MSC #5 – Vertically and Crosswise: Developing Multiplication Shortcuts
The Vertically and Crosswise 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.
This type of Multiplication can be done from either from left to right or right to left. In a 2 x 2 left to right multiplication, there are three steps: first is a vertical multiplication of the tens’ digits, then a middle cross-multiplication step and finally another vertical multiplication of the units’ digits.
In mental calculations, it is often easier to start with the middle crosswise step because it is the most complicated. Doing so also gives us a deeper understanding of how many multiplication shortcuts are developed.
Ms. Angelica S. Prudente, Center Director of MATH-Inic San Pablo City, will discuss the techniques in squaring numbers ending in 5, multiplying complementary numbers and squaring numbers beginning in 5 which can be easily explained by performing the middle crosswise step first on the second day of the Inspirational Maths from India (Year 4) on Dec 5, 2021.
Our example for today shows how to quickly multiply two 2-digit numbers with their tens’ digits adding up to 10 while having the same units’ digits.
For 78 x 38 the answer will be in two parts: the first part is obtained by multiplying the tens’ digit and adding the units digit, (7 x 3 ) + 8 = 29 and the second part is the square of the units digit, 64. So 78 x 38 = 2964.
Similarly, we have
76 x 36 = 2736
86 x 26 = 2236
96 x 16 = 1536
66 x 46 = 3036
Now using the techniques discussed in the 1st 5 Math Specials for Christmas, can you mentally compute 59 x 39 ?