Multiplication without Papers

Multiplication without paper

Multiplication can be made an interesting exercise by learning some tricks.Don’t you think that you should have knowledge of some super-duper trick which could have been saved your time and multiplication could have been done mentally without using pen and paper?

There are hundreds of such magical trick which help to do calculation mentally and without pen and paper. Do you know what is more interesting here that there are absolutely no chance of mistake?  Let me ask you a simple question first: -

 What is 100 times 456789?

I am really in a serious mood and not joking guys despite the fact that I know you can do this multiplication in fraction of second by just putting two zeros after 456789 and you will return back with your answer 4567890. The fact of the matter is that when you are asked to multiply a number by the multiple of 10, like 10, 100, 1000, 10000… you just put the number of zeros in front of the number to be multiplied by noticing how many numbers of zeros are in multiplier which is the multiple of 10’s. Likewise, the method discussed here will let you get the answer in seconds.

Hey guys, are you ready for the journey of multiplication fantasy? If your answer is a big YES, then here I begin.

1.      When the sum of unit digit is 10 and ten’s digit are same

Rule: - a) The answer will have two parts. Multiply the unit parts. The product should have exactly two digits. If you get the lesser digit put a zero before.

            b) Second Part = Ten’s digit x (Ten’s digit + 1)

Example: - 42 × 48 =?

Solution: - Here the sum of unit digit is 10 (2 + 8 = 10) and ten’s digit in both multiplicand and multiplier are same.

Unit Part = 2 × 8 = 16

Second Part = 4 × 5 = 20

Hence, 42 × 48 = 2016

Example: - 74 × 76 =?

Solution: - Sum of unit digit = 10 (4+ 6 = 10) and ten’s digit in both multiplicand and multiplier are same (7).

Unit Part = 4 × 6 = 24

Second Part = 7 × 8 = 56

Hence, 74 × 76 = 5624

Example: - 99 × 91 =?

Solution: - Sum of unit digit = 10 (9+ 1= 10) and ten’s digit in both multiplicand and multiplier are same (9).

Unit Part = 9 × 1 = 09 (In order to fulfill the condition of two digits in the product 0 is put before 9)

Second Part = 9 ×10 = 90

Hence, 99 × 91 = 9009

2.      Sum of ten’s digit is 10 and unit digit are same

Rule:-The answer will have two parts

a)      LHS = Product of ten’s digit + Unit digit

RHS = Product of Unit digits

Always remember there should be exactly two digits in the RHS. In case there is a single digit in RHS, put a zero before the product you get

Example: - 84 × 24 =?

Solution: - Sum of ten’s digit = 10 (8+2 = 10)           and Unit digit in multiplicand and multiplier are same (4)

LHS = Product of ten’s digit + Unit digit = 8×2 + 4 = 20                                                 
     RHS = Product of Unit digit = 4 × 4 = 16                                                                                         Hence, 84 × 24 = 2016   

Example: - 93 × 13 =?

Solution: - Sum of ten’s digit = 10 (9+1 = 10)           and 

Unit digit in multiplicand and multiplier are same (3)

LHS = Product of ten’s digit + Unit digit = 9 × 1 + 3 = 12                                               

RHS = Product of Unit digit = 3 × 3 = 09                                                                                                                

(one Zero is put due to less number of digit in the product)                                              

Hence, 93 × 13 = 1209                       

Example: - 75 × 35 =?

Solution: - Sum of ten’s digit = 10 (7+3 = 10)           and 

Unit digit in multiplicand and multiplier are same (5)

LHS = Product of ten’s digit + Unit digit = 7× 3 + 5 = 26                                                    

RHS = Product of Unit digit = 5 × 5 = 25                                                                                         

Hence, 75 × 35 = 2625                                                   

3.      When the difference between the digits to be multiplied is 1

When two consecutive numbers are to be multiplied, follow this technique for quicker multiplication.

a)      Square the smaller/ greater number.                                                                              

    b) Add / subtract the smaller/ larger number to the previous result

Example: - Multiply 23 by 24

Solution: - 

a) Square the smaller number = 23 x 23 = 529                                                                                  
 b) Add the smaller number to the previous result =529 + 23 = 552                                              Hence, 23 × 24 = 552

Example: - Multiply 75 by 76

Solution: - 

a) Square the smaller number = 75 x 75 = 5625                                                                                
  b) Add the smaller number to the previous result =5625 + 75 = 5700                                         Hence, 75 × 76 = 5700                                                    

                                                                   

4.      When the difference between the digits to be multiplied is 2

a)      Find the mean and square it. The mean of two numbers a and b = a + b / 2

b)      Subtract 1

Example: - Multiply 25 by 27

Solution: - a) Mean = 25 + 27 / 2 = 26. (Mean can be found by adding 1 to smaller or subtracting 1 from the larger number in this case.)

