Having dealt in fairly sufficient detail with the
application of the Nikhilam Sutra to special cases of multiplication, we now proceed
to deal with ऊर्ध्वतिर्यभ्याम्
(Urdhva -Tiryagbhayam) Sutra
which is the General Formula applicable to all cases of multiplication and will
also be found very useful, later on , in the division of a large number by
another large number.
The formula itself is very short and terse, consisting of only one compound word and means"vertically and crosswise (criss-cross)"
The applications of this brief and terse Sutra are
manifold (as well be seen again and again, later on). First we take it up in
its most elementary application namely, to Multiplication in general.
Sanskrit Name:-
ऊर्ध्वतिर्यभ्याम्
Urdhva- tiryak means "vertically and crosswise (criss-cross)"
A simple example will suffice to clarify the modus operandi thereof.
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78 x 63 by Urdhva –Tiryak rule:- (i) We multiply the left-hand-most digit 7 of
the multiplicand vertically by the left-hand most digit 6 of the multiplier,
get 42 and see it down as the left - hand most part of the answer. (ii) We then multiply 7 and 3 , and 8 and 6
cross- wise, add the two, get 69, as the sum and set it down as the middle
part of the answer; and (iii)We multiply 8 and 3 vertically , get
24 as their product and put it down as the the last the right-hand- most part
of the answer .
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