Vedic Maths Multiplication Shortcut Techniques : Nikhilam Method Part 2

Hi friends, I am Rupali from Pune. A maths lecturer by profession. I used to write Vedic maths shortcuts techniques in gr8ambitionz.com (old readers of gr8 might remember me i guess). I stopped writing due to hectic work pressure. Recently, I have unexpectedly got 15 days of free time and I want to make the better use of this time. From today onwards, I will be sharing some vedic maths shortcut techniques for Multiplications and Divisions (if time permits I will be sharing a few techniques for Squares and Cubes too).

This post (Part 2) is direct continuation to my Previous Post, Nikhilam Method Part I. If you have the basic idea on Vedic Maths, then you can continue with the Nikhilm Method Part I post, but if you are new to vedic maths, then please read the following lessons, before reading this lesson, so that you can cope with the posts. Happy Reading :)

• Technique to calculate Complements (This technique is heart for almost all multiplication techniques. So please read it carefully)
• Multiplication Shortcut Technique - Lesson 1
• Multiplication Shortcut Technique - Lesson 2
• Multiplication Shortcut Technique - Lesson 3
• Multiplication Shortcut Technique - Lesson 4
• Multiplication Trick for some specific cases 
• Multiplication Shortcut Techniques - Nikhilam Method (Part I) 

So far (till our last lesson), all the numbers that were selected for multiplications are less than the base value. In today's lesson we shall see the technique for multiplying the numbers which are higher than the base. 

Multiplication of the Numbers which are higher than the base 

Example 6 : 106 x 106  = ?

Details :

1. Both the given numbers are nearer to 100. Hence 100 can be taken as the base.

2. The first number given is 106. The difference of this number and the base is +6. Similarly the difference of the second number and the base is +6. Multiply these two differences. Put the product in the two RHS blanks of the result. 

Present Status :

3. Add the differences to the given numbers. 106 + 06 = 112

Put this value in the LHS blanks of the result. 

Present Status :

Multiplication of the numbers with one number higher than the base, and the other number Smaller than the base. 

Example 7 : 107 x 94 = ?

1. Both the given numbers are near to 100. Hence 100 can be taken as the base. 

2. The first number given is 107. The difference of this number and the base is +7 (107 - 100). Similarly the difference of the second number and the base is -6 (94 - 100).

3. Multiply the differences (+07) and (+06). The product is -42. 

4. Add the differences to the given numbers. 

107 + (-06) = 101

or

94 + (+07) = 101

Present Status :

100 - 42  = 58

6. Present status :

=> 107 x 94 = 10058

Multiplications of numbers when the product of the differences is negative and also its magnitude is higher than the base. 

Example 8 : 112 x 88 = ?

1. Both the given numbers are nearer to 100. Hence 100 can be taken as the base. 

2. Put the numbers as follows. 

Present Status :

 => 112 x 88 = 9856

Example 9 : 1005 x 987  = ?

1. Both the given numbers are nearer to 1000. Hence 1000 can be taken as the base. 

2. Put the numbers as follows

=> 1005 x 987 = 991935

In my next lesson, I am going to teach you the technique to multiple the numbers which are away from the base.

Read more Vedic Maths Shortcuts from here

About The Author                                             

Rupali Shete (M.Sc., M.Phil., Ph.D) is a gold medalist from Osmania University (Hyderabad), one of the working members of Rananujan Mathematics Academy and Institute of Scientific Research on Vedas (ISERVE), Currently working in University of Pune.

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Vedic Maths Multiplication Shortcut Techniques : Nikhilam Method Part 1

Friends, today we shall discuss a shortcut method for Multiplications. This method is called Nikhilam. Nikhilam means Complement (please read the process of finding complements from here if you are new to this). This sutra can be used for multiplications in some special cases. If the numbers to be multiplied are nearer to 10, or 100 or 1000 etc., the result can be obtained very easily.

Important Note : Having a quick glance of this post wont help you much. Take a pen and paper and practice the following procedure so that you can understand the procedure well.  

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Vedic Math Shortcut Techniques - Subtractions

Friends, yesterday we've discussed the Dot method for Additions. Today we shall learn the Dot method for Subtractions. The method that is being taught presently is suitable for subtracting small numbers from big numbers. In this method, when a big number has to be subtracted from a small number, we borrow ( a value 10) from the adjacent digit on the left hand side (LHS). The borrowed number is added to the small number and the big number is subtracted.

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Vedic Maths Short Cut Techniques - Additions

Hi friends, For the sake of new readers, today I am starting with the basic Dot Method,  a Simple technique for Additions. If you already know this method, then you can chek my previous posts on Vedic Math from here in which I have shared some techniques for Addition, Subtraction & Multiplication.

