# What is Vedic Maths?

- Updated on 27 Oct 2020
- Teacher's Corner

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## What is Vedic Maths? Techniques And Shortcuts To Master Numerical Calculations

Many times, you will find yourself in a situation where you need to or rather you want to quickly multiply or divide complicated numbers. And given the traditional methods of learning mathematics, you may not be able to do so. Moreover, with the growing dependence on calculators is slowly crippling you.

This article explains the importance of a very interesting and powerful study that’s of ancient Indian origin. It teaches you important techniques on how you can carry out complicated calculations with ease and without the use of any devices. This study, known as Vedic Maths, and it gets its techniques from the sixteen sutras or word formulae found in the Indian Vedas. Vedic maths is a collection of techniques or sutras that help make mathematical problem solving faster and easier, without the use of any calculators, computers, or devices. It comprises 16 sutras or word formulae and 13 sub-sutras or sub formulae that can help solve problems related to arithmetic, algebra, geometry, calculus, conics, etc. Vedic maths gets its name

because of its Vedic origin. Veda in Sanskrit means ‘knowledge’. The benefits of Vedic maths are manifold, and this article will also highlight them for later on.

Let’s first understand a little more about Vedic maths. Here are 5 rules of Vedic maths with examples or five important sutras that contribute to the simplicity and greatness of Vedic maths, along with examples:

**Nikhilam Navatashcaramam Dashatah – meaning all from 9 and last from 10.**You can use this method for the multiplication of numbers closest to any power of 10. It uses a combination of addition, subtraction, multiplication, and division to make complicated multiplications easier and quicker.

Let’s take an example of 96 X 94 and understand the step by step process of executing this multiplication.

I. Depending on the numbers used for multiplication, you need to select the closest base that is a power of 10.

Here, the base would be 100.

II. Apply the principle of Nikhalam sutra, which is, subtracting the digits from the base.

96 – 100 = -4 (A)

94 – 100 = -6 (B)

III. Multiplication of the excess or deficiency remainder with each number.

-4 X -6 = 24 (C)

IV. Addition of any one of the numbers with the excess or deficiency of the other from the base.

96 – 6 = 90 or 94 – 4 = 90 (D)

V. The final answer will be the combination of (D) and (C) put together.**(D) & (C) = 90 & 24 = 9024.**

**Anurupyena- Shunyamanyat – a sub-formula of Nikhalam sutra**You can use this method when the numbers that you are multiplying are close to one another like 60, 70, 80, etc. and not close to a power of 10 but close to a multiple of 10. In this concept, you work the base and then using Nikhalam sutra.With an example, you can understand the process of using this sutra as below:

Multiplying numbers 52 X 48.

I. Working base concept – here you can see that the two numbers are close to the base 50. The working base you take is 50 or 5X10, rather than 100 or 10.

II. Applying the Nikhalam sutra,

52 – 50 = 2 (A)

48 – 50 = -2 (B)III. Multiplying the excesses gives you

2 X -2 = -4 (C)Here your working base has two digits, hence the number you will use is 04.

IV. Cross addition of any number with the excess of the other gives you

52 – 2 = 50 or 48 + 2 = 50 (D)

V. In this sutra, however, before you put the two answers together, first you have to multiply the cross-addition answer in the previous step with 5. This gives you

50 X 5 = 250 (E)

VI. Putting together (E) and (C), we get

**250 & -4 = 2500 – 4 = 2496.****Urdhva Tiryak Sutra – meaning, vertically and crosswise**You can use this method for any 3-digit, 4-digit, or even higher digit number. You will understand better using an example as given below.

*To multiple 145 X 373,*

I. Vertically multiply the first digit of both numbers.

1 X 3 = 3

II. Cross multiply the first two digits of the two numbers and add.

1 X 7 = 7

4 X 3 = 12

7 + 12 = 19

III. Cross multiply all three 3 digits of both the numbers and add.

(1X3) & (1X7) + (3X4) & (1X3) + (4X7) + (5X3) & (4X3) + (5X7) & (5X3)

IV. Vertically multiply the last digit of each number

5 X 3 = 15

V. For every step, except the first, the final number needs to have only one digit. If this is not the case, then we carry forward the initial digit to the previous compartment.

