Vedic Multiplication

Mental Math · Axiom Academy

Urdhva-Tiryagbhyam — "vertically and crosswise" — is not one trick. It is a reading order: walk the positions from the right, take every digit pair that belongs at each one, and let the carries ripple at the end. Write 41 × 12 with one number above the other and number the digit slots from the right , starting at 0. In 41 the 1 sits in slot 0 and the 4 in slot 1; the 12 below it is numbered the same way. Now walk a window from right to left across three stops , numbered 0, 1, 2. At each stop you take every pair of digits whose slot numbers add up to the stop number — nothing more, nothing less. That single sentence is the whole method. Stop 0 — one pair — vertical Only slot 0 with slot 0. Read straight down: 1 × 2 = 2 . Stop 1 — two pairs — crosswise Slot 0 with slot 1, and slot 1 with slot 0. Read across: 1 × 1 + 4 × 2 = 1 + 8 = 9 . Stop 2 — one pair — vertical Only slot 1 with slot 1. Straight down again: 4 × 1 = 4 . Read the three stop totals from the right: 2, then 9, then 4 — the answer is 492 . Vertical, crosswise, vertical. The window opened to two pairs in the middle and closed again. One stop at a time, right to left Count the digit positions from the right, starting at 0. A stop is chosen by adding two slot numbers, so the rule reads the same whatever size the numbers are. The outermost stops always hold exactly one pair and are read straight down. Everything in between is read across.

This is the written version of the interactive lesson above. See the full Mental Math course.