**Vedic Maths** is a mathematical system that originated in India around 1500 BC. It is based on 16 sutras or principles and 13 sub-sutras or corollaries, which were first introduced by the ancient Indian mathematician Bharati Krishna Tirthaji Maharaja.

The system of Vedic Maths is known for its speed and simplicity, and it has become increasingly popular in recent years due to its ability to solve complex mathematical problems quickly.

**2 Second Maths Tricks:** One of the most impressive features of Vedic Maths is its ability to solve mathematical problems quickly. Some Vedic Maths techniques can be performed in just a few seconds, making it an excellent tool for anyone who needs to do mental calculations quickly. Here are some examples of Vedic Maths tricks that can be performed in just a few seconds:

- Multiplying two-digit numbers: To multiply two two-digit numbers, you can use the “vertically and crosswise” method. Here’s how it works:

Example: 23 x 27 Step 1: Multiply the tens digits together and add a zero. (2 x 2 = 4, add a zero = 40) Step 2: Multiply the units digits together. (3 x 7 = 21) Step 3: Add the two results together. (40 + 21 = 61) Answer: 23 x 27 = 621

- Squaring numbers ending in 5: To square a number ending in 5, you can use the “25” trick. Here’s how it works:

Example: 35^2 Step 1: Take the tens digit (3) and multiply it by the next higher number (4). (3 x 4 = 12) Step 2: Write “25” after the result from step 1. (125) Answer: 35^2 = 1225

- Multiplying by 9: To multiply a number by 9, you can use the “finger trick”. Here’s how it works:

Example: 6 x 9 Step 1: Hold out both hands with fingers extended. Step 2: Count the number you want to multiply (6) from left to right and bend that finger down. (The sixth finger from the left is the left thumb.) Step 3: Count the number of fingers to the left of the bent finger (5) and the number of fingers to the right of the bent finger (4). Step 4: Write down the number formed by the two digits (54). Answer: 6 x 9 = 54

- Multiplying by 11: To multiply a two-digit number by 11, you can use the “11” trick. Here’s how it works:

Example: 35 x 11 Step 1: Write down the first digit of the two-digit number (3). Step 2: Add the two digits together (3 + 5 = 8) and write the result in the middle. (38) Step 3: Write down the second digit of the two-digit number (5). Answer: 35 x 11 = 385

**Benefits of Vedic Maths: Learning Vedic Maths can offer many benefits, including:**

- Improved mental agility: By learning Vedic Maths, you can improve your mental agility and ability to perform mental calculations quickly. This can be helpful in many areas of life, from doing simple math at the grocery store to more complex calculations in academic or professional settings.
- Improved problem-solving skills: Vedic Maths encourages creative problem-solving, which can help you to develop a more flexible and adaptive mindset.

## Vedic Maths Tricks

Class: | 6 to 12 |

Contents: | Vedic Maths |

## Vedic Maths Tricks

This Mathematics is a collection of Techniques/Sutras to solve arithmetical problems in an easy and faster way. It consists of 16 Sutras and 13 sub-sutras which can be used for questions involved in arithmetic, algebra, geometry, calculus, conic. The sutras are basically the formulas which we use in the mathematical calculation.

Vedic Maths book was previously included in the syllabus of Madhya Pradesh and Uttar Pradesh Board affiliated Schools. Some of the schools and organizations run by Hindu nationalist groups, also have included methods in their syllabus, even those groups which are outside India. The Hindu nationalists also tried to include these curricula in the NCERT books.

In earlier classes, we studied that during the period of dwelling in Sringeri Matha, Mysore Swami Bharati Krishna Tirtha did an arduous ascetic fervor for eight years. In the highest position of accomplishment, he got the perceptive vision of mathematics formulae mentioned in Vedas, the holiest scriptures and expressed his spiritual feelings in the form of Mantras (formulae).

These mantras were named Vedic Mathematical Formulae, which is exactly true. According to the scholars of Vedas, the knowledge of Vedas is beyond human power.

The knowledge of Vedas cannot be obtained only by thinking or learning. It is an accomplish-feeling and expression it in the form of Mantras. In this perspective, the formulae formed by Swamiji are Vedic Mathematics Mantras.

