History

The origins of Vedic Maths can be traced back to ancient Indian scriptures known as the Vedas. These mathematical principles were rediscovered and popularized by Sri Bharati Krishna Tirthaji Maharaja in the early 20th century.

Introduction to Vedic Maths

Vedic Mathematics is a system of mathematical techniques that originated in ancient India. It involves a set of short-cuts and tricks to solve mathematical problems quickly and efficiently.

Vedic Mathematics is a system of mathematics that originated in ancient India and was rediscovered in the early 20th century. It offers a simplified approach to arithmetic and algebraic operations, making complex calculations easier and faster.

For example, one of the basic principles of Vedic Maths is the sutra (aphorism) "Ekadhikena Purvena," which translates to "By one more than the previous one." This principle simplifies multiplication and division by breaking down numbers into smaller, more manageable parts.

The Benefits of Vedic Maths

Speed and Accuracy: Vedic Maths techniques enable faster calculations with increased accuracy. For instance, using Vedic Maths, you can multiply large numbers mentally within seconds.
Improved Mental Agility: Practicing Vedic Maths exercises can enhance mental math skills and improve cognitive abilities. For example, techniques like "Vertically and Crosswise" require mental agility and concentration.
Applicability: Vedic Maths techniques can be applied to various mathematical operations, including arithmetic, algebra, geometry, and calculus. These techniques provide versatile tools for solving a wide range of mathematical problems.

Key Concepts in Vedic Maths

Vertically and Crosswise: A technique for multiplying numbers. For instance, to multiply 23 by 12 using this technique, you multiply the vertical and crosswise elements to get the result (2*1 + 3*2 = 6 and 2*2 = 4), resulting in 276.
By Addition and Subtraction: A method for quickly multiplying numbers by breaking them down into smaller parts. For example, to multiply 35 by 9, you can break 9 into 10-1 and add/subtract accordingly, resulting in 315.
Digit Sums: Using the digital root of numbers to simplify calculations. For instance, to find the digital root of 345, you add the digits (3+4+5 = 12, and 1+2 = 3), resulting in 3.

Resources for Learning Vedic Maths

Books: Several books are available on Vedic Mathematics, including "Vedic Mathematics" by Swami Bharati Krishna Tirtha.
Online Courses: Websites offer online courses and tutorials on Vedic Maths for self-paced learning.
Workshops and Seminars: Attend workshops and seminars conducted by experts in Vedic Mathematics for hands-on learning.

Swami Bharati Krishna Tirtha's Vedic Mathematics

Swami Bharati Krishna Tirtha’s Vedic Mathematics system is based on sixteen primary Sutras and thirteen Upasutras.

Sixteen Primary Sutras:

Ekādhikena Pūrvena
Nikhilam Navatashcaramam Dashatah
Urdhva-Tiryagbhyam
Parāvartya Yojayet
Shūnyam Saamyasamuccaye
Shesanyankena Charamena
Antyayor Dasakepi
Antyayor Dasakepī
Antyayor Dasakepīti
Antyayoreva
Antyayoreva
Vilokanam
Yāvadūnam
Yavadūnam
Yavadūnam Tavadūnīkṛtya
Yaavadūnam Tavadūnīkṛtya

Thirteen Upasutras:

Ekadhikina Purvena
Anurupyena
Shunyam Saamyasamuccaye
Adyamadyenantyamantyena
Kevalaih Saptakam Gunyat
Ekanyunena Purvena
Gunitasamuccayah Samuccayagunitah
Samuccayagunitah
Yavadunam Tavadunikrtya Varga Yojayet
Shesanyankena Charamena
Sopantyadvayamantyam
Ekanyunena Purvena
Gunitasamuccayah

Advanced Vedic Maths Tactics

Here are some advanced Vedic Maths tactics that can be useful for various purposes:

Double-Digit Multiplication Techniques
Digit Sum Method for Checking Calculations
Square Roots with Vedic Mathematics
Fast Division Techniques

Applications

Vedic Maths techniques are beneficial for:

Students for quick and accurate calculations
Teachers to teach math in an engaging way
Government exam aspirants for aptitude test preparation
Enhancing overall mental sharpness

Examples

1. Multiplication using Vertically and Crosswise Method

Question: Calculate 84 × 73 using Vedic Maths.

Solution:

            84
          × 73
          ------
            84
          + 84 × 7 (Crosswise)
          + 3 × 84 (Crosswise)
          ------
          = 84
          + 588 (Crosswise)
          + 252 (Crosswise)
          ------
          = 6132

So, 84 × 73 = 6132.

2. Square of a Two-Digit Number Ending in 5

Question: Find the square of 65 using Vedic Maths.

Solution:

Step 1: Multiply the tens digit by its successor (6 × 7) = 42

Step 2: Write down the square of the units digit (25).

Step 3: Combine the results: 6 (from step 1) | 25 (from step 2)

Step 4: Add a '0' at the end: 4225

So, the square of 65 = 4225.

Vedic Maths: A Systematic Approach to Mathematics

Vedic Maths