Chapter V: Vedic Math

Introduction to Vedic Math

The Vedic math category of the Math is Easy website will discuss and teach you about the amazing and fun Vedic Mathematics, which is a system in mathematics using 16 main sutras or formulae along with 16 sub-sutras.

Each of the sutras has a principle of mental math strategies using simple and easily understandable methods to calculate or solve problems in mathematics.vedic math triangle

Moreover, you will never get bored in learning Vedic math because the sutras’ methods will enable you to solve simple and difficult operations in many ways that you will never expect. So what better way to have fun math and do some tricks in magic math with your family and friends? The Vedic math sutras are the answer.

The Vedic math sutras are a simple but enjoyable way to educate children and adults about math. The sutras will never cease to amaze you on how simple and easy they can help you solve arithmetic operations and even algebra expressions just by using your mind or through simple written calculations.

If you are not yet a member of the Math is Easy site, then subscribe now and start learning and practicing the sutras of the Vedic mathematics. If you had difficulty before in solving even the simplest math operations, you will be amazed and surprised of how you will easily solve simple to difficult problems by applying the sutras that you learned.

When you become a Math is Easy member, you will have limitless access to the procedures and steps in learning the 16 Vedic math sutras and the sub-sutras. Moreover, you can practice your mental math skills through the various exercises for each sutra. You should not worry about the pace of learning because the tutorials will teach you step-by-step in learning the sutras and in applying them when you do the practice exercises.

Overview of Vedic Mathematics

An Indian scholar named Jagadguru Swami Sri Bharati Krishna Tirthaji rediscovered Vedic mathematics from the Vedas between the years 1911 and 1918. The Vedas are a set of sacred texts based on the Hindu religion. According to Mr. Tirthaji, Vedic math is an ancient system of mathematics that uses 16 sutras or word formulae.

Mr. Tirthaji said that the 16 formulae describe the methods of how the mind works naturally and the sutras are the guides that will direct a person to find a proper solution to a problem, including mathematical problems.

The following are the 16 main sutras or formulae of Vedic math and their meaning in English:

No. Indian sutra English definition
1 Ekadhikina Purvena By one more than the previous one
2 Nikhilam Navatashcaraman Dashatah All from 9 and the last from 10
3 Urdvha – Tiryagbyham Vertically and crosswise
4 Paraavartya Yojayet Transpose and adjust
5 Shunyam Saamyasamuccaye If the Samuccaya is the same, that Samuccaya is zero
6 (Anuruppye) Shunyamanyat If one ratio is in ratio, the other is zero
7 Sankalana-vyavakalanabhyam By addition and by subtraction
8 Puranapuranabyham By the completion or non-completion
9 Chalana-Kalanabyham Differential calculus (Also known as difference and similarities)
10 Yavadunam Whatever the extent of its deficiency (Also known as By the deficiency)
11 Vyashtisamanstih Specific and general
12 Shesanyankena Charamena The remainders by the last digit
13 Sopantyadvayamantyam The ultimate and twice the penultimate
14 Ekanyunena Purvena By one less than the previous one
15 Gunitasamuchyah The product of the sum is equal to the sum of the product
16 Gunakasamuchyah All the multipliers (Also known as the factors of the sum is equal to the sum of the factors)

The summarized principles of the 16 main sutras:

  1. By one more than the previous one – This expresses how one idea will lead to another idea just by resting your mind on an idea when another idea shows up.
  2. All from nine and the last from ten – This interprets nine and ten by looking at them more as general objects instead of numbers.
  3. Vertically and crosswise – This refers to decision-making and evaluation process because in the assessment of the figures, you can come to a final decision by summing up all the results of the operation.
  4. Transpose and adjust – This refers to the concept that we usually look at something from the other person’s point of view instead of seeing it from our own point of view.
  5. When the sum is the same, that sum is zero – This refers to an interpretation that the total or combination is the same as the result, which is zero.
  6. If one ratio is in ratio, the other one is zero – This refers to assuming something as true or given and takes this assumption as the only truth for the moment.
  7. By addition and by subtraction – This is the mental process of comparison because in comparing two things, we look for the similarities – addition, and the differences – subtraction, between them.
  8. By the completion or non-completion – This refers to seeing a whole thing even if that whole is not actually there.
  9. Differences calculus – This refers to the constant change and motion that are fundamental parts of creation.
  10. Whatever the extent of its deficiency – This refers to the concept that variations from the normal things will always stand out and we will always notice them.
  11. Specific and general – This refers to the mental process of generalization from the specific point that people usually do all the time.
  12. The remainders by the last digit – This refers to the concept that all the things that you see in the world are continually changed by the things around them.
  13. The ultimate and twice the penultimate – This refers to nature when we usually see that one thing that happens will trigger another related event.
  14. By one less than the previous one – This refers to standing back and taking a look at the bigger picture of the situation rather than looking at what is in front of us.
  15. The product of the sum is equal to the sum of the product – This refers to assimilating several ideas and making a result or product from those ideas.
  16. All the multipliers – This refers to bringing together all the ideas until you come up with a summary of all the things you collected.

The 16 sub-sutras are:

  1. The product of the sum;
  2. All the multipliers;
  3. Proportionately;
  4. The remainder remains constant;
  5. The first by the first and the last by the last;
  6. For 7 the multiplicand is 143;
  7. By osculation;
  8. Lessen by the deficiency;
  9. Whatever the extent of its deficiency, lessen it still further to that very extent, and also set up the square (of the deficiency);
  10. By one more than the previous one;
  11. Last totaling ten;
  12. The sum of the products;
  13. By (alternative) elimination and retention (of the highest and lowest powers);
  14. By mere observation;
  15. The product of the sum is the sum of the products; and
  16. On the flag.

One of the most popular sutras in Vedic math is the “Vertically and crosswise” pattern, which is very effective for various cases of multiplication operations.

The image below summarizes the steps of the pattern of the “Vertically and crosswise” sutra if you multiply a three-figure number. For now, we will use letters to represent the three-figure number.

Take note of the direction and sequence of the lines in the pattern. You will notice that the sequence of the arrows follows the left to right pattern of reading and multiplying the numbers even though the product in a multiplication operation is still the same whether you reverse the multiplier and multiplicand. That is because you can also perform some addition operations using the vertical and crosswise pattern, which is one of the main advantages of the Vedic approach.

The Vedic math sutras have the advantage of multi-tasking because you can do several arithmetic operations in one problem using the short-cut methods of the sutras without getting confused on where you should start and what to do next. The simple steps of each sutra will guide you and you can easily understand them because all of them follow a pattern in calculating an operation.

Hence, become a member of the Math is Easy program and start learning the Vedic math sutras that will help you overcome your fear of numbers, develop your mental math abilities and more importantly, practice fun math by solving simple to hard problems without much difficulty.

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