The Dot Method for Addition

The process of adding the values of two numbers is called addition. This is also called as Samkalana in Sanskrit. This is the easiest one among all the arithmetic operations.

Normally people find it difficulty when more than two numbers are to be added. For this purpose the Dot method is used.

Example 1 :879 + 466 + 587 = ?

Step 1 :

879

466

587

__________

__________

In the above numbers, if we look at in units place, from the bottom, we find the digits 7, 6, 9. If we start adding in that sequence, first we have to add 6 to 7. Then we get 7+6 = 13.

This 13 can be visualized as 10+3. To indicate the number 10, we put a dot on 6. Temporarily we can forget about 10. Then we take 3 and add to 9. We get 3+9 = 12.

This can be visualised as 10+2. To indicate this 10, we put a dot on 9. The remaining digit 2 is written in units place in the answer.

Present Status :

Step 2 : Now we have to add the digits 8, 6, 7 of the 10's place. Before this, we have to count the number of dots put in the units place earlier. In the given problem the dots were written on the digits 6 and 9. Thus there are only two dots. This has to be added to the digit 8.

We get 2+8 = 10. To indicate this 10, we put a dot on 8.

We proceed further with the remaining '0' of the 10 obtained above.

0+6 = 6

The value 6 thus obtained is less than 10. Hence, there is no need for a dot on 6. We can proceed further with this 6 itself.

6+7 = 13

To indicate the 10 in the number 13, we put a dot on 7. Then 3 remains which has to be posted in the 10's place of the result.

Present Status :

Step 3 :

Following the same procedure, we count the number of dots (=2) in the 10's place and add to 5, 4 and 8 of the 100's place.

2+5=7, 5               No dot is needed on 5.

7+4 = 11; 4           Put a dot on 4.

1+8=9; 8               No dot is needed on 8.

The 9 obtained in the last step has to be written in the 100's place.

Present Status :

Step 4 :

There are no digits in the 1000's place. But, there is one dot in the 100's place. Hence, the number 1 has to be written in the 1000's place.

Present Status :

Thus, this dot method is highly useful when we get 10 or more than 10, while adding several numbers. Let's have a look at a few more examples.

Examples :

That's all for now friends. We shall learn another vedic math shortcut tomorrow. Happy Reading.

Note : If you have any doubts in above method, you can use the comments box below to ask. I will try to answer. Or else, you can read another version of this method from here for clarification. 

Read more Vedic Maths Shortcuts from here

About The Author                                             

Rupali Shete (M.Sc., M.Phil., Ph.D) is a gold medalist from Osmania University (Hyderabad), one of the working members of Rananujan Mathematics Academy and Institute of Scientific Research on Vedas (ISERVE), Currently working in University of Pune.

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Vedic Maths - Calculating Complements

Many of our friends are asking us to post detailed notes about finding Complements. This post is for them, who don't have the basic idea bout Complements. Happy Reading :).

What is Complement of a number ?

The Complement of a number is the difference between that number and the next higher power of 10. 3 is the complement of 7 (as next higher power of 7 is 10). 34 is the complement of 66 (as next higher power of 66 is 100). Still confused ? Let it be more simple.

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Vedic Maths Multiplication Shortcut Techniques - Lesson 3

Friends, we have already discussed a few multiplication shortcut techniques. Today we shall discuss another shortcut technique called "Antyayordasakepi". This means "When the sum of the digits in units place is 10". Now lets have a detailed look of this method.

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Vedic Mathematics Shortcuts for Multiplication - Lesson 1

Friends, we have already discussed some Special Cases of Vedic math Multiplication in our last post. Today we shall discuss a simple method to perform multiplications. This method is called "Nikhilam Method". In this method the process of multiplication is carried out with the aid of basic Vedic formulae such as "Nikhilam navatascaramam Dasatah".

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Vedic Maths Shortcut Technique for Subtraction

Friends, in yesterday's post we have discussed about the vedic maths shortcut for addition. Today we shall discuss about the subtraction shortcut technique. Finding the difference of two numbers is known as Subtraction. We call it as Vyavakalana in Sanskrit. Subtraciton is the second easiest operation in Mathematics. However, students as well as elders may get confusion while doing subtraction, especially while subtracting bigger digits from smaller ones. Actually, while subtracting smaller number from a bigger number our present traditional method holds good. But, when it happens to subtract a bigger digit from a smaller digit we have to borrow 10 from the preceding digit, add it to the smaller digit and then we have to subtract the bigger digit. As an alternate, there is a method in our 'Vedic Mathematics' known as "Bindvankana Method", which is very much useful, easier, practicable and advisable in the operation of subtractions. It is also called as "Dot Method". In this method the operation addition, used in a different way gives the result of subtraction. It is clearly explained in the following example.

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