LEVEL I

1. The product of 11 and any 2-digit number begins and ends with the two digits of the multiplier; the number in the middle is the sum of the original two digits.

Example: 34 x 11 ----> 3+4=7 ; answer:   374.
                 
                   53 x 11 ---> 5+3 = 8; answer: 583

                   27 x 11 ----> 2+7 = 9; answer: 297


For a multiplier whose digits sum to a number greater than 9, you have to carry.

Example: 57 x 11----> 5+7=12;carry the 1 from 12 to the 5 ;answer: 627.

                  29 x 11 ----> 2+9 =11;
carry the 1 from 11 to the 2 ;answer:319


2. The product of 11and any 3-digit number also begins and ends with  the first and last digits of the multiplier, although the first digit can change from carries. In the middle,insert the result of adding the first and second digits and the second and third digits.
 
 
Example: 425x11--->4+2=6 and 2+5 =7; answer :4675.

                   675 x 11 ---> 7+5 = 12; carry 1 from 12 to sum of 6+7=13 (it will become 14); carry 1 from 14 to 6; answer 7425
 


3. To multiply two numbers that are both between 10 and 20,add the first number and the last digit of the second number,multiply the result by10, then add that result to the product of the last digits in both numbers of the original problem.

Example:13 x 15--->13+5 =18,18×10=180,3 x 5=15,180+15=195;
                 answer:13 x 15 =195


4. When an addition sum has a carry, like 77 + 18 you can add them in your head, like this:   In  77 + 18 you get 8 tens or 80.            
                                                                                                                                   7 7
Then in the units you have 7 + 8=15. And 80 + 15 = 95.                            +  1 8
So 77 + 18 = 95.                                                                                                    81 5

You could also write this as 77 + 18 =815=95, writing the15 as 15 to show that the 1 in the 15 has to be carried to the left.

Example: 58 + 24 = 712=82
                 37 +63 = 910=100

                

5.
To  square  a  2-digit  number  that  ends  in  5,  multiply  the  first digit  in the number  by the next higher  digit, then attach  25 at the end.
      Example: 452 --> 4 x 5=20; answer: 2025.
 
      For3-digit numbers,  multiply  the  first  two  numbers  together  by  the  next higher number, then attach 25.
      Example: 4152-->41 x 42=1722;  answer: 172,225.



6.  When  an  addition  sum  has  a  carry,  like  46  +  37  you  can  add  them  in  your  head,  like  this:

In  46  +  37  you  get  7  tens  or  70.                                                                      4    6

Then  in  the  units  you  have 7  +  6  =  13.  And  70  +  13  =  83.                +    3    7

So  46  +  37  =  83.                                                                                                   7 1   3

You  could  also  write  this  as  46  +  37  =  7 1 3  =  83,  writing  the  13  as   13  to  show  that  the
1  in  the  13  has  to  be  carried  to  the  left.



7.   You  should  know  the  five  pairs  of  numbers  that  add  up  to  10:
 
1  +  9  =  10,                  2  +  8  =  10,                   3  +  7  =  10,                  4  +  6  =  10,            5  +  5  =  10.



8. In Vedic  Matematics  by  the  Deficiency  relates  to  the  natural  ability  to  see  how  much  something  differs  from  wholeness:

     26  is  close  to  30  and  is  short  of  30,  and  that  48  is  close  to  50  and  is  short  of  50.




9. To  multiply  two  2-digit  numbers  that  have  the  same  first    digit  and  last  digits  that  sum  to  10,  multiply  the  first  digit  by  the  next  higher  digit,  then  attach  the  product  of  the  last  digits  in  the  original  two  numbers. 

Example:  i. 73  ×  77  -->    7  ×  8  =  56  and  3  ×  7  =  21;  answer:  5621.

                ii. 56 x 54 --> 5 x 6 = 30 and 6 x 4 = 24; answer: 3024
                
                iii. 32 x 38 --> 3 x 4 = 12 and 2 x 8 = 16; answer: 1216

10.
To  multiply  a  number  between  10  and  20  by  a  single digit  number,  multiply  the  single digit  number  by  10,  then  multiply  it  by  the  second  digit  in  the  double digit  number,  and  add  the  products.  Example:  17  ×  8  -->  (8  ×  10)  +  (7  ×  8)  =  80  +  56;  answer:  136.


11. 
To  multiply  two  numbers  that  are  both  between  10  and  20,  add  the first  number  and  the  last  digit  of  the  second  number. Then  multiply  the  result  by  10,    then  add  that  result  to  the  product  of  thelast  digits  in  both  numbers  of  the  original  problem. 

Example:  12  ×  13 -->  12 + 3 =  15,  15  ×  10  =  150,  2  ×3  =  6,  150  +  6  =  156;  answer:  156

 
                        12  ×  15 -->  12 + 5 =  17,  17  ×  10  =  170,  2  × 5  = 10,  170  +  10  =  180;  answer:  180

                  13  ×  15 -->  13 + 5 =  18,  18  ×  10  =  180,  3  ×5  = 15,  180  + 15  =  195;  answer:  195                
 



12.    One can complete multiples of ten for sum of bigger numbers:

For  example  given  17  +  6  +  3  one  can  see  that  17  +  3  makes  a  whole  20  soone can  add  these  first  and  then  6.
 
So  sum of 17  +  6  +  3  =  26.
 
Let’s assume you  want to get the sum of   74  +  25  +   36  +8. You  will find that the  74   and  36  make  a  multiple  of  ten,  so  you  add  these  first  to  get110.  Then  adding  25  gives  135,  and  then  8  makesit 143.
 
So sum of 74  +  25  +   36  + 8 = 143

13.
To multiply 22 with any number between 20 and 29, multiply the number by 2 and then add 4 to the product and at the end write product of unit digit of the number and 2. If the product of unit digit of the number and 2 if more than 9, then add the carry to sum of product of number and  2, and 4.
 
Example :
 
i)                  24 x 22 à24 x 2 + 4 = 48 + 4= 52; 4 x 2 = 8;
Answer : 528
ii)               26 x 22 à26 x 2 + 4 = 52 + 4 = 56; 6 x 2 = 12;
Carry 1 to add to 56 ie. 56 + 1= 57;
                  2 6
                  2 2
                ------
(26 x 2) + 4; 6 x 2 = 12
  5 6  1 2 = 572
Answer : 572        
     
 
 
To multiply 22 with any number between 30 and 39, multiply the number by 2 and then add 6 ( 3 x 2) to the product and at the end write product of unit digit of the number and 2. If the product of unit digit of the number and 2 if more than 9, then add the carry to sum of product of number and  2, and 6.
 
Example :
 
i)                  30 x 22 -->30 x 2 + 6= 60 + 6= 66; 0 x 2 = 0;
Answer : 660
ii)               35 x 22-->35 x 2 + 6 = 70 + 6 = 76; 5 x 2 = 10;
Carry 1 to add to 76 ie. 76 + 1= 77; number is 770
 
                  3 5
                  2 2
                ------
(35 x 2) + 6; 5 x 2 = 10
  76  1 0 = 770
Answer : 770