# The A-Z Guide to The Ancient Vedic Mathematics of India

Vedic Mathematics is an Indian method of solving numerical problems. We can solve maths problems much faster and more accurate using the tricks of Vedic Maths.

A lot of people (kids and adults alike) in and outside of India are expressing more interest in learning Vedic Mathematics. However, very few people know and understand the true essence of Vedic Maths.

So, in this article, we are proving the A-Z guide of Vedic Maths for all the enthusiastic learners out there.

**Meaning of Vedic Maths **

Vedic Maths is a collection of sutras or techniques that solves mathematical equations quickly and effectively. It is composed of 16 Sutras/Formulae, 13 sub-sutras/Sub Formae, which can be used to solve problems in calculus.

**History of Vedic Maths**

This methodology of mathematics was reintroduced from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji. He’s regarded as the father of Vedic Maths.

According to him, Vedic mathematics is founded on 16 Sutras or formulas. These equations are designed to represent how the mind naturally operates, and are thus intended to be of considerable assistance in pointing the learner to the suitable technique of solution.

**The Annual Survey of Education 2012 **

According to the Annual Survey of Education 2012, conducted by Pratham, 46 per cent of Standard 5 kids are unable to complete simple calculations like two-digit multiplications or subtractions.

This data is agreeing with the Programme for International Student Assessment (PISA), which placed India in the 73rd position out of 74 nations in the study of science, maths, and reading abilities.

**Vedic Maths Sutras **

As mentioned earlier, there are 16 formulas and 13 sub-formulas in Vedic Mathematics. Let’s first talk about the former.

S.no | Sutras | Meaning |
---|---|---|

1 | Ekadhiken Purvena | One plus the previous one |

2 | Nikhilam Navatacharamam Dasatah | The last digit from 10 and the rest from 9 |

3 | Urdhva-Tiryagbyham | Vertically & crosswise |

4 | Paravartya Yojayet | Transpose & adjust |

5 | Sunyma Samyasamuchaye | This Implies to equating with 0 (sunya) |

6 | (Anurupye) Sunyamanyat | If one is in ratio then the other is zero |

7 | Sankalana-vyavakalamnabyam | By addition & subtraction |

8 | Puranapuranabhyam | By the non-completion or completion |

9 | Chalana-Kalanabhyam | Sequential Motion |

10 | Yavadunam | Whatever the degree of its deficiency |

11 | Vyastisamastih | Part & Whole |

12 | Sesanyankena Caramena | The remainders by the last unit |

13 | Sopantyadvayamantyam | The ultimate and twice the penultimate |

14 | Ekanyunena Purvena | By one less than the preceding |

15 | Gunitasamuccayah | The sum of the product is equal to the product of the sum |

16 | Gunakasamuccayah | The sum of the factors is equal to the factors of the sum |

**Ekadhikina Purvena**

[Implying “One plus the previous one”]

This Sutra is used if the sum of the unit digits of the two numbers equals 10.

Example:

Q: 33 x 37

The sum of unit digits of both numbers (3+7) is 10. So, the sutra can be utilised here.

(first digit x one more than the first) (Unit digit of 1st number x Unit digit of the 2nd number)

(3 x 4) (3 x 7)

= 1221

**Nikhilam Navatashcaramam Dashatah**

[Implying “The last digit starts at 10 and the remainder begins at 9”]

It is generally used in the subtraction of a number from the powers of 10.

Example:

Q: 99910 – 2958 = ?

99910

– 2958

_________

= 7042

_________

**Urdhva-Tiryagbyham**

[Implying “Vertically & crosswise”]

This sutra is used for multiplication and the formula is —

ab x cd = (ac) (ad + bc) (bd)

Example:

Q: 14 x 12

(1 x 1) ((1 x 2) + (4 x 1)) (4 x 2)

1 6 8

You got your answer. It’s 168.

**Paraavartya Yojayet**

[Implying “Transpose & adjust”]

This sutra is employed to solve division computations when the divisor is slightly greater than the closest power of 10.

**Shunyam Saamyasamuccaye**

This Implies to equating to 0 (sunya). This is applied in six cases.

**(Anurupye) Shunyamanyat**

[Implying “If one is in ratio then the other is zero”]

This technique is used to determine the product of two numbers that have the same base, such as 40, 40, etc (multiples of powers of 10).

**Sankalana-vyavakalanabhyam**

[Implying “By addition & subtraction”]

That is, the coefficient of the first variable in equation 1 should be equal to the coefficient of the second variable in the second equation.

Similarly, the coefficient of the second variable in equation 1 should be equal to the coefficient of the first variable in equation 2.

If so, the two equations can then be added and subtracted to solve for variables.

Example:

[Equation 1] 2x + y=5

[Equation 2] x + 2y=1

Now add equations 1 and 2.

