# 30MSC 2023 #13: Vertically and Crosswise Multiplication

The Vertically and Crosswise (V&C) sutra is the basis of the general multiplication method in Vedic Mathematics whether using numbers or polynomials. It is also used in division, squaring, and extracting square roots and computations involving fractions and mixed numbers.

It is also useful in analytic geometry and in trigonometry when using triples.

Unlike the traditional multiplication method taught in schools which always start from the right, V&C can be performed from the left or from the right. Extending the use of this technique to Algebra, polynomial multiplications are easily done mentally.

If two three-digit numbers, ABC and abc are multiplied, the following partial products are obtained:

Step I: A x a = Aa

Step II: A x b + B x a = (Ab + Ba)

Step III: A x c + B x b + C x a = (Ac + Bb + Ca)

Step IV: B x c + C x b = (Bc + Cb)

Step V: C x c = Cc

In this question from the 3nd International Vedic Mathematics Olympiad, Upper Primary Level, “When using Vertically and crosswise to calculate 427 x 223, what is the result of the third step before any carry digits have been added?”,  the answer can be easily calculated easily as:

4 x 3 + 2 x 2 + 7 x 2 = 12 + 4 + 14 = 30

More applications of vertically and Crosswise are discussed in Chapter 3 of our forthcoming book 30 Master Strategies in Computing, Vol II

Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #14: Squaring