Urdhva Tiryakbhyam (Urdhva Tiryak)

Shortcut (General) Method of multiplication in Vedic Mathematics for all types of numbers

Commonly called as:

Urdhva Tiryak (we will call it as UT Method).

Sanskrit Name:

ऊर्ध्वतिर्यभ्याम्

English Translation:

Vertically and Crosswise (Criss-Cross)

Prerequisites

• There are no such Prerequisites as this method is applicable to all forms of numbers. But if numbers have larger digits then Vinculum can be used. (for simplicity)

Also Read => More Vedic Mathematics Sutras for Multiplication.

Shortcut to Multiply 2 digit numbers

Formula :

(ax+b)(cx+d) = acx² + (ad+bc)x + bd

Process: (Left –> Right)

1. Vertical Multiplication of 1st digits of the numbers.
2. Crosswise Multiplication Addition (i.e. Crosswise Multiplication and adding them).
3. Vertical Multiplication of last digits of the numbers.
4. For all steps, except 1st step, each step (compartment) needs to have ONLY 1 digits. If not then carry forward initial digits to previous compartment (Check below examples to understand).

Shortcut to Multiply 3 digit numbers

Formula :

(ax²+bx+c)(dx²+ex+f) = adx⁴ + (ae+bd)x³ + (af+be+cd)x² + (bf+ce)x + cf

Process: (Left –> Right)

1. Vertical Multiplication of 1st digits of 2 numbers.
2. Crosswise Multiplication Addition of 1st 2 digits 2 numbers.
3. Crosswise Multiplication Addition of all 3 digits of both the numbers.
4. Crosswise Multiplication Addition of last 2 digits 2 numbers.
5. Vertical Multiplication of last digits 2 numbers.
6. For all steps, except 1st step, each compartment needs to have ONLY 1 digits. If not then carry forward initial digits to previous compartment (Check below examples to understand).

Examples:

Urdhva Tiryak Multiplication using Vinculum Process:

Tricks to Multiply 4 digit numbers

Process: (Left –> Right)

1. Vertical Multiplication of 1st digits.
2. Crosswise Multiplication Addition of 1st 2 digits.
3. Crosswise Multiplication  Addition of 1st 3 digits.
4. Crosswise Multiplication  Addition of all digits.
5. Crosswise Multiplication  Addition of last 3 digits.
6. Crosswise Multiplication  Addition of last 2 digits.
7. Vertical Multiplication of last digits.

Example:

Similarly Urdhva Tiryak multiplication tricks  can be applied numbers have more than 4 digits.

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