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# Vedic Math Sutra: Sutra 3 – Urdhava – Tiryagbyham

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In Vedic mathematics, “Urdhava-Tiryagbyham” is a sutra that refers to a multiplication technique. It is often translated as “vertically and crosswise.”

The Urdhava-Tiryagbyham sutra is used for multiplying two-digit numbers mentally and quickly. It allows for multiplying numbers by breaking them down into more uncomplicated steps.

Recommended Readings: VEDIC MATH FOR KIDS: WHY IT IS IMPORTANT

Here’s a step-by-step explanation of how the Urdhava-Tiryagbyham sutra works:

#### Part 1

Let’s apply the Urdhava-Tiryagbyham method to multiply two-digit numbers 12×24

Step 1: Multiply the right digits of the two numbers  vertically

2×4-=8

Step 2: Diagonally multiply the digits of our numbers

(1×4)+(2×2)=8

8 is the second digit of our answer.

Step 3: Vertically multiply the left digits of the two numbers

1×2=2

2 is the most left digit of our answer.

So, using the Urdhava-Tiryagbyham method, 12×24 =288.

#### Part 2

Let’s apply the Urdhava-Tiryagbyham method to multiply

three-digit number 244×432

Step 1: Multiply the extreme right numbers vertically

4×2=8

8 is the first digit of our answer: we are going right to left

Step 2:  Multiply the last two digits of the numbers diagonally

(4×2)+(3×4)

8+12=20

Zero is the second digit of our answer. Carryover 2.

Step 3: Now multiply the extreme left and extreme right digits diagonally. Multiply the middle digits vertically.

(2×2) + (4×4) + (4×3)

4+16+12=32

32+2=34

4 is the third digit of the answer. Carryover 3.

Step 4: Now, multiply the first two digits of the numbers diagonally.

(2×3) + (4×4)

6+16=22

22+3=25

5 is the fourth digit of the answer. Carryover 2

Step 5: Take the first digits of the numbers and multiply them vertically.

2×4=8

Now add carried-over number = 8+2=10

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