Vedic Mathematics/Sutras/Urdhva-Tiryagbyham

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Multiplication of a 2 figure integer $ab$ by another 2 figures integer $cd$ :

${\begin{matrix}a&&b\\\vert &\times &\vert \\c&&d\\a*c&ad+bc&b*d\end{matrix}}$ For Example, 12 × 23 = ( 1×2 ) | ( 1×3 + 2×2 ) | ( 3×2 ) = 276

or in base 10:

$(10a+b)(10c+d)=100(a*c)+10(ad+cb)+(b*d)$

of course, the cases where $(ad+cb)>10$ or $b+d>10$ are to be considered.

Let us take the above example in another way. While multiplying 2 digit numbers with each other,

• Step 1: the product of the last digits in both numbers becomes the last digit of the result. Therefore the last digit of the result is 2*3=6
• Step 2: the first digit of the first number is multiplied with the second digit of the second number i.e.1*3=3. Now,the last digit of the first number is multiplied with the first digit of the second number i.e.
  • 2*2=4. Both these numbers are now added
  • 3+4=7. This becomes the second digit of the result
• Step 3: The first digit of the product is obtained by multiplying the first digits of both numbers, i.e. 1*2=2

Our final answer is 276.