Have you ever encountered the term 'Vedic Mathematics' and wondered what it means? Don't worry; you're not alone. This powerful yet underappreciated mathematical system has been shrouded in mystery for centuries. But fear not; we're here to illuminate your path in exploring this fascinating world.
Contrary to popular belief, Vedic Mathematics isn't a complex subject reserved only for math wizards. Rather, it's a simplified and efficient calculation approach rooted in ancient Indian scriptures called the Vedas. It offers a unique method of calculations based on simple rules and principles, encapsulated in what we call 'Sutras', turning complex calculations into child's play.
Imagine solving a problem in seconds, which would have required lengthy calculations! That's the power of Vedic Maths. But why should you, as a student, care about it? Let's find out as we delve deeper.
Learn All About Vedic Maths
Vedic Maths is an ancient system of mathematics that originated in India and is based on the Vedas, ancient Hindu scriptures. It offers a unique and holistic approach to mathematics, focusing on mental calculations, quick problem-solving techniques, and mathematical shortcuts. Learning Vedic Maths can be a transformative experience for students, helping them develop a deeper understanding of numbers and arithmetic operations while enhancing their mental agility and problem-solving skills.
One of the key aspects of Vedic Maths is the use of Sutras or aphorisms, which are concise and powerful formulas that provide shortcuts for various mathematical operations. These Sutras enable students to perform calculations mentally and with remarkable speed. By mastering these Sutras, students can perform complex calculations such as addition, subtraction, multiplication, and division in a fraction of the time it would take using conventional methods.
Vedic Maths is not just about finding shortcuts; it also emphasizes understanding the underlying mathematical concepts and patterns. It encourages students to explore alternative methods, think creatively, and develop problem-solving strategies. This approach instils confidence and self-reliance in students, as they become proficient in mentally performing calculations without relying heavily on external aids such as calculators or pen and paper.
Furthermore, Vedic Maths has applications beyond basic arithmetic. It can be applied to algebra, geometry, calculus, and advanced mathematical concepts. By building a strong foundation in Vedic Maths, students gain a versatile toolkit of mathematical techniques that they can apply to various problems.
Learning Vedic Maths can be an exciting and rewarding journey, empowering students with valuable skills beyond mathematics. It enhances their logical thinking, concentration, and memory while promoting a love for numbers and a deep appreciation for the beauty and elegance of mathematics.
Whether you are a student looking to excel in exams, a teacher seeking innovative teaching methods, or an adult wanting to enhance your mental calculation abilities, delving into Vedic Maths opens up a realm of possibilities. So, embark on this fascinating journey, and unlock the secrets of Vedic Maths to uncover a whole new dimension of mathematical prowess.
16 Vedic Maths Sutras
At the heart of Vedic Maths are 16 sutras, or aphorisms, that guide its problem-solving approach. Here's a closer look at these magical sutras and a brief glimpse into what they stand for:
| Sutras Of Vedic Maths | Meaning |
|---|---|
| Ekadhikena Purvena | "By one more than the previous one." This sutra is mainly used in calculations involving division by specific numbers. |
| Nikhilam Navatashcaramam Dashatah | "All from 9 and the last from 10." It’s useful in the multiplication of numbers close to powers of 10. |
| Urdhva-Tiryagbhyam | "Vertically and crosswise." This sutra is a general method used in multiplication and is very useful for large digits. |
| Paravartya Yojayet | "Transpose and adjust." It’s used to simplify complex fractions and divisions. |
| Shunyam Saamyasamuccaye | "When the sum is the same, that sum is zero." It helps in solving simultaneous quadratic equations. |
| Anurupye - Shunyamanyat | "If one is in ratio, the other one is zero." It’s used in solving special types of equations. |
| Sankalana-vyavakalanabhyam | "By addition and by subtraction." This sutra helps in solving calculus problems." |
| Puranapuranabhyam | "By the completion or non-completion." It aids in solving algebraic equations. |
| Calana-Kalana-bhyam | "Differences and Similarities." It’s useful in solving problems based on differentiation. |
| Yavadunam | It’s used in solving problems related to progressions and series. |
| Vyastisamanstih | It’s applied in calculating ratios and proportions. |
| Shesanyankena Charamena | "The remainders by the last digit." It’s useful in complex multiplication problems. |
| Sopaantyadvayamantyam | The ultimate and twice the penultimate." This sutra helps in solving special types of multiplications. |
| Ekanyunena Purvena | "By one less than the previous one." This sutra is useful in squaring numbers and complex multiplications. |
| Gunitasamuchyah | "The product of the sum is the sum of the product." It’s used in solving equations of higher degrees. |
| Gunakasamuchyah | "The factors of the sum are equal to the sum of the factors." This sutra is used in solving higher-degree equations. |
How Do We Use Vedic Maths In Daily Life?
- Vertically and Crosswise: This technique can be used to multiply two numbers quickly. It involves multiplying the digits in the ones place and tens place separately and then adding them together.For instance, to multiply 23 and 45, you would multiply 3 and 5 to get 15, and then multiply 2 and 4 to get 8. Finally, you add the two results together to get 1035.
- All from 9 and the last from 10: This technique can be used to subtract a number from 100 or a multiple of 100. To use this technique, you simply subtract each digit in the number from 9, except for the last digit, which you subtract from 10.For example, to subtract 37 from 100, you would subtract 3 from 9 to get 6, and subtract 7 from 10 to get 3. The answer is therefore 63.
