Math Concepts

Addition and Subtraction Tricks

3rd Nov '2010 views6 mins read

11 November  2020

Reading Time: 6 Minutes

Introduction

Do you want to get 10 times faster at calculations?

Do you want to master addition and subtraction?

Mathematics has always seemed to be challenging to study for many. To make it friendly to learners, continued efforts, research, and advancements are continuously made throughout human beings’ history. In ancient times, easy methods of mathematical operations, namely, addition and subtraction, etc. had been in practice. Vedic mathematics simplifies mathematical operations. Formulae and concepts of Vedic mathematics are widely accepted world over.

Vedic mathematics was an ancient method of solving mathematics problems. Later, Shankaracharya Swami Bharati Krishna Tirtha discovered Vedic mathematics. He is called the Father of Vedic mathematics.

Vedic mathematics image

Source: Hinduscriptures.com

  1. Vedic mathematics tricks are beneficial in competitive examination.
  2. Vedic is a Sanskrit word, the root word being Vid.
  3. It means knowledge; Ved means knowing all without limit. Vedic mathematics consists of Sutras to solve mathematical problems easily and speedily.
  4. Though it is outdated, it is helpful to solve mathematical problems mentally and easily.
  5. The name Vedic signifies its origin as Vedas.
  6. Of the 4 Vedas, Vedic mathematics is part of Atharva Veda, the 4th Veda.
  7. Veda is all-embracing i.e., Engineering, mathematics, science, medicine, and sculpture, etc.
  8. Vedic mathematics covers applications to arithmetical calculations, number theory, algebraic equations, simultaneous equations, partial fractions, calculus, square root, cube root, coordinate geometry etc.

 

Also read:


Here are some Vedic Maths Tricks

  • There are techniques for solving mathematical problems. This blog talks about addition and subtraction.
  • These techniques are tricks resulting in efficiency and speed in solving mathematical problems. It ultimately leads to mental calculations. It consists of operations made repeated. Vedic mathematics tricks give answers in one step.
  • Efficiency and ability for memorizing reduce calculations. Hence speed, time, money, and accuracy are not compromised.
  • In ancient times, first mathematical operation was by counting from 1 and adding 1 further as below:

                    1 + 1 = 2,

                    2 + 1 = 3 

                    3 + 1 = 4
                   ……………
                   9 + 1 = 10 and further with multiple additions.

  • Counting was done by use of fingers and other rude methods earlier.
  • Over time, they became known and familiar results in memory. Thus, counting and adding existed. By repetition of these processes, again and again, we are familiar with most common numbers. 
  • The most basic arithmetic sequence is ‘Memorize and no need to calculate’.

Basic sets to memorize

1. All sums up to 10 

Example

 

 

  2 + 4 = 6

  3 + 5= 8

  4 + 6 = 10

  5 + 5 = 10

2. Addition of all single digit numbers.

Example 

 

 

 5 + 5 = 10 

 6 + 7 = 13 

 7 + 7 = 14 

 9 + 8 = 17 etc.

3. All compositions of 10.

Example 

 

 

5 + ? = 10      

 6 + ? = 10

 ? + 6 = 10 


Additioin Tricks! Get better at calculations

Some special number pairs that add to 10

Example 

 

 

 1 + 9 = 10

 2 + 8 = 10     

 3 + 7 = 10     

 4 + 6 = 10     

 5 + 5 = 10

Merely on seeing such pairs, the sum is understood mentally.

Benchmarks

To add one-digit number to another digit number, the technique involves having a basic number for easy calculation. To have multiples of 10 as benchmarks is safe and easy.

Example 

 

 

  1. 23 + 8. Take 20 as a benchmark. Then 23 + 8 = 20 + 3 + 8 = 20 +11 = 31.
  2. 126 + 8. Benchmark 130. 

              126 + 4 + 4 = 130 + 4 = 134.

Breaking apart by place value

  Decimal place value system for every number is used.

Example 

 

 

    14 + 77

      = 10 + 4 + 70 + 7 = 10 + 70 + 4 + 7 = 80 + 11 = 91           

      42 + 66 = (40 + 2) + (60 + 6) = (40 + 60) + (2 + 6) = 100 + 8  = 108.

Nature of additions

1. Additions are Commutative

In sums for additions, the numbers can be rearranged or interchanged.

The result will be the same, even after the rearrangements.

Example 

 

 

 8 + 3 = 3 + 8 = 11

 6 + 41 = 41 + 6  = 47

 22 + 63 = 63 + 22 = 85

Generalizing, a + b = b + a

Multiplication of numbers in a sum is also commutative.

(operations in subtraction and division are not commutative.

