Vertically and crosswise

Urdhva-Tiryagbhyam

This sutra provides a systematic crosswise-and-vertical multiplication method that works for any pair of numbers. For two-digit numbers, it breaks multiplication into three simple steps that can be done left to right or right to left.

How It Works

1.Write the two numbers as ab × cd (e.g. 23 × 14 → a=2, b=3, c=1, d=4).
2.Step 1 (vertical right): Multiply the units digits: b × d. Write the units digit, carry the tens.
3.Step 2 (crosswise): Compute a×d + b×c. Add any carry from Step 1. Write the units digit, carry the tens.
4.Step 3 (vertical left): Multiply the tens digits: a × c. Add any carry from Step 2. This is the leftmost part.
5.Read the result from left to right.

Examples

23 × 14

Step 1 / 5

Multiply 23 × 14. Split into digits: 23 × 14.

a (tens of first)2

b (units of first)3

c (tens of second)1

d (units of second)4

Try It Yourself

34 × 21

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