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Vedic Maths for Multiplication

Vedic Maths is a super-fast way of making all Mathematical calculations easy and gives accurate results. It is a domain of mathematical tricks written by an Indian monk, “Late Swami Sri Bharati Krishna Tirthaji'’

He has given us various tricks to solve any type of mathematical problem is hardly a few minutes.

These formulas are in the form of sutras, under each sutra we can see the mathematical operations hidden. Starting from addition, subtraction, multiplication, division, decimals, fractions, HCF/LCM, squares, cubes - its roots and along with Algebra, Trigonometry, Geometry, Calculus, etc,… When compared to our conventional method, the steps might be a little lengthier, but here the tricks can find solutions in a very simple way. That's the reason why most of the students are falling for the Vedic Maths Method.

Mostly under Arithmetic, Multiplication topics are more under Vedic Maths Sutras. You can check our Roadmap. I have explained all the Multiplication Topics under the Multiplication Mastery Course in detail.

Multiplication is nothing but when two numbers are multiplied, any one of them is the multiplicand and the other is a multiplier.

Students generally learn multiplication by the conventional method, i.e., We just have multiplicand and multiplier and need to multiply given numbers and write the final answer, but under the Vedic Method, for every type of number or question, we have a method to calculate.

Excited to know what they are???

Don't worry I will explain it in detail.

In the Multiplication Mastery Course, we have interesting tricks which make multiplication very easy.

Most of the students might have faced difficulty in solving bigger numbers right, here we have tricks to solve multiplication for nearly 5x5 digits too.

Now let’s see what are the topics under Multiplication:-

1- Multiplication with 9, 99, 999,….

2- Magic with 11

3- Multiplication by 12,13,14,....19

4- Multiplication of Numbers Near the Base

5- Multiplication by 5,25,50,250,....

6- Vertically and Crosswise Multiplication

7- Times Tables

8- Algebraic Multiplication etc,…

Let’s understand the topics with examples:-

1- Multiplication with 9, 99, 999,….

To multiply given numbers with 9999’s.., we have an interesting formula,

Step-1:- By one less than one before

Step-2:- All from nine and last from ten

Eg- 46 x 99:-

46 is a 2 digit number and 99 also has two 9’s in it.

For LHS, subtract 1 from 46, i.e., 46 - 1 = 45

For RHS, write the complement of 46, i.e., (100-46) = 54

So, the answer is 4554.

Multiplication with 9, 99, 999, | TheVedicMaths
Multiplication with 9, 99, 999

2- Magic with 11:-

This method is also very interesting, same as multiplication by 999’s, here also we just have a one-line formula. I.e., just write the given numbers on both sides as it is and add both the numbers and write in between, check the below example.

Eg- 62 x 11:-

Write 6 and 2 on the corners, and the sum of 6 and 2, (6+2=8) in between. Therefore, the answer is 682.

Magic with 11 | TheVedicMaths
Magic with 11 | TheVedicMaths

3- Multiplication by 12,13,14,....19:-

You need not memorize tables from 12...why because it can be found mentally using Vedic Tricks. Just learn tables from 2-9, the rest can be solved easily.

Eg-43 x 12:-

a- Dot sandwich method, put dot on both the sides of the given number = . 43 . (dot is considered as 0 )

b- Starting from the RHS dot, taking 2 digits at a time, multiply the given number by 2 and add previous numbers.

(2x3)+0 = 6

c- Considering next pair, i.e., 43 (4 is second last digit

and 3 is the last digit), we get: (2x4)+3 = 8+3 = 11, 1 carry over.

d- Next pair, i.e., .4 (dot is the second last and 4 is the last digit), we get: (2x0)+4 = 4

4+1 (carry) = 5

So, the answer is 43 x 12 = 516.

Similarly, we have tricks for 13...19, check out the Multiplication Mastery Course.

Multiplication by 12,13,14,....19 | TheVedicMaths
Multiplication by 12,13,14,....19 | TheVedicMaths

4- Multiplication of Numbers Near the Base:-

This comes under “Paravartya Yojayet Sutra”, here we have 3 cases under base method,

a- When the numbers are Above the Base

b- When the numbers are Below the Base

c- When the numbers are Mixed Base

You can check the 3rd chapter under Beginners guide, under Paravartya yojayet we have the above topics explained, and also under Multiplication Mastery, we have the above topics under chapter-6 in detail. The formula used here is “All from Nine and Last from Ten”.