              b) Square the mean = 26 ² = 676

            c) Subtract 1 from the last result = 676 – 1 = 675

Hence, 25 x 27 = 675

Example: - Multiply 74 by76                                                                                                
Solution: - a) Mean = (74 + 76)/ 2 = 75. (Mean can be found by adding 1 to smaller or subtracting 1 from the larger number in this case.)

              b) Square the mean = 75 ² = 5625

            c) Subtract 1 from the last result = 5625 – 1 = 5624

Hence, 74 x 76 = 5624

5.  When the difference between the digits to be multiplied is 3

Rule: - 

a) Add 1 to the smaller number and square it                                                                                  

  b) Subtract 1 from the smaller number and add to the previous result                           

Example: - Multiply 28 by 31

Solution: - 

Here the smaller number is 28.                                                                                                    

  a) Add 1 to it = 28 + 1 = 29                                                                                                                   b) Square it = 29² = 841                                                                                                                   

  c) Subtract 1 from the smaller number and add to the previous result = 841 + 28 – 1 = 868 

Hence, 28 × 31 = 868

Example: - Multiply 24 by 27

Solution: -

 Here the smaller number is 24.                                                                                                     

 a) Add 1 to it = 24 + 1 = 25                                                                                                                   b) Square it = 25² = 625                                                                                                                    

 c) Subtract 1 from the smaller number and add to the previous result = 625 + 24 – 1 = 648 

Hence, 24 × 27 = 648

6.  When the difference between the two numbers to be multiplied is 4

Rule: 

a) Take the mean of numbers. If the numbers are a and b; where a >b then mean is either a – 2 or b + 2                                                                                                                                                              b) Take the square of mean number.                                                                                                         

 c) Subtract 4 from the result.       

Example: - Multiply 65 by 69?

Solution: Here the difference between the numbers to be multiplied is 4. Take its mean.                             

a) Mean = 65 + 2 = 67                                                                                                                            b) Square it = 67² = 4489                                                                                                                

   c) Subtract 4 from the previous result = 4489 – 4 = 4485                                                     

 Hence, 65 × 69 = 4485

Example: - Multiply 84 by 88?

Solution: Here the difference between the numbers to be multiplied is 4. Take its mean.                             

a) Mean = 84 + 2 = 86                                                                                                                            b) Square it = 86² = 7396                                                                                                               

 c) Subtract 4 from the previous result = 7396 – 4 = 7392                                                     

 Hence, 84 × 88 = 7392

7.  When the difference between the two numbers to be multiplied is 6

Rule: a) Take the mean of numbers.                                                                                                   

b) Take the square of mean number.                                                                                                          c) Subtract 9 from the result.       

Example: - Multiply 42 by 48?

Solution: Here the difference between the numbers to be multiplied is 6. Take its mean.                             

a) Mean = 42 +3 = 45                                                                                                                             b) Square it = 45² = 2025                                                                                                                 

  c) Subtract 9 from the previous result = 2025 – 9 = 2016                                                      

Hence, 42 × 48 = 2016

8.  When the difference between the two numbers to be multiplied is 8

Rule: a) Take the mean of numbers. If the numbers are a and b; where a >b then mean is either a – 4 orb+4                                                                                                                                                         

    

b) Take the square of mean number.                                                                                                          c) Subtract 16 from the result.       

Example: - Multiply 64 by 72?

Solution: Here the difference between the numbers to be multiplied is 8. Take its mean.                             

a) Mean = 64 + 4 = 68                                                                                                                            b) Square it = 68² = 4624                                                                                                                

   c) Subtract 16 from the previous result = 4624 – 16 = 4608                                                

    Hence, 64 × 72 = 4608

9.  When the difference between the two numbers to be multiplied is 10

Rule: a) Take the mean of numbers. If the numbers are a and b; where a >b then

 mean is either a – 5 or b + 5                                                                                                                                                    

b) Take the square of mean number.                                                                                                          c) Subtract 25 from the result.       

Example: - Multiply 84 by 94?

Solution: Here the difference between the numbers to be multiplied is 10. Take its mean.                           

a) Mean = 84 + 5 = 89                                                                                                                            b) Square it = 89² = 7921                                                                                                                

   c) Subtract 25 from the previous result = 7921 – 25 = 7896                                                 

   Hence, 84 × 94 = 7896

Courtesy :- From Maths made Easy - Rupa Publication by Rajesh Kumar Thakur

(Book available on different website  / e- books also available)

Rajesh Kumar Thakur

rkthakur1974@gmail.com