Any multiplication: vertically and crosswise
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Ūrdhva-tiryagbhyām: the general method that works for every multiplication.
ऊर्ध्वतिर्यग्भ्याम्
Ūrdhva-tiryagbhyām
Meaning: Vertically and crosswise
Example: 23 × 41
- Right digits, vertically: 3 × 1 = 3.
- Crosswise: 2 × 1 + 3 × 4 = 14.
- Left digits, vertically: 2 × 4 = 8.
- Combine from the right, carrying: 8 | 14 | 3 → 943.
Answer: 943
Write the numbers one below the other. Multiply the right-hand digits vertically, then add the two crosswise products, then multiply the left-hand digits vertically. Keep one digit in each place and carry the rest to the left. The same pattern extends to 3-digit and larger numbers, and to algebra.