**Importance of Vedic Mathematics**

**Important Definitions Related to Vedic Mathematics**

- Sutras: The word “sutra” means “thread” in Sanskrit, and it refers to a set of 16 mathematical principles or formulas that form the foundation of Vedic Mathematics. These sutras are used to solve a wide range of mathematical problems, and they are known for their simplicity and elegance.
- Corollaries: In addition to the 16 sutras, there are 13 sub-sutras or corollaries that are used in Vedic Mathematics. These corollaries are derived from the sutras and help to further explain and clarify their meaning.
- Ekadhikena Purvena: This is a Vedic Maths sutra that means “by one more than the previous one”. It is used to multiply numbers that differ by one, such as 14 x 15 or 24 x 25.
- Nikhilam Navatashcaramam Dashatah: This is a Vedic Maths sutra that means “all from 9 and the last from 10”. It is used to subtract numbers quickly, particularly when one or both of the numbers are close to a power of 10.
- Urdhva-Tiryagbhyam: This is a Vedic Maths sutra that means “vertically and crosswise”. It is used to multiply two-digit numbers quickly, by multiplying the tens digits together, then cross-multiplying and adding the results.
- Dwandva Yoga: This is a Vedic Maths corollary that means “the combination of the last terms”. It is used to add or subtract numbers with repeating digits, such as 111 + 222 + 333.
- Vinculum: A vinculum is a horizontal line placed over a group of numbers or terms to indicate that they should be treated as a single entity. Vinculums are often used in Vedic Mathematics to simplify calculations and make them easier to perform mentally.
- Beejank: Beejank refers to the last digit of a number. In Vedic Mathematics, numbers are often represented as a combination of digits and beejanks, which can be used to perform calculations quickly.
- Ekanyunena Purvena: This is a Vedic Maths sutra that means “by one less than the previous one”. It is used to multiply numbers that differ by one, such as 16 x 15 or 25 x 24.
- Yavadunam Tavadunikrtya Varga Mulani: This is a Vedic Maths sutra that means “whatever the extent of its deficiency, lessen that and set up the square of the remainder”. It is used to find the square of any number, including numbers with decimals or fractio

**Vedic Maths** involves memorizing a set of sutras

Improved memory: Vedic Maths involves memorizing a set of sutras and corollaries, which can help improve your memory and cognitive function.

Enhanced academic performance: Students who learn Vedic Maths often experience improved academic performance, particularly in math-related subjects. This is because the system helps students to develop a deeper understanding of mathematical concepts and improves their ability to solve problems quickly and accurately.

Increased confidence: Learning Vedic Maths can also boost your confidence in your mathematical abilities. By mastering mental math techniques, you can feel more confident in your ability to perform calculations quickly and accurately.

## Vedic Maths Addition:

Addition is a fundamental operation in mathematics, and Vedic Mathematics provides several sutras and techniques to perform addition quickly and efficiently.

One of the most basic and commonly used Vedic Maths sutras for addition is called “Ekadhikena Purvena,” which means “one more than the previous one.” This sutra can be used to add any two numbers whose difference is 1.

**Here’s an example of how to use this sutra to add 17 and 18:**

Step 1: Choose the larger number, which in this case is 18, and add 1 to it. This gives us 19. Step 2: Add the smaller number, which is 17, to the new number we got in step 1. This gives us 19 + 17 = 36.

**So, 17 + 18 = 36 using the “Ekadhikena Purvena” sutra.**

Another Vedic Maths sutra for addition is called “Yavadunam Tavadunikrtya Varganca Yojayet,” which means “whatever the deficiency, lessen it further to that extent, and also set up the square of that deficiency.” This sutra can be used to add any two numbers that are close to the same base, and the difference between them is a perfect square.

**Here’s an example of how to use this sutra to add 32 and 37:**

Step 1: Find the difference between the two numbers, which is 5.

Step 2: Since 5 is a perfect square, we can use the sutra. Subtract the difference from the smaller number, which gives us 32 – 5 = 27.

Step 3: Square the difference, which is 5 x 5 = 25.

Step 4: Add the square of the difference to the larger number, which is 37 + 25 = 62.

**So, 32 + 37 = 62 using the “Yavadunam Tavadunikrtya Varganca Yojayet” sutra.**

In addition to these sutras, Vedic Mathematics also provides techniques for adding a series of numbers, adding numbers with multiple digits, and more. By mastering these techniques, you can become more efficient and accurate in your addition calculations.

## Vedic Maths **Subtraction:**

Subtraction is one of the four basic mathematical operations, and it involves finding the difference between two numbers. In Vedic Mathematics, there are several sutras and corollaries that can be used to perform subtraction quickly and accurately.

One of the most commonly used Vedic Maths sutras for subtraction is Nikhilam Navatashcaramam Dashatah. This sutra means “all from 9 and the last from 10”, and it is particularly useful for subtracting numbers that are close to a power of 10.

Here’s an example of how this sutra can be used to subtract 27 from 50:

Step 1: Find the difference between the larger number and the nearest power of 10 (in this case, 50 – 10 = 40). Step 2: Subtract the smaller number from the result of step 1 (in this case, 40 – 27 = 13). Step 3: Subtract the last digit of the smaller number (in this case, 7) from 10 (10 – 7 = 3). Step 4: Combine the results of steps 2 and 3 (in this case, 13 and 3) to get the final answer: 23.

