Mathematics, often considered a difficult subject, has always been an essential part of our lives, whether we realize it or not. From calculating bills at the grocery store to managing finances, its applications are ubiquitous. However, many struggle with traditional methods of mathematical computation, finding them complex and time-consuming. This is where Vedic Maths Formulas come into play, offering a simpler and more efficient approach to solving mathematical problems.

How is Vedic Maths Formulas useful in our daily lives?

Vedic Maths makes it possible to calculate complex equations mentally, swiftly, and accurately. By employing ancient Indian techniques, Vedic Maths simplifies arithmetic operations such as addition, subtraction, multiplication, and division. These methods not only save time but also enhance mental agility and numerical aptitude. Moreover, Vedic Maths instills a deeper understanding of numbers and patterns, fostering a love for mathematics among learners. It promotes mental math, reducing dependence on calculators and offers a holistic approach to mathematical problem-solving. This proficiency in mental arithmetic enhances problem-solving skills, a crucial asset in today’s fast-paced world.

29 Vedic Maths Formulas

1.Vertically and Crosswise:

This technique simplifies multiplication of numbers by breaking them down into smaller, more manageable parts.

2.Urdhva-Tiryagbhyam:

A method for squaring numbers mentally, ideal for lightning-fast calculations.

3.Nikhilam Navatashcaramam Dashatah: 

A formula for finding complements, making subtraction a breeze.

4.Paravartya Yojayet: 

Swapping the terms in a subtraction problem to simplify the calculation.

5.Anurupyena:

Proportionality technique used for division, ensuring accuracy without the need for long division.

6.Shunyam Saamyasamuccaye: 

Zero in one group equalizing the other group, a technique for balancing equations effortlessly.

7.Ekadhikena Purvena: 

Adding one more to the previous number, a handy trick for mental addition.

8.Puranapuranabhyam: 

Completing the square technique, useful for solving quadratic equations.

9.Chalana-Kalanabyham: 

The method of difference, simplifying subtraction through the principle of canceling.

10.Yaavadunam: 

The “as much as possible” method for solving complex multiplication problems.

11.Vilokanam:

A visualization technique for solving equations involving consecutive numbers.

12.Antyayor Dasakepi: 

Working with the last digits to simplify calculations, particularly useful for finding remainders.

13.Antyayor Dasake’pi: 

A variation of the above formula, focusing on the last two digits.

14.Antyayoreva:

Simplifying multiplication by focusing on the last digits.

15.Vinculum: 

The technique of using bar notation for fractions, aiding in simplification.

16.Adyamadyenantyamantyena:

 Working with the first and last digits of numbers for faster calculations.

17.Antyayor Dasakepi Chaaramena:

A formula for finding the last digit of a product without actually multiplying.

18.Ekanyunena Purvena: 

One less than the previous number, a technique for mental subtraction.

19.Shesanyankena Charamena: 

The remaining digit by the last one, simplifying multiplication.

20.Sankalana-vyavakalanabhyam: 

The method of addition and subtraction for simplifying equations.

21.Gunakasamuccayah: 

The product of the sum method, useful for mental multiplication.

22.Vyashtisamanstih: 

Working with individual digits for faster calculations.

23.Yavadunam Tavadunikritya Varganca Yojayet: 

Squaring technique for numbers close to a base.

24.Anurupye Shunyamanyat: 

If one is in ratio, the other is zero, a helpful formula for solving proportions.

25.Sopaantyadvayamantyam: 

The product of the last two digits method, simplifying multiplication.

26.Antyayor Dasakepi Chaaramena: 

A variation of the above formula for finding the last digit.

27.Antyayor Dasakepi: 

A general formula for finding the last digit of a product.

28.Vargankisham:

A technique for multiplying numbers close to powers of ten.

29.Yavadunam Tavadunikritya Varganca Yojayet: 

Squaring numbers near a base, another method for quick mental math.

16 Vedic Maths Sutras

1. Ekadhikena Purvena (By One More Than the Previous One):

   This sutra teaches us to add numbers by focusing on the excess or deficit over a base number. For example, to add 23 and 17, we take the excess over 20 (3 and 7), add it to the base (20), and then add the result to the other number, yielding 40.

2. Nikhilam Navatascaramam Dasatah (All From 9 and the Last From 10):

   This sutra simplifies subtraction by complementing numbers to the nearest power of 10. For instance, to subtract 48 from 100, we subtract each digit from 9 (9-4=5, 9-8=1), and add 1 to the last digit, giving us 52.

