Vedic Maths: Fast Calculation Tricks

Vedic Mathematics is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas (the religious texts of ancient India) between 1911 and 1918 by Sri Bharati Krishna Tirtha. BKT, a Sankaracarya (head of a Hindu monastery) was distressed that traditional mathematical computations were so cumbersome. After contemplation of the Vedas, he was inspired to develop easier techniques for doing mathematics. This resulted in him writing a book, Vedic Mathematics, first published in 1965.

In this book are sutras (techniques), to solve mathematical problem sets in a fast and easy way. These tricks introduce wonderful applications of arithmetical computation, theory of numbers, mathematical and algebraic operations, higher-level mathematics, calculus, and coordinate geometry.

Perhaps the most striking feature of the Vedic system is its coherence. Instead of a hotchpotch of unrelated techniques, the whole system is beautifully intertwined and unified with each other. For example, three of the easy-to-learn techniques from Vedic Mathematics are general multiplication strategies, a simple squaring technique, and factoring different expressions.

General Multiplication:

This sutra, called the Urdhva-Tribhagyam (vertically and crosswise), makes 2-digit multiplication easier and quicker to solve. The formula used for this strategy is as follows: ab * cd = (ac) (ad + bc) (bd) where each parenthesis is a respective place value. An example of this formula can be used when given the problem 24*12. Using the formula given we get, (2*1) (2*2 + 4*1) (4*2), which is 2 8 8. Using very minimal calculations, we get the answer of 24 * 12, 288.

Squaring Technique:

This technique known as the Yavadunam is used for finding squares of numbers close to the powers of base 10. You find the difference of the number close to 10 and square it. This becomes the unit place of the answer. Then add the excess to the original number which becomes the left part of the answer. Let’s try understanding this with an example. If we try to find the 12 squared, we first find the difference (12 - 10) and square it. This gives us 4 (the unit place of our answer). Then, add the excess we had earlier (2) to our original number 12, which gives us the left part of our answer. Put together the 14 and 4 to get the answer of 12 squared, 144.

12² = (12+2) (2)(2) = 144

Factoring Expressions Check:

The Gunita Samuchaya is used to find the correctness of the answers in factorization problems. It states that the sum of the coefficients in the product is equal to the sum of the coefficients of the factors. If this condition is satisfied, you know that both sides of the equation are balanced and equivalent to one another. For example, let’s consider the quadratic equation 8x² + 11x + 3, which factors out to (x+1)(8x+3). Taking the sum of coefficients from the left side of the equation (8 + 11 + 3) gives us 22. And with the factors, (1+1)(8+3) = (2)(11), which is also equal to 22. Since both sides hold true to the condition, you know that they are equal.

This sutra can also be applied to equations such as a cubic one. An example of this being applied can be used in the equation x³ + 10x² + 11x - 70 = (x+5)(x+7)(x-2). Using the same concept from above, we can see that the sum of the coefficients are (1 + 10 + 11 - 70) = -48. The product of the sum of coefficients in the factors is (1+5)(1+7)(1 - 2), which is also -48. This proves that both sides of the equation are true.

To conclude, these basic sutras help give you an edge when solving different math problems and can be applied anywhere. The simplicity of Vedic Mathematics means that calculations can be carried out mentally. There is real beauty and effectiveness in the Vedic System and one can see that it is perhaps the most refined and efficient mathematical system possible.

Thank you for reading my article, and I hope to see you all in the next one.