Keywords: Vedic mathematics tricks, mental math, fast calculation, learn Vedic math, multiplication tricks, math shortcuts, speed math.

Vedic  Math and its tricks

Introduction:

As a mathematics teacher, I always look for ways to make numbers easy and interesting. When I found Vedic Mathematics, I saw how simple tricks can make even big calculations quick and fun for students.

Math is a fundamental part of our daily lives, from counting to measuring to more complex calculations. Using mathematics, we can identify relationships.

What is Vedic Math? 

Vedic Mathematics is an ancient system of quick and easy calculation tricks. It comes from the Atharva Veda, one of the four Vedas. Indian mathematician Jagadguru Shri Bharati Krishna Tirthaji rediscovered it between 1911 and 1918. He later published these methods in his book “Vedic Mathematics” in 1965. The system includes 16 main sutras and 13 sub-sutras that make math simple and fast.

The simplicity of Vedic mathematics means that calculations can be carried out mentally (though the methods can also be written down). There are many advantages in using a flexible, mental system. Pupils can invent their own methods; they are not limited to the one 'correct' method. This leads to more creative, interested, and intelligent pupils.

Historical Background

 

Bharati Krishna Tirtha was born in March 1884 in Puri, Orissa. He was talented in mathematics, science, humanities, and Sanskrit. He loved meditation and a spiritual life. While meditating in a forest near Shringeri for eight years, he discovered the Vedic Sutras. He said this knowledge came from the Atharva Veda and the Rig Veda, which is why it is called Vedic Mathematics. He wrote the first 16 Sutras in 1957. He wanted to write more, but his eyesight became weak, and he passed away in 1960.

Main Principles (16 Sutras + 13 Sub-Sutras)

The concept of Vedic Math is based on sixteen sutras. So, we list all sixteen sutras with their meaning and uses in the table below.

Where to

S.No.	Sutras Name	Meaning	Where to use
1	Ekadhikina Purvena	By one more than the previous one	Squaring of a number ending with 5
2	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10	Multiplication of numbers, which are near the base, like 10, 100, 1000
3	Urdhva-Tiryagbyham	Vertically and crosswise	It is the general formula, applicable to all cases of multiplication of two large numbers
4	Paraavartya Yojayet	Transpose and adjust	When the divisor is greater than 10
5	Shunyam Saamyasamuccaye	When the sum is the same, that sum is zero	If there is a common term in the equation and the sum of the equation i 0, then the common term can be equated to 0
6	Anurupyena- Sunyamanyat	If one is in ratio, the other is zero	To find out the product of two numbers when both are near the common b, such as 40, 40, etc. (multiples of powers of 10).
7	Sankalana-Vyavakalanabhyam	By addition and by subtraction	It is used to solve simultaneous simple equations that have the coefficients of the variables interchanged.
8	Puranapuranabyham	By the completion or non-completion	Used to simplify or solve algebra problems.
9	Chalana-Kalanabyham	Differences and Similarities	To find the roots of a quadratic and to factorize expressions of the 3rd, 4th, and 5th degrees.
10	Yaavadunam	Whatever the extent of its deficiency	Applicable to obtain the square of a number close to the bases of powers of 10
11	Vyashtisamanstih	Part and Whole	Help in the factorization of the quadratic equation of types
12	Shesanyankena Charamena	The remainders by the last digit	It is to express a fraction as a decimal to all its decimal places
13	Sopaantyadvayamantyam	The ultimate and twice the penultimate	-
14	Ekanyunena Purvena	By one less than the previous one	This sutra is used in case of multiplication by 9, 99…
15	Gunitasamuchyah	The product of the sum is equal to the sum of the product	-
16	Gunakasamuchyah	The factors of the sum are equal to the sum of the factors	Used in the factorization of cubics, biquadratics