3. Urdhva-Tiryagbhyam (Vertically and Crosswise):

   This sutra facilitates multiplication of numbers with multiple digits through crosswise calculation. For example, to multiply 23 by 21, we cross-multiply (2×2=4, 3×1=3), and then combine the results, yielding 483.

4. Paravartya Yojayet (Transpose and Apply):

   This sutra simplifies division by reversing the digits of the divisor and applying a specific method. For example, to divide 864 by 24, we reverse 24 to get 42 and divide 864 by 42, yielding 20.

5. Shunyam Saamyasamuccaye (When the Sum Is the Same That Sum Is Zero):

   This sutra aids in finding complements to simplify calculations. For instance, to multiply 8 by 9, we subtract each digit from 10 (10-8=2, 10-9=1), yielding 72, the complement of 8 and 9.

6. Anurupye Shunyamanyat (If One Is in Ratio, the Other Is Zero):

   This sutra is useful in proportionality problems, stating that if one ratio is given, the other ratio is zero. For example, if the ratio of the height and base of a triangle is given as 3:4, and the height is 15, then the base is 20.

7. Sankalana-vyavakalanabhyam (By Addition and by Subtraction):

   This sutra simplifies factorization and simplification of algebraic expressions by combining and separating terms. For example, to factorize x² – 5x + 6, we look for two numbers that add up to -5 and multiply to 6, which are -2 and -3, giving us (x – 2)(x – 3).

8. Puranapuranabhyam (By the Completion or Non-Completion):

   This sutra simplifies algebraic equations involving squares. For example, to factorize x² + 6x + 9, we recognize it as (x + 3)².

9. Chalana-Kalanabyham (Differences and Similarities):

   This sutra simplifies algebraic expressions by identifying differences and similarities. For example, to simplify (a + b)² – (a – b)², we use the formula a² + 2ab + b² – (a² – 2ab + b²), which simplifies to 4ab.

10. Yaavadunam (Whatever the Extent of Its Deficiency):

    This sutra simplifies problems involving squares. For instance, to find the square of 8, we subtract 8 from the base 10, getting 2, then multiply it by 8, giving us 64, and finally, subtract the square of the deficiency from the base square, yielding 36.

11. Vyashtisamanstih (Part and Whole):

    This sutra simplifies problems involving fractions and ratios. For example, to find 3/7 of 84, we divide 84 by 7 (12) and multiply it by 3, yielding 36.

12. Shesanyankena Charamena (The Remainders by the Last Digit):

    This sutra simplifies problems involving remainders. For instance, to find the remainder when 121 is divided by 7, we focus on the last digit (1) and apply the rule for finding remainders by the last digit (1).

13. Sopaantyadvayamantyam (The Ultimate and Twice the Penultimate):

    This sutra simplifies problems involving the sum of squares. For example, to find the sum of squares of numbers from 1 to 10, we use the formula (10(10 + 1)(2(10) + 1))/6, yielding 385.

14. Ekanyunena Purvena (By One Less Than the Previous One):

    This sutra simplifies multiplication by focusing on the deficit from a base number. For example, to multiply 17 by 13, we take the deficit from 20 (3 and 7), subtract it from the base (20), and then subtract the result from the other number, yielding 221.

15. Gunitasamuchyah (The Product of the Sum):
    
    This sutra simplifies problems involving multiplication of fractions. For instance, to multiply 2/3 by 3/4, we multiply the numerators and denominators, yielding 6/12, which simplifies to 1/2.
    
16. Samuccayah Samuccayagunitah (The Product of the Sum Is the Sum of the Product):
    
    This sutra simplifies problems involving simultaneous equations. For example, if x + y = 10 and xy = 16, then x² + y² = (x + y)² – 2xy, yielding 100 – 32 = 68.

Conclusion

In Maths, solving questions and equations with efficiency and speed is important, Vedic Maths Formulas offer a refreshing alternative to traditional mathematical techniques. If you’re a student grappling with math homework or an adult managing finances, these methods provide a practical solution to everyday mathematical challenges. At Medh, we recognize the importance of making mathematics accessible and enjoyable for everyone. That’s why we offer courses in Vedic Maths, tailored to suit learners of all ages and skill levels. With our expert guidance, anyone can learn and apply Vedic Maths formulas in their daily lives and make doing Maths fun rather than a challenge!