Sutra 3 :URDHVA TIRYAGBHYAM Sutra (Multiplication of Two Integers) -Adyamadyenantyamantyena


Urdhva – tiryagbhyam is the general formula applicable to all cases of multiplication and also in the division of a large number by another large number. It means “Vertically and cross wise.”

Qn 1: 8 x 7
1. You subtract 10-8 -> 2 and 10-7 -> 3.
2. You subtract crosswise to get equal results: 8-3 = 7 – 2 = 5, the first figure of the answer is 5.
3. Multiply vertically: 2 x 3 to get 6, the last figure of the answer. Hence 8 x 7 = 56

Qn 2: 88 x 97
1. You subtract 100-88 -> 12 and 100-97 -> 3
2. You subtract crosswise to get equal results: 88-3 = 97-12 = 85, the first figure of the answer is 85.
3. Multiply vertically: 12 x 3 to get 36, the last figure of the answer. Hence 88 x 97 = 8536

Qn 3: 104 x 107
1. You subtract 104-100 -> 4 and 107-100 -> 7
2. You add crosswise to get equal results: 104+7 = 107+4 = 111, the first figure of the answer is 111.
3. Multiply vertically: 4 x 7 to get 28, the last figure of the answer. Hence 104 x 107 = 11128

Qn 4 :    Divide (12X2 –8X-32) by (X-2)

The quotient can be written as (12X+k)

We also know that –8x = kx – 24x Hence k = 16 cross-check –2k = -32 third term

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