiply each numerator by the other fraction's denominator and compare the products.

Interactive Visualization
Formula

Comparing Fractions Calculator Formula

Cross-Multiplication Method:

To compare a/b and c/d, compute:

  • Product 1 = a × d
  • Product 2 = c × b

If Product 1 > Product 2 → a/b > c/d

If Product 1 < Product 2 → a/b < c/d

If Product 1 = Product 2 → a/b = c/d

Example: Compare 3/4 and 5/7

3 × 7 = 21, 5 × 4 = 20. Since 21 > 20, 3/4 > 5/7.

Examples

Worked Examples

Compare 2/3 and 3/5

Cross multiply: 2×5=10, 3×3=9. Since 10 > 9, 2/3 > 3/5.

Compare 1/4 and 2/8

Cross multiply: 1×8=8, 2×4=8. Since 8 = 8, 1/4 = 2/8.

Compare 5/6 and 7/9

Cross multiply: 5×9=45, 7×6=42. Since 45 > 42, 5/6 > 7/9.

Compare 3/8 and 1/3

Cross multiply: 3×3=9, 1×8=8. Since 9 > 8, 3/8 > 1/3.

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FAQ

Frequently Asked Questions

Common questions about the comparing fractions calculator.

Use cross-multiplication: multiply each numerator by the other's denominator. Compare the products to determine which fraction is larger. Example: 2/5 vs 3/7 → 2×7=14, 3×5=15 → 14 < 15 → 2/5 < 3/7.

Yes. Divide each numerator by its denominator to get decimal values. Example: 3/4 = 0.75 and 2/3 ≈ 0.667. Since 0.75 > 0.667, 3/4 > 2/3.

When denominators are the same, simply compare the numerators. The fraction with the larger numerator is the larger fraction. Example: 5/8 > 3/8 because 5 > 3.

When numerators are the same, the fraction with the smaller denominator is the larger fraction. Example: 3/4 > 3/5 because fourths are larger pieces than fifths.

Compare each fraction to a benchmark like 1/2. If one fraction is greater than 1/2 and the other is less, the comparison is immediate. Example: 3/5 > 1/2 and 2/7 < 1/2, so 3/5 > 2/7.