Two Basic Concepts of Gems of Vedic Mathematics

Gems of Vedic Mathematics Let’s start the wonderful journey of Vedic Mathematics with the two basic concepts – Base and Complements.

The whole number system is made up of only 10 numbers (0 to 9). All these numbers repeat themselves in a specific order after numbers like 10, 100, 1000, and so on, which are called Bases.

Bases are the numbers starting with I and followed by any number of 0’s e.g. 10, 100, 1000, 10000 and so on.

Base numbers are the first number for ‘those many digits’ like 10 is the first number for 2-digit numbers, 100 is the first number for 3-digit numbers and so on.

Gems of Vedic Mathematics

A base number should not have any other digit at the starting except I and it should be followed only by 0’s. So, numbers such as 200, 1001, 1200 are not bases.

Embarking on the fascinating journey of Vedic Mathematics unveils a realm of ancient wisdom that simplifies mathematical computations. At the core of this system lie two fundamental concepts: Bases and Complements. In this exploration, we delve into the essence of Bases, elucidating their significance and characteristics.

Understanding Bases: The Pillars of the Number System

In the Gems of Vedic Mathematics framework, the entire number system is elegantly structured around the concept of Bases. These Bases are not arbitrary; they are specific numbers that serve as the foundation for various numerical categories. The set of natural numbers from 0 to 9 constitutes the essence of this system.

Bases manifest themselves as numbers preceded by ‘1’ and followed by any number of ‘0’s. For instance, 10, 100, 1000, and 10,000 are quintessential examples of Bases. These numbers represent critical milestones in the numerical sequence, delineating the transition to new orders of magnitude.

The Role of Bases in Digit Categorization Gems of Vedic Mathematics

Bases play a pivotal role in categorizing digits based on the number of places they occupy. Take, for instance, the number 10, which marks the initiation of 2-digit numbers. Similarly, 100 serves as the starting point for 3-digit numbers, and the pattern continues. Understanding the significance of these Bases unlocks a streamlined approach to dealing with numbers of varying magnitudes.

Key Characteristics of Bases: Purity and Order Gems of Vedic Mathematics

To qualify as a Base, a number must adhere to specific criteria. Firstly, it must commence with ‘1,’ setting a pristine foundation for the subsequent digits. Any deviation from this criterion disqualifies a number from being a Base. For instance, numbers like 200, 1001, or 1200 fail to meet the purity standards of a Base.

Secondly, a genuine Base should only be succeeded by ‘0’s. This adherence to zero-padding ensures a systematic and orderly progression in the number system. Thus, numbers like 200, where a non-zero digit follows ‘1,’ disrupt the purity and orderliness expected of Bases.

Reconstructing the Invalid Bases: A Clarification with Examples

Consider the number 200. Although it starts with ‘2,’ it violates the criteria of purity by lacking the initial ‘1’ required for a genuine Base. Similarly, 1001 deviates from the definition of a Base as it introduces a non-zero digit after ‘1.’ Lastly, 1200 fails to qualify as a Base because it combines a non-zero digit with ‘1,’ thus breaching the fundamental principles that define Bases.

Conclusion: Navigating the Mathematical Landscape with Vedic Precision

In unraveling the foundational concepts of Gems of Vedic Mathematics, Bases emerge as the bedrock upon which numerical structures are erected. Their purity and adherence to a systematic order lay the groundwork for efficient and elegant mathematical computations. By understanding the essence of Bases, enthusiasts of Vedic Mathematics embark on a journey that not only simplifies arithmetic but also unveils the profound simplicity embedded in the ancient wisdom of numerical sciences.

EXERCISE 1.1

Say whether the following numbers are bases or not.

COMPLEMENTS

The concept of complement Gems of Vedic Mathematics is important to understand because these complements are very useful in making many kinds of calculations easy and interesting which includes subtraction, multiplication, division, finding squares, cubes and many more.

So, first we understand what complements are and in the following chapters, we shall see their use in different types of calculations.

Those two numbers which when added with each other results in the next nearest base, are called Complements of each other. 

48 +52 = 100, 23 + 77 = 100.

So, 48 is the complement of 52 and 52 is the complement of 48.

In other words, a complement of a number can be calculated by subtracting it out from its nearest base, like:

complement of 76=100-76=24

complement of 358 = 1000-358 = 642

But, finding complements of bigger numbers means subtraction from bigger bases, like finding the complement of 24368 means 100000 24368 which requires the borrowing process at each column.

In Vedic Maths, to simplify this, we use the formula “All from 9 and last from 10”. This means that:

To find the complement of any number, subtract all the digits from 9 and the last digit from 10 (where the last digit means the unit’s place digit.)

Example 1: Find the complement of 4356.

Complement of 4356 can be found by subtracting each of 4, 3 and 5 from 9 and the last digit 6 from 10

Example 2: Find the complement of 8375.  Gems of Vedic Mathematics

Complement of 8375 = 1 6 2 5

(9-8) (9-3) (9-7) (10-5)

Similarly, complement of 4397 = 5603

and complement of 9158=0847

When a 0 comes in between the number

When a 0 comes in between the number, treat this 0 as any other digit, i.e. subtract it from 9 like other digits.

Example 3: Find the complement of 3059.

Complement of 3059 can simply be found as:

So, the complement of 3059= 6941

When a 0 comes at the end of the number

When a 0 comes at the end of the number, write that 0 as it is in the complement and treat the last non-zero digit as the last digit, i.e. subtract the last non-zero digit from 10 and rest of the numbers from 9.

Example 4: Find the complement of 3420. Gems of Vedic Mathematics

It can be found by subtracting digits 3 and 4 from 9 and considering 2 as the last digit, subtract it from 10 and write the 0 as it is, as shown below: 

So, the complement of 3420 = 6580. Similarly, complement of 25390 is 74610. And complement of 7400 is 2600.

EXERCISE 1.2 Gems of Vedic Mathematics

Find the complements of the following numbers:

1. 243
2. 84056
3. 731
4. 1298 7. 700
5. 4763
6. 80900
7. 7060 9. 9100 10. 80050

When a decimal comes in between the number

Numbers with decimals are treated like any other numbers, but

the decimal point must come at its place in the complement.

Example 5: Find the complement of 437.26    Gems of Vedic Mathematics

So, complement of the 437.26562.74 Similarly, complement of 830.25 = 169.75

complement of 523.043 = 476.957

EXERCISE 1.3 Gems of Vedic Mathematics

Find the complements of the following numbers:

1. 638.26 
2. 724.850 
3. 9306.002
4. 29346.83
5. 58600