Vedic Maths Shortcut Tecnique for Multiplication - some Specific Cases

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Friends, we have already discussed vedic maths shortcut techniques for addition and subtractions. Today we shall discuss vedic math shortcut techniques for Multiplication. According to the vedic mathematics, a student who knows simple addition and subtraction and the multiplication table up to five times of five (5x5=25) can improvise all the necessary multiplication tables at any point of time and can himself do all the requisite multiplications even with a large numbers.

There are basically two methods of multiplication. Those are

1. Nikhilam Method
2. Urdhva Tiryak Method

In addition of these, there are certain shortcuts in some special cases. In this post we shall discuss some special cases. From our next post we shall discuss nikhilam method.

Concept 1 :

Product of two numbers when the digits in the unit's place are 5's and the digits in the Ten's place are same,  in other words square of a number in which the digit in the unit's place is 5 :

Examples : 

1. Find 35 x 35

Solution :

Step 1 : Here, in this case first we should multiply 5 by 5

5x5 = 25

Step 2 : Observe that, 3's are there in Tense place. We should increase one of the 3's by 1  then we get 4, we should multiply 4 by 3 then we get 12. So, the required answer is 1225

2. Find 115x115 

Solution :

Step 1 : Here, in this case first we should multiply 5 by 5

5x5 = 25

Step 2 : Observe that, 11's are there in Tense place. We should increase one of the 11's by 1  then we get 12, we should multiply 11 by 12  

Note : Here we can get 11x12 easily, as we know 11² is 121 and then we should add 11 to 121 then we get 132

so 115 x 115 = 13225

Concept 2 :

a) Product of two numbers when the sum of the digits in the unit's place is 10 and the digits in the Ten's place and hundred's place are the same.

Example :

124 x 126 = 15624

Step 1 : First by multiplying the digits in the Unit's place we get  24

Step 2 :  We should write the product of 12 & 13  to the left of 24

124 x 126 = 15624

(we know that 12² is  144 and then we should add 12 to 144 to get 12x13 = 156)

'It may be noted that the product of any two numbers irrespective of the number of digits satisfying the above condition can be found in the same way'.

b) Product of two big numbers satisfying the above condition

Example : 353 x 357

Step 1 : First by multiplying the digits in the one's  place we get 21

Step 2 :  We should write the product of 35 & 36 to the left of 21

353x357 = 126021

Note : Here we can get 35 x 36 = 1260 as we know 35² is  1225 and then, we should add 35 to 1225  to get 35 x 36 = 1260

Important Points to Note :

1. There are basically two methods of multiplication, Nikhilam Method & Urdhva Tiryak Method. In addition to these there are certain shortcuts in some specific cases.
2. When we have to find the square of a number with 5 in the unit's place we have to multiply 5 by 5 to get the right part of the answer. The left part of the answer can be obtained by multiplying the other part of the number with the next number.
3. When we have to find the product of two numbers with sum of the digits in unit's place 10, and when the digits in the other places are same, we have to multiply the digits in the unit's place to get the right side of the answer. To obtain the left side of the answer we have to multiply the other part of the number with the next number. 

Now lets do some exercises  (answers will be posted in tomorrow's lesson)

1. 65x65
2. 85x85
3. 95x95
4. 75x75
5. 55x55
6. 125x125
7. 135x135
8. 145x145
9. 165x165
10. 105x105
11. 175x175
12. 155x155
13. 253x257
14. 354x356
15. 459x451
16. 652x658
17. 857x853
18. 959x951

Answers to yesterday's Subtraction Exercises

1. 0146
2. 0176
3. 0226
4. 0033
5. 0327
6. 3224
7. 3226
8. 0654
9. 4944
10. 4415

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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