Another Vedic Maths sutra that can be used for subtraction is Ekadhikena Purvena, which means “by one more than the previous one”. This sutra is useful for subtracting numbers that differ by one, such as 14 – 15 or 24 – 25.

To use this sutra, you start by finding the larger number, and then adding one to the smaller number. For example, to subtract 24 from 25, you would start with 25 and add one to 24, which gives you 25. Then, you multiply the two numbers together, which gives you the answer of 1.

In addition to these sutras, there are several other Vedic Maths corollaries and techniques that can be used for subtraction, including Dwandva Yoga, which is used for subtracting numbers with repeating digits, and Vinculum, which is used to simplify calculations by grouping numbers together under a single line.

By mastering these Vedic Maths sutras and corollaries, you can perform subtraction quickly and accurately, even when working with large or complex numbers. This can be a valuable skill in a wide range of fields, including mathematics, engineering, and finance.

## Vedic Maths **Multiplication:**

Multiplication is another fundamental mathematical operation, and Vedic Mathematics provides several sutras and techniques to perform multiplication quickly and efficiently.

One of the most well-known Vedic Maths sutras for multiplication is called “Urdhva-Tiryagbhyam,” which means “vertically and crosswise.” This sutra can be used to multiply any two-digit numbers together, and it involves four simple steps:

Step 1: Multiply the first digit of both numbers together. Step 2: Multiply the last digit of both numbers together. Step 3: Add the two products from steps 1 and 2 together. Step 4: Multiply the middle digits of both numbers together, and add this product to the result of step 3.

**Here’s an example of how to use this sutra to multiply 23 and 45:**

Step 1: Multiply the first digit of both numbers together: 2 x 4 = 8 Step 2: Multiply the last digit of both numbers together: 3 x 5 = 15 Step 3: Add the two products from steps 1 and 2 together: 8 + 15 = 23 Step 4: Multiply the middle digits of both numbers together: 3 x 4 = 12. Then, add this product to the result of step 3: 23 + 12 = 35.

**So, 23 x 45 = 1035.**

Another Vedic Maths sutra that can be used for multiplication is called “Nikhilam Navatashcaramam Dashatah,” which we previously discussed for subtraction. This sutra can also be used for multiplication when the numbers being multiplied are close to a power of 10.

To use this sutra for multiplication, you start by finding the difference between each number and the nearest power of 10, and then subtracting these differences from 10. Finally, you multiply the two results together to get the final answer.

Here’s an example of how to use this sutra to multiply 98 and 93:

Step 1: Find the difference between each number and the nearest power of 10: 98 – 100 = -2 and 93 – 100 = -7 Step 2: Subtract the differences from 10: 10 – (-2) = 12 and 10 – (-7) = 17 Step 3: Multiply the two results together: 12 x 17 = 204

**So, 98 x 93 = 9,114.**

In addition to these sutras, Vedic Mathematics also provides techniques for multiplying numbers by 11, multiplying numbers with repeating digits, and more. By mastering these techniques, you can become more efficient and accurate in your multiplication calculations.

## Vedic Maths **Division:**

Division is another essential operation in mathematics, and Vedic Mathematics provides several sutras and techniques to perform division quickly and efficiently.

One of the most well-known Vedic Maths sutras for division is called “Nikhilam Navatashcaramam Dashatah,” which we previously discussed for subtraction and multiplication. This sutra can also be used for division when the numbers being divided are close to a power of 10.

To use this sutra for division, you start by finding the difference between each number and the nearest power of 10, and then subtracting these differences from 10. Finally, you divide the two results to get the final answer.

**Here’s an example of how to use this sutra to divide 798 by 99:**

Step 1: Find the difference between each number and the nearest power of 10: 798 – 800 = -2 and 99 – 100 = -1 Step 2: Subtract the differences from 10: 10 – (-2) = 12 and 10 – (-1) = 11 Step 3: Divide the two results: 12 / 11 = 1 with a remainder of 1.

So, 798 divided by 99 is 1 with a remainder of 1.

Another Vedic Maths sutra for division is called “Antyayor Dasakepi,” which means “the last digits remain constant.” This sutra can be used to divide any two numbers whose last digits add up to 10.

**Here’s an example of how to use this sutra to divide 574 by 24:**

- Step 1: Since the last digits add up to 10, we can apply the sutra. The first digit of the quotient is the first digit of the dividend (5) divided by the divisor (2), which is 2 with a remainder of 1.
- Step 2: We bring down the next digit of the dividend (7) and add it to the remainder from the previous step, which gives us 17.
- Step 3: We divide 17 by the divisor (2), which gives us 8 with a remainder of 1.
- Step 4: We bring down the next digit of the dividend (4) and add it to the remainder from the previous step, which gives us 14. Step 5: We divide 14 by the divisor (2), which gives us 7 with no remainder.

