Compare two fractions or mixed numbers instantly with greater than (>), less than (<), or equal (=) inequality symbols. Includes butterfly cross-multiplication, LCD proofs, and decimal equivalents.
Comparing fractions determines which fraction represents a larger portion of a whole. While decimal conversion is simple, algebraic proofs using cross-multiplication or common denominators provide exact mathematical certainty without rounding errors:
Input whole integers, numerators, and denominators for both fractions.
Multiply numerator of first by denominator of second (a×d) and vice-versa (b×c).
If a·d > b·c, A is greater. If a·d < b·c, B is greater.
Observe both fractions scaled to a shared denominator for visual confirmation.
The fastest technique for two fractions. Multiply diagonally across:
Requires zero denominator computation.
Scale both fractions to have identical denominators, then compare numerators:
Essential when ordering 3 or more fractions.
Divide numerator by denominator for each fraction to obtain decimals:
Intuitive for standard decimal comparison.
Cross-multiply: 5 × 11 = 55, and 8 × 7 = 56. Since 55 < 56, 5/8 is less than 7/11.
When numerators are equal, dividing into fewer parts produces larger slices. Denominator 7 < 8, so 3/7 > 3/8.
Comparing subtle interest rates or stock yield fractions like 5/8% vs 7/11% without decimal estimation errors.
Mechanics and woodworkers sorting imperial drill bits and socket wrenches (e.g., verifying if 5/16 in is larger or smaller than 11/32 in).
The butterfly cross-multiplication method compares fractions instantly in your head or on screen without computing large Least Common Denominators.
Clarifies tricky negative fraction comparisons on the real number line where numbers with greater absolute magnitude are actually smaller values.
Cross-multiplies numerators and denominators (a·d vs b·c) with full intermediate products.
Scales both fractions to their shared LCD so you can directly compare like-sized pieces.
Interactive visual weight meter displays which fraction tips the balance, showing percentage and difference.
| Method | Speed | Exactness | Best Used For |
|---|---|---|---|
| Butterfly Cross-Multiplication | Fastest | 100% Exact (Integer math) | Comparing exactly 2 fractions |
| Least Common Denominator | Moderate | 100% Exact | Ordering 3 or more fractions |
| Decimal Conversion | Fast (with calculator) | Subject to rounding on repeating decimals | Quick estimation and real-world units |
All-in-one arithmetic operations for fractions and mixed numbers.
Solve for unknown terms in direct and inverse proportions.
Reduce fractions to simplest form using Euclidean GCD.
Convert terminating and recurring decimals to simplified fractions.
Solve operations with mixed fractions and integer borrowing.
Solve proportions, simplify ratios, and scale part-to-whole totals.