Example 

 

 

 6 - 3 ≠ 3 - 6 and 6 ÷ 3 = 2 ≠ 3 ÷ 6 = 12

2. Addition is  Associative

This is another law of addition.

As per this law, problems of additions with a greater number of additions, the items can be   added in any order. The answer will not change.

Example 

 

 

  (1 + 8) + 5 = 1 + (8 + 5) = 14

  4 + (21 + 6) = (4 + 21) + 6 = 31

General rule: 

  a + (b + c) = (a + b) + c

3. Partitioning and Reasoning 

When 1 is added to any positive number,

If the last digit is not 9, the last digit of the number is raised to the next higher number.

Example 

 

 

6897 + 1 = 6898

If all the digits are nines, except the first digit, replace them with zeros and raise the first digit to the next higher number.

Example 

 

 

6999 + 1 = 7000.


Subtraction Tricks! Get better at calculations

Subtraction is the opposite of the addition process. By going through the following examples, substitution can be learnt.

Subtraction is made easy and simple mathematical operation by Vedic mathematics.

1. Subtracting 1

    10 - 1 =9

    100 - 1 = 99

When subtracting 1 from zero, the answer contains only 9s.

2. Subtraction from power of 10 

In this technique, we take the nearest power of 10 for the numbers involved and subtract the numbers from the base.

Another rule called Nikhilam rule helps us. Nikhilam is one of the 16 main Sutras of Vedic mathematics.

Nikhilam rule says, “All from 9 and the last from 10”.

Example 

 

 

10000-8675

 99910 - 8675   =1325 Answer.

In this, we subtract each digit of the number simply from 9 for all digits except for the last digit, which is subtracted from 10.

If the number has a smaller number of digits, add leading zeros to have more digits.

Example 

 

 

100000-875 = 999910-00875
                    = 999910 - 00875
                    = 99125 Answer.

Example

 

 

  • Subtrahend is less than minuend.

3625 - 1789

Subtract the subtrahend from the highest next power of 10 by Nikhilam rule.

99910 - 1789 = 8211

Add the result to the minuend, i.e., 3625 + 8211 = 11836.

Deleting the first digit, 1, the answer is 1836. 

  • 4529 - 2380

In this, 2380, the last digit from the left is zero. Here ‘8’ is to be subtracted from 10, keeping the zero as the last digit from left.

Then, 

99100 –  23 80 = 7620 + 4529 
                         = 12149

Deleting the left first digit, the answer is 2149.

  • 45827 - 398 (subtrahend is of less digits than minuend)

i.e., 45827 - 00398

i.e., 999910 - 00398 = 99602 ---------(1)

Add (1) with 45827

99602 + 45827 = 145429

Deleting 1, the answer is 45429.

  • Minuend less than subtrahend

351 - 497

Apply NIKHILAM rule to Minuend

9910 - 351 = 649

Add subtrahend 

649 + 497 = 1146

Deleting 1, first digit at left, the answer is -146.


Summary

This blog talks about the addition and subtraction tricks for fast calculation. Apart from getting quick at calculations, vedic maths helps develop a child's mind and improves his/her cognitive ability. Some features of vedic maths are:  

  • Vedic Mathematics gives the answers in mathematical problems of addition, subtraction and multiplication etc in one step.
  • Vedic Mathematics is outdated.
  • Yet, it is easy and simple.
  • Problems can be solved quickly in Vedic Mathematics.
  • Hence it is helpful in competitive examinations of CBSE, ECSE mathematics or JEE problems in less time and with high accuracy. 
  • No need arises for any calculation when Vedic Mathematics is used for mathematical problems.

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FAQs

How do you add using Vedic Maths?

In Vedic maths, addition operation is made as follows:

  1. By associative method 
  2. By commutative method
  3. By using benchmark, and 
  4. By breaking apart based on place value.

How do you subtract using Vedic Maths?

In Vedic maths, subtracting is done by following techniques:

  1. Subtracting the number in the question, the operation is started from the nearest power of 10,
  2. Using the Nikhilam rule, “All from 9 and the last from 10”.

What is Nikhilam formula?

  1. Nikhilam formula is used in the mathematical processes of subtraction and multiplication.
  2. Nikhilam formula (Sutra) is one of the 16 sutras of Vedic Mathematics.
  3. Nikhilam's formula states, “All from nine and the last from ten”. 
  4. i.e., Nikhilam is applied to a number, subtract each digit from 9 and the last digit from 10.

How many formulas are there in Vedic Maths?

There are 16 formulas in Vedic Maths.


External References

Wikipedia.org - Vedic Mathematics 


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