**So, 574 divided by 24 is 23 with a remainder of 7.**

In addition to these sutras, Vedic Mathematics also provides techniques for division by a two-digit divisor, division by a large number, and more. By mastering these techniques, you can become more efficient and accurate in your division calculations.

### Vedic Maths Advantages and Uses

Once the student understands the system of mental Vedic Maths, they will become more creative and start thinking logically. This maths is very flexible for them. The students can easily play with numbers with the help of this system.

Regular mathematical methods are sometimes complex and time-consuming. But if use Vedic Mathematicâ€™s Procedure and Techniques, some of the calculations such as, sets of given data, can be done very fast. Some of the more useful advantages of this Mathematics are;

- Its more than 1700% times faster than General Math. Thus, it could be considered as the Worldâ€™s Fastest.

It helps a child to lose the Math fear from his mind. Usually, students are scared of doing mathematical calculation because of the logic they have to use to solve it. Thus, this ancient Maths will help to solve the problems in the easiest way.

It helps to increase the thinking capability and intelligence, along with a sharpening of the mind. - Helps in increasing the speed and giving accurate answers.
- Students feel very confident about this subject, after improving their memory power.
- Students get interested more in numbers, they just have to apply their skills and have knowledge of tables to learn this.
- These maths calculation are of great use while preparing for competitive exams.

### Vedic Maths Sutras

As mentioned before, it consists of 16 sutras. Below are the names of the Sutras and Upa sutras with their meaning and corollary.

Name | Upa Sutra | Meaning | Corollary |

Ekadhikena Purvena | Anurupyena | By one more than the previous one | Proportionately |

Nikhilam Navatashcaramam Dashatah | Sisyate Sesasamjnah | All from 9 and the last from 10 | The Remainder Remains Constant |

Urdhva-Tiryagbyham | Adyamadyenantyamantyena | Vertically and crosswise | First by the First and the Last by the Last |

Paraavartya Yojayet | Kevalaih Saptakam Gunyat | Transpose and adjust | For 7 the Multiplicand is 143 |

Shunyam Saamyasamuccaye | Vestanam | When the sum is the same that sum is zero | By Osculation |

Anurupye Shunyamanyat | Yavadunam Tavadunam | If one is in ratio, the other is zero | Lessen by the Deficiency |

Sankalana-vyavakalanabhyam | Yavadunam Tavadunikritya Varga Yojayet | By addition and by subtraction | Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency |

Puranapuranabyham | Antyayordashakeâ€™pi | By the completion or non-completion | Last Totalling 10 |

Chalana-Kalanabyham | Antyayoreva | Differences and Similarities | Only the Last Terms |

Yaavadunam | Samuccayagunitah | Whatever the extent of its deficiency | The Sum of the Products |

Vyashtisamanstih | Lopanasthapanabhyam | Part and Whole | By Alternate Elimination and Retention |

Shesanyankena Charamena | Vilokanam | The remainders by the last digit | By Mere Observation |

Sopaantyadvayamantyam | Gunitasamuccayah Samuccayagunitah | The ultimate and twice the penultimate | The Product of the Sum is the Sum of the Products |

Ekanyunena Purvena | Dhvajanka | By one less than the previous one. | On the Flag |

Gunitasamuchyah | Dwandwa Yogiji | The product of the sum is equal to the sum of the product. | â€“ |

Gunakasamuchyah | Adyam Antyam Madhyam | The factors of the sum are equal to the sum of the factors | â€“ |

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## Frequently Asked Questions â€“ Vedic Maths Tricks

### What is Vedic Maths?

It is the way to improve calculations and make it as fast as possible.

### Is Vedic Maths helpful for higher classes?

Vedic Mathematics is useful for all classes. Standard 6 to standard 12 can use it for quicker computation.

### How to download PDF for Vedic Mathematics tricks?

PDF for Vedic Mathematics tricks are given for each topic. You can download it for offline use.

### How are Vedic Maths Books helpful for us?

Keeping books of Vedic Maths is quite comfortable to study it frequently.

### Can Vedic Maths make Multiplication or Division faster?

Vedic Maths Tricks make not only multiplications, divisions but also addition and subtractions also.

## Conclusion:

Vedic Maths is a powerful mathematical system that can help you to perform calculations quickly and accurately. By learning Vedic Maths techniques, you can improve your mental agility, problem-solving skills, memory, academic performance, and confidence. Whether you’re a student, a professional, or just someone who wants to improve your math skills, Vedic Maths can be an excellent tool for achieving your goals.

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