- Digital Roots: This technique can be used to find the digital root of a number (the single digit that results from adding all the digits in the number together). To find the digital root, you simply keep adding the digits in the number together until you get a single digit.For example, the digital root of 1234 is 1+2+3+4=10, and since 10 is not a single digit, you add 1+0=1, which is the digital root.
Vedic Maths Tricks
Vedic Math is very useful if you want to calculate faster, children who practice the techniques can find themselves mentally more agile. Here are some basic examples of vedic maths techniques you can apply in your Maths classes:
| Vedic Math Tricks | How To Use Them? |
|---|---|
| Squaring Numbers Ending in 5 | To square a two-digit number ending in 5, take the tens digit, multiply it by itself plus 1, and then append 25 to the result. For example, to square 35: (3 x 4) = 12, so the answer is 1225. |
| Multiplying Numbers Near a Base | When multiplying numbers close to a base like 10, 100, 1000, etc., it's easier to work with the deviations from the base and then adjust the result afterward. For example, to multiply 98 by 103, you can calculate (98 x 3) + (98 x -2) = 303 + (-196) = 107. |
| Crosswise Multiplication | For the multiplication of two-digit numbers, use the crosswise multiplication method. Multiply the digits diagonally and then add the results. For example, to multiply 14 by 23, multiply 1x3 and 4x2, then add the results: (1x3) + (4x2) = 3 + 8 = 38. |
| Finding the Square of Any Two-Digit Number | To square any two-digit number, use this method: Step 1: Find the difference between the number and the nearest multiple of 10. Step 2: Square the difference. Step 3: Add the result from Step 2 to the number minus the difference, and then append the square of the difference. For example, to square 47: Step 1: 47 - 50 = -3 Step 2: (-3)^2 = 9 Step 3: (47 - 3) = 44, so the square of 47 is 2025. |
| Checking for Divisibility | To check if a number is divisible by 9, add up the digits. If the sum is divisible by 9, the original number is also divisible by 9. This rule can be applied repeatedly for divisibility by larger multiples of 9. |
| Casting Out Nines | Use casting out nines to check for errors in arithmetic calculations. This method involves summing the digits of a number and then reducing it to a single digit. If the resulting single-digit doesn't match the expected single digit, an error may have occurred in the calculation. |
Vedic Mathematics Examples
- Multiplication by 11: To multiply a two-digit number by 11, simply add the digits of the original number and place the sum between the original digits. For example: 34 x 11 = 3 (3+4) 4 = 374
- Squaring numbers ending in 5: To square a number that ends in 5, take the digit before 5 and multiply it by its successor. Then, append 25 to the result. For example: 35^2 = (3 x (3+1)) 25 = 1225
- Multiplication of two-digit numbers: Suppose you need to multiply two numbers, say 17 and 12. a) Break down the numbers into parts: 17 can be written as (10 + 7) and 12 as (10 + 2). b) Cross-multiply the parts: Multiply 10 by 10 and 7 by 2. c) Add the cross-products: 10 x 10 = 100 and 7 x 2 = 14. So, the result is 100 (cross-product) + 14 (cross-product) = 114.
- Division by 9: If you want to divide a number by 9, find the sum of its digits. If the sum is greater than 9, keep adding the digits until you get a single-digit number. The quotient will be that single-digit number. For example: 486 ÷ 9 = (4+8+6) ÷ 9 = (18) ÷ 9 = 1 + 8 = 9. Therefore, the quotient is 9.
Can I Learn Vedic Math at Home?
Yes, absolutely! With the advent of online learning platforms and the resources available, learning Vedic Maths from your home has always been challenging. Here are a few tips on how you can embark on this journey:
Understand the Basics
Start with the basics, understanding the Vedic Maths sutras, their meanings, and their applications. This forms the foundation of your learning process.
Practice Regularly
Like any new skill, regular practice is key to mastering Vedic Maths. Allocate a specific time slot in your daily routine to study and practice Vedic Maths. For instance, if you're learning the 'Urdhva-Tiryagbhyam' sutra for multiplication, practice it with different sets of numbers until you're comfortable with the process.
Use Online Learning Resources
Make use of the wealth of online learning resources available. Websites, apps, and video tutorials can greatly assist in your learning process. Platforms like Khan Academy, Coursera, and Superprof provide comprehensive courses in Vedic Maths.
For example, Superprof offers an array of experienced tutors who can guide you through your Vedic Maths journey. The platform's interactive one-on-one lessons can greatly aid in understanding the intricate concepts of Vedic Maths, clearing doubts, and improving your calculation speed.
Test Your Progress
Always test your progress: attempt practice problems, quizzes, and tests to gauge your understanding of Vedic Maths. Keep track of your progress and work on the areas where you face difficulty.
Vedic Math Tricks for Students
If you're a student planning to appear in competitive exams, Vedic Maths tricks and tips can be your secret weapon. Its speed and efficiency are invaluable in tests like the SAT, GMAT, CAT, and banking exams, where every second counts.
Speed is Key
In these exams, you often face multiple calculations that can consume considerable time if done using conventional methods. With its innovative tricks, Vedic Maths can significantly speed up your calculations, saving precious time for other sections.
For instance, imagine finding the cube of 13 during an exam. Conventionally, this would involve lengthy multiplication. But with Vedic Maths, you can use the 'Anurupyena' sutra. Break 13 into 10 + 3, then cube each separately, simplifying the calculation: 1 cube (for the 10's place) is 1, and 3 cube is 27. Thus, the answer is 2197.
Accuracy
Apart from speed, accuracy is another critical factor in competitive exams. Since Vedic Maths reduces the steps involved in calculations, the chances of making mistakes diminish.
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