What is Urdhva-Tiryagbhyam ?

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The sutra “Urdhva-Tiryagbhyam” translates to “Vertically and Crosswise” in English. This sutra is particularly useful for multiplication, especially when multiplying numbers with multiple digits. Here’s how it works:

  1. Split the numbers vertically: Write down the two numbers you want to multiply, one above the other, vertically.
  2. Multiply vertically: Multiply the digits in the same column vertically and write down the partial products beneath each column.
  3. Crosswise multiplication: Multiply the digits diagonally or crosswise and add the results.
  4. Combine the results: Add up all the partial products obtained from the vertical and crosswise multiplication to get the final product.

Let’s take an example to illustrate:

Let’s multiply 23 by 45 using the Urdhva-Tiryagbhyam method.

scss
2 3 (23)
x 4 5 (45)
---------
15 (3 * 5)
10 (2 * 5)
+ 6 (3 * 4)
+ 8 (2 * 4)
---------
1035 (Result)

In this example:

  • The vertical multiplication gives us partial products of 15 and 10.
  • The crosswise multiplication gives us partial products of 6 and 8.
  • Adding these partial products together, we get the final product of 1035.

This sutra simplifies the process of multiplication by breaking it down into steps that involve vertical and crosswise multiplication. It’s a useful mental technique for quick calculations and is one of the many efficient methods taught in Vedic Mathematics.