3 19 46 47 15**This leaves you with the final answer: 54085**

This method is applicable only where the multipliers completely consist of 9s.**Ekayunena Purvena Sutra – meaning, one less than the previous**

In Ekanyunena purvena, you can see 3 cases of multiplication:

I. digits of the multiplier and the multiplicand are the same.

2 X 9 = | 1 | 8 |

3 X 9 = | 2 | 7 |

4 X 9 = | 3 | 6 |

5 X 9 = | 4 | 5 |

The first digit of the sum is one less than the multiplicand, while the second digit of the product is the complement of the multiplicand with 9.

II. Multiplier’s digits are less than the multiplicand.

11 X 9 = | 9 | 9 |

12 X 9 = | 10 | 8 |

13 X 9 = | 11 | 7 |

Here, if the multiplicand starts with 1, then we subtract two from it, to arrive at the first part of the product, and if it starts with 2, then we subtract 3 from it, and so on.

The second part, as can be seen in case ‘I’, will be the complement of the last digit of the multiplicand.

III. The multiplier has more digits than multiplicand.

1 X 99 = | 0 | 9 | 9 |

2 X 99 = | 1 | 9 | 8 |

13 X 9 = | 2 | 9 | 7 |

The first column of the product is the number you arrive at when you subtract 1 from the multiplicand. The second column is 9, always. The third column is 10’s complement of the multiplicand.

In this method, the last digits of all numbers should total up to 10, and the remainder of the previous numbers to be the same.**Antyaordasake’pi – meaning, last totalling as 10.**

Example: 34 X 36

I. Check if the last digits total up to 10

4 + 6 = 10

II. If yes, multiply the two and write them in the second column of the product.

4 X 6 = 24

34 X 36 = | ? | 24 |

III. Apply the Ekadhikena Purvena sutra for the other digits by adding 1 to the remaining digits.

3 X 4 = 12, 3 X 6 = 18, adding 1 we get 112 & 118.

Apply Ekadhikena Purvena sutra on 11, to multiply 11 X 12 and arrive at the answer

34 X 36 = | 12 | 24 |

The lists above only give a brief idea about the various scenarios where Vedic maths can help make calculations easier and faster. There’s a lot more of an in-depth study that you have to put into the sutras and sub-sutras to really ace Vedic maths. Now that you know the basic 5 rules of Vedic maths with examples, let’s have a look at the advantages and benefits of Vedic maths for an individual:

- It is
, making it an activity of choice for adults as well as children.*simple, easy, and very interesting to learn and use* - It does away with putting any stress or load on the brain as it requires you to
.*only memorize tables up to 9* - Faster calculations so it saves a lot of time.
- It helps increase concentration and improve confidence in individuals.
- You will start understanding the connectivity and link between the different branches of maths, and thus
.*enriching knowledge and understanding of maths much better* - It’s unconventional, simple, and straightforward.
- It allows you to solve problems and then cross-check them too, for a thorough and
.*error-proof calculation* - Keeps an individual and their mind always
.*alert and lively* - The choice and flexibility of the system
.*help clear your intuition and thoughts* - Leads to
of an individual.*improved mental agility, sharpness, creativity, and intelligence* - There is
when you are practising Vedic maths.*no need for calculators* - Enables students to excel at school.
- It
and gives them a competitive advantage among their peers.*improves the IQ of students* - Improves memory and aptitude.
- There is
for Vedic maths.*no need to remember any complicated formulae* - A Vedic maths student can mentally and easily calculate
like squares, cubes, cube roots, etc.*cumbersome calculations*

From all the above, it is reasonably clear that Vedic maths is a boon to the education system. It will propel a healthy growth for children especially, encouraging them to develop a liking towards a subject that is dreaded by most. Students and adults can implement the techniques and shortcuts to master numerical calculations with Vedic maths.