Cross-Multiplication Trick

For two-digit numbers close to 100, there is a beautiful shortcut. Take 97 x 96: each number is 3 and 4 away from 100. Subtract crosswise: 97 - 4 = 93 (or 96 - 3 = 93). Multiply the distances: 3 x 4 = 12. Answer: 9312.

This crosswise trick is popularized by 20th-century Vedic Mathematics, and the algebra behind it is simple: (100-a)(100-b) = (100-a-b) x 100 + ab. It feels like magic at first, but the pattern is easy to see. The method extends to any base: 48 x 46 uses base 50, and 998 x 997 uses base 1000.