Multiplication of Numbers Near the Base | TheVedicMaths
Multiplication of Numbers Near the Base | TheVedicMaths

5- Multiplication by 5,25,50,250,...:-

A unique advantage of Vedic maths is that many calculations can be done by mere observation only.

a:- Multiplying any number by 5

Since, 5 = 10/2, so it means, first multiply the number by 10 and then half it.

Eg- 24 x 5

24x5 = 240 / 2 = 120.

b:- Multiplying any number by 50

Since, 50=100/2, so when multiplied the number by 50, add two 0’s to its right and a half it.

Eg- 42 x 50

42 x 50 = 4200 / 2 = 2100.

Multiplication by 5,25,50,250 | TheVedicMaths
Multiplication by 5,25,50,250 | TheVedicMaths

c:- Multiplying any number by 25

Since, 25=100/4, so when multiplying the number by 25, add two 0’s to its right and a half it twice.

Eg- 64 x 25

64 x 25 = 6400 / 2x2 = 1600.

Similarly, we have formulas for 250, 500, etc.

Multiplication by 5,25,50,250 | TheVedicMaths
Multiplication by 5,25,50,250 | TheVedicMaths

6- Vertically and Crosswise Multiplication:-

This is the general way of multiplying any two given numbers. The formula used is “Vertically and Crosswise”, this comes under Sutra “Urdhva-Tiryagbhyam”.

Here we have formulas for multiplication up to 5 x 5 digits.

Eg- Find 47 x 28? ( | X | )

Step-1:- Multiply vertically in the right-hand column

7x8=56 (5 is carried over)

Step-2:- Multiply crosswise and add the results for ten’s place. (4x8)+(7x2) = 46

46 + 5(carry) = 51 (5 is carried over)

Step-3:- Multiply vertically in the left hand column and add carry over. 4x2=8

8+5 (carry) = 13.

So, the answer is 1316.

Vertically and Crosswise Multiplication | TheVedicMaths
Vertically and Crosswise Multiplication | TheVedicMaths

7- Times Tables upto 19:-

Firstly, we need to know Tables from 2-9, then it's easy to calculate tables up to 99 too.

Eg-1:- 3 x 6 = 18 13 x 6 = 78 (6+1=7, take 8 from 18 as it is)

Eg-2:- 4 x 8 = 32 14 x 8 = 112 (8+3=11, take 2 from 32 as it is)

Eg-3:- 9 x 6 = 54 19 x 6 = 114 (6+5=11, take 4 as it is)

To get the answer, you need to add just the factor (of the corresponding table) to the ten’s place digit of the corresponding product. The one’s digit remains as it is. Please check the Multiplication Mastery Course for Tables upto 99.

Times Tables upto 19 | TheVedicMaths
Times Tables upto 19 | TheVedicMaths

8- Algebraic Multiplication:-

This chapter explains to us the Algebraic Expression, like binomials and trinomials in just one line, as compared to conventional maths where we usually do it in 4-5 steps.

The Formula used is “Vertically and Crosswise”, this is the same as Multiplication by vertically and crosswise method i.e., “Urdhva-Tiryagbhyam Sutra”.

The only difference is there we learned under Arithmetic Computation, here it is in Algebraic Expression.

Eg- (x+2) (3x+4)

We use the same Vertically and Crosswise formula, ( | X | )

Step-1:- Write one binomial under the other as shown.

Multiply vertically the digits in the right-hand column,

2 * 4 = 8

Step-2:- Multiply crosswise and add the products,

(4 * x) + (2 * 3x) = 4x+6x = 10x.

Step-3:- Multiply vertically in the left hand column,

x * 3x = 3x²

So, the answer for (x+2) (3x+4) = 3x² + 10x + 8

Algebraic Multiplication | TheVedicMaths
Algebraic Multiplication | TheVedicMaths

By now you would have had an idea of how Vedic Maths is used under Multiplication. So similarly we have few other courses which explain each topic in detail. Once you get into the courses you will have a clear picture and as it has lifetime access along with the Vedic Maths community for clearing doubts, you can excel in maths and throw away your maths phobia.

Good Luck!


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