The Butterfly Method

Comparing, adding, or subtracting two fractions becomes visual with the butterfly method. Write the fractions side by side, cross-multiply diagonally (like butterfly wings), then multiply the denominators for the common bottom. The resulting fractions share a denominator and combine instantly.

For 2/3 vs. 4/7: cross-multiply to get 2 times 7 = 14 and 3 times 4 = 12. Since 14 > 12, the first fraction (2/3) is larger. No common-denominator computation needed — just two quick multiplications and a comparison. The butterfly always reveals which fraction wins.