We get:

3x + 3y=6

(x + y)=2

X + y = 2[This is equation 3]

Now subtract equation 2 from equation 1

We get x -y =4

X – y = 4 [Equation 4]

On Solving the the equation 3&4 we get

x=3

y=-1

**Puranapuranabyham**

[Implying “By the non-completion or completion”]

This sutra can be applied to solve addition equations when the unit digits of the numbers add up to 10.

Example: Let’s try 346 + 29 + 14 + 71

First, sort the numbers in order so the unit digits make 10.

(346 + 14) + (29 + 71)

360 + 100

= 460

**Chalana-Kalanabyham**

[Implying “Sequential Motion”]

This sutra is used in calculus to discover the roots of a quadratic equation, and it can also be used in differential calculus to factor 3rd, 4th, and 5th degree expressions. This sutra has extremely specific applicability in advanced mathematics.

**Yaavadunam**

[Implying “Whatever the degree of its deficiency”]

This is used to identify squares of numerals that are near to base-10 powers. Find the shortfall or excess by comparing the number to the base.

One element of the answer is to square the difference, which forms the unit part of the solution; another part is to reduce or raise the given number by the difference it has to the power of base 10. Add if it’s excess, less if it’s deficit.

Example: Let’s find 13^{2 }

Step 1 – 13 is close to 10. The excess over the base is 3.

Step 2 – Square of the excess is 3 x 3 = 9. This is the unit part of the answer.

Step 3 – 13 + 3 = 16

Solution is 169

**Vyashtisamanstih**

This implies “Part & Whole.”

**Shesanyankena Charamena**

[Implying “The remainders by the last unit”]

This sutra helps you to convert the fractions to decimals..

**Sopaantyadvayamantyam**

[Implying “The ultimate and twice the penultimate”]

This sutra is applied to solve the equations in the following manner

1/ ab + 1/ac=1/ad + 1/bc

Where a, b, c and d are in arithmetic progression

b=a + z

c=a + 2z

d=a + 3z

Solution for such equations is 2c + d=0

Example: Let’s solve 1/(x+2)(x+3) + 1/(x+2)(x+4) = 1/(x+2)(x+5) + 1/(x+3)(x+4)

Solution is 2c + d = 0

2 (x+4) + (x+5) = 0

2x + 8 + x + 5 = 0

X = -13/3

**Ekanyunena Purvena**

[Implying “By one less than the preceding”]

This sutra can be used for multiplication.

When the multiplier is only 9, this sutra may be used to determine the product of two numbers.

Example: For example 24 x 99=?

The process to solve it is:

Step 1 – Reduce 1 from multiplicand ie. 24-1 = 23

Step 2 – The other part of the answer would be 99 – 23 = 76

Hence the answer is 2376

**Gunitasamuchyah**

[Implying “The sum of the product is equal to the product of the sum”]

It is used to determine the validity of answers in factorization problems, and it indicates that the total of the coefficients in the product is equal to the sum of the coefficients in the factors.

If this condition is met, the equation is called balanced.

Example: Let us consider a quadratic equation

6x^{2} + 8x + 2 = (x+1)(6x+2)

In this example, the sum of coefficients is 6+8+2 = 16

Product of the sum of coefficients of the factors is (1+1)(6+2) = 2 x 8 = 16

Since both the totals tally, the equation is balanced.

**Gunakasamuchyah**

[Implying “The sum of the factors is equal to the factors of the sum”]

This sutra is applied for a perfect number to find the factors of it.

Example: Let’s find the factors of number 28.

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

Thus the factors of 28 are 1+2+4+7+14 = 28. This is a perfect number.

**Difference Between Vedic Maths and Modern Maths**

The biggest difference between the both is the coherent techniques of Vedic Maths. They are simple to understand and apply to various kinds of mathematical problems.

Vedic Mathematics varies from modern mathematics in that it is cohesive and focuses on applying a single strategy to solve unique problems rather than employing different strategies for different problems.

This is the biggest advantage of learning Vedic Mathematics as in this way, it creates a strong maths foundation for students.

**Importance and features of Vedic Maths**

The significance of Vedic Mathematics is so much that we need a whole fresh article to discuss it. To mention a few points:

- It makes maths fun and engaging.
- Since it’s quite easy to understand, kids will grow up with a love for numbers and equations.
- Because of the purity of the Vedic Mathematics curriculum, learning becomes simple.
- Boosts academic performance.
- Improves the brain activity of the kid.
- Promotes creative thinking and problem-solving.
- Improves your memory and concentration.
- Improve skills.
- Vedic Maths is distinguished by its simplicity.
- Quick and Accurate Outcome.

**How does this Ancient Method of Mathematics work well?**

Re-establishing the same fact, coherence. The formulas and sub-formulas are so simple to understand that it makes learning maths fun.

One other thing is that this methodology promotes human’s natural way of logical thinking. Once a technique is understood, you will agree that it is the possibly logical way of solving a problem.

This is why Vedic Maths work.

However, few people think of it as something too easy. Remember, everything must be practised to get the benefits of it. You can’t simply learn it once and think you are an expert.

It takes practice to master anything including Vedic Maths.

There you go.

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