Sub-Sutras of Vedic Maths

No	Sub-Sutras	Meaning	Uses
1	Antyayordashakepi	The last digit remains the same	This sub-sutra aids in quickly determining the last digit of a product.
2	Sopantyadvayamantyam	The last two of the last	Useful for solving problems where the last two digits are required.
3	Ekaadhikena Purvena	One more than the previous	This sub-Sutra extends the "Ekadhikena Purvena" technique for squaring numbers closer to the base
4	Paravartya Sutra	Transposition and adjustment	Helps in solving linear equations and balance problems
5	Calana-Kalanabhyam	Differences and Similarities	Offers additional methods for solving ratio and proportion problems.
6	Gunakasamuccayah	The product of the sum	Useful for solving problems involving the product of two sums.
7	Gunita Samuccayah	The product of the sum is the sum of products	Aids in simplifying algebraic expressions.
8	Yavadunam Tavatirekena Varga Yojayet	By one less than the one, so much is the square	Provides an alternative approach for finding squares.
9	Antyayordasake'pi	The last digit is as it is	Useful for quick calculations involving the last digit of numbers
10	Antyayorekadhikaduhitayor	On the last two digits	Enables efficient calculations when focusing on the last two digits.
11	Ardhasamuccayah Samuccayoh	The sum of the half-sums is the sum	A technique for adding fractions with common denominators
12	Ekanyunena Sesena	One less than the one followed by the last	Facilitates quick division.
13	Sesanyankena Caramena	The last by the last, and the ultimate by one less than the last	A technique for division, especially when dealing with recurring decimals.

Quran and Hadith Connection 

The Quran tells us to seek knowledge and use it well. Allah says: 

“Read in the name of your Lord who created” (Al-Alaq 96:1).

The Prophet ﷺ said: “Seeking knowledge is wajib for every Muslim.” 

Learning Vedic Maths trains the mind, improves focus, and makes thinking faster. Islam teaches us to use our skills in daily life. Vedic Maths helps in exams, work, and everyday calculations. Using these tricks is a good way to apply knowledge wisely.

Benefits of Learning Vedic Maths

Vedic math helps students solve problems faster and with confidence. It saves time and makes calculations easy to understand. The tricks are simple and fun, so students enjoy learning math instead of feeling afraid of it. It also improves memory, focus, and mental speed. These methods make children sharper and more interested in numbers. Vedic math is helpful in exams and in daily life, where quick thinking is important. Vedic math helps people solve sums 10 to 15 times faster. The methods promote smart and quick thinking. They are useful for students in classes 9 and 10 and for junior classes too. The workload becomes lighter because tables up to nine are enough. These tricks reduce scratch work and finger counting. 

Popular Tricks (Examples)

Mathematical calculations are extremely challenging and prone to errors. In such scenarios, tricks from Vedic math are quite helpful. This is particularly true when you are planning to appear for various competitive exams. To help you with this, we are here with simple Vedic math tricks for quick calculations.

Vedic math tricks for quick calculations

1. Squaring a number ending with 5

1. For this Vedic Math trick, first, multiply the unit digit of the number, that is, 5, by 5.
2. Next, multiply the number preceding 5 by the next higher number.
3. Finally, place them sequentially to obtain an accurate result.

Let’s say you take the number 145 for this calculation.

Step 1: Multiply 5 of 145 by 5 to get 25.
5X5 = 25
Step 2: Multiply the preceding number (14 in this case) by the immediate next number, which is 15, to get 210.
14 X 15 = 210
Step 3: Finally, place them sequentially to get the square of 145 as 21,025.

2. Multiplying any number by 5 

For this, in the case of even numbers, divide them by 2 and add a 0 at the end of the result.
For example, if you take the number 48,

Step 1: Divide the number 48 by 2 to get 24.
48/2 = 24
Step 2: Add a 0 at the end to get 240 as the result.

For odd numbers, first subtract 1 from it, divide it by 2, and then add 5 at the end.
Say you take a number 9.

Step 1: Subtract 1 from 9 to get 8.
9 – 1 = 8
Step 2: Divide 8 by 2 to get 4.
8/2 = 4
Step 3: Place 5 at the end to get 45 as the result.

3. Multiplication of 2-digit numbers (11–19)

1. For this, add the unit digit of the smaller number to the larger number.
2. Then multiply the sum by 10.
3. Then multiply the unit digits of the two original numbers.
4. Finally, add two results (steps 2 and 3) to get the desired outcome of your problem.

For example, let’s multiply 14 and 15:

Step 1: To multiply 14 and 15, first add the unit digit of the smaller number (4) with the larger number (15) to get 19.
4 + 15 = 19
Step 2: Next, multiply 19 by 10 to get 190.
19 X 10 = 190
Step 3: After that, multiply both unit digits (4 and 5) to get 20.
4 X 5 = 20
Step 4: Finally, add 190 and 20 to obtain the result of 210.

4. Multiplying any two-digit number by 11

In this, when multiplying a 2-digit number by 11, place both the digits at each end and place the sum of these digits at its centre.
For example, take 13 x 11.

Step 1: Place 1 and 3 at each end.
Step 2: Add 3+1 to get 4.
3 + 1 = 4
Step 3: Place 4 at the centre to get the result of 143.

5. Subtracting any number from 100, 1000, 10000, and other multiples of 10.

To subtract any number from 100, 1000, 10000… using the Vedic Math trick, follow these steps:

1. If the number you are subtracting from (let’s say 1000) has more than a 1-digit difference from the number you are subtracting (let’s say 23), then add 1 more zero to the left of your original number. In any case, you should add zeroes till the number of digits in your original number is 1 less than the number you are subtracting from.
2. Subtract the unit digit from 10 and each remaining digit of the number from 9.
3. Then, place them sequentially to obtain the result.

To subtract 23 from 1000, we will first add zeros. Since we are subtracting from 1000, which is a 4-digit number, and our original number has 2 digits, we will add just 1 zero.
= 023

Step 1: Subtract 3 from 10 to get 7.
10 – 3 = 7
Step 2: Subtract 2 from 9 to obtain 7.
9 – 2 = 7
Step 3: Subtract 0 from 9 to obtain 9.
9 – 0 = 9
Step 4: Place the numbers sequentially to obtain 977 as the result.

6. Dividing a large number by 5

1. First, multiply the entire number by 2.
2. Next, place a decimal right before the unit digit of the resulting number to obtain the final result.

For example, take the number 368.

Step 1: Multiply 368 by 2 to get 736.
368 X 2 = 736.
Step 2: Place a decimal before the unit digit so it becomes 73.6, which is the accurate result.

7. Finding the square value of a number

1. Select a base number closer to the original number.
2. Calculate the difference between the base and the original number.
3. Add the original number and the difference arrived at, and multiply it by the base.
4. Add the square of the difference between the base and the original number, with the result obtained above, to get the final result.

For example, take a number, say 102.

Step 1: Take the base number to be 100.
Step 2: The difference between 102 and 100 is 2.
102 – 100 = 2
Step 3: Now, add 2 to 102 to get 104.
2 + 102 = 104
Step 4: Multiply 104 by 100 to get 10400.
104 X 100 = 10400
Step 5: Add the square of 2, that is, 4, to 10400 to get 10404 as your answer.

8. Ekadhikena Purvena (By One More than the Previous One)

Steps:

1. Look for numbers close to 10, 100, or 1000.

2. Add one more to the previous number.

3. Subtract the difference.

Example: 59 + 12 → (60 + 12) − 1 = 7

Comparison with Modern Mathematics    Vedic Mathematics and Modern Mathematics differ significantly, and here are five points highlighting their distinctions: Origins and Historical Context Vedic Mathematics: Originating in ancient Indian scriptures known as the Vedas, it can be traced back to Bharati Krishna Tirthaji, who developed its techniques and principles from Vedic literature thousands of years ago. Modern Mathematics: Modern mathematics has evolved over centuries through contributions by mathematicians from around the globe, with disciplines like algebra, calculus, geometry, and more developing through rigorous formalization and systematic reasoning.

Conclusion

Vedic Maths is a powerful and fun way to learn numbers. It makes calculations faster and easier. Students enjoy solving problems and feel more confident in math. These tricks improve focus, memory, and mental speed. With a little practice, anyone can use these methods in exams and daily life. Thanks to Bharati Krishna Tirtha, this ancient knowledge is available to everyone today.