"ASWAMEDHAM" GS PRADEEP vs VS NEBU Rounds 4

"Ratna Kanchuka Dharini " SANDHRA KOLLAM

MATHS TRICK #7

Maths Trick # 7 plays the multiplication of a number which is greater than 100 .

Example #1

                   625 X 11

Step 1 : Prefix a zero before the number given here... Then the  new number is    0 6 2 5

Step 2 : The unit digit of the number  should  be placed at the unit place of the product without any hesitation.
        
              0 6 2 5       X       11
           
                       5
Step 3 : Add up the unit and tens and the sum is placed at tens place


             0 6 2 5         X       11

                    75
 Step 4 : Add up the numbers  in the places tens and hundreds

              0 6 2 5       X         11

                 8 7 5
Step 5 :  Add up the places Hundreds and the already given zero

               0 6 2 5       X        11
                  
               6 8 7 5
               =====

Example # 2

                         5 4 2 1  X  1 1

Step 1 :            0 5 4 2 1
Step 2 :                        1
Step 3 :                     3 1       (2+1   = 3)
step 4  :                  6 3 1       (4+2   = 6)
Step 5 :               9 6 3 1       (5+4   = 9)        
Step 6 :            5 9 6 3 1       (0 + 5 = 5)

5421  X  11  =  59631
                         =====

Example #3

                  695 X 11

Step 1 :          0 6 9 5
Step 2 :                   5
Step 3 :                4 5  (9 + 5 = 14,   put 4  in the 10th place and the remainder 1 is added   to 100th place. Then the 100th place is 7 instead of 6)
Step 4 :             6  4 5    (7 + 9 = 16 . Put 6 in the 100th place and add the remainder 1 to 1000th place)
Step 5 :          7 6  4 5     (1 + 6 = 7)

695 X 11 = 7645

Example # 4

                      65321 X 11

                                             0   6   5   3    2  1
                                             7   1   8   5    3  1

Exercise
1. 5689 X 11       2.  7259 X 11

MATHS TRICK # 6

Maths Trick  # 6 plays the multiplication of a 2 digit number by 11

Example #1 : 
                      72 X 11
Step 1 : Separate the digits     --    7--2
Step 2 : Add up the digits       --   7 + 2 = 9
Step 3 :  Insert the sum between the separated digits .
             Then the product of 72 and 11 is   7 9 2 

Example # 2
                     95 X 11
Step 1 :   9--5
Step 2 :   9 + 5 = 14
Step 3 :   Here the sum of the digits  is greater than 9 . So the unit digit of the sum is inserted into the gap and Tens is added to the Tens place of the number.
                Then the result is  1045

 Maths can be fun

Example # 3

                      45 X 11

                     = 495
                       
Example # 4      
                        76 X 11
                                      = 836

Exercise : 

                1.  29X 11    2. 39 X 11     3. 62 X 11  (Calculation must be in the head)



 

MATHS TRICK 5

MATH TRICK 5 says the short cut  of multiplication between 11 and 20  but one of the numbers is  a decimal.

Example 1 

11.5 x 12
(The short cut of 11 x 12 has been studied in Maths Trick 1)
Here the base number is  10
Step 1.   11.5 + 2    = 13.5  (OR 12 + 1.5 = 13.5      1.5 and 2 are unit digits)
Step 2    13.5 x 10   = 135 ( 10 is the base number)
Step 3     1.5 x 2      =     3    (This is also explained in Maths Trick 1)
Step 4      135 + 3    = 138
                                  == ===
Yes . That is the answer.

Example 2.

12.5 x 13
12.5  + 3   = 15.5
15.5 x 10  = 155
2.5 x 3      =  7.5
Add up : 155 + 7.5  = 162.5
Yes . That is the answer.

Example 3.

15.4  x  11
15.4 + 1 = 16.4 x 10 = 164 +1 x 5.4 = 169.4
                                                            =====

Example 4

17.2 x 12
Calculation should be in the head.
17.2 + 2 =19.2         192 + 2 x 7.2 = 206.4

Exercise

1.      16.5 x 11

2.      19. 5 x 13

3.      18 x 13.5

4.      14 x 14.4

5.      15 x12.5

MATHS TRICK 4

 Maths Trick 1 says how to multiply up to 20 x 20 in our head.
Here we can play more .
MATHS TRICK 4 says how to multiply up to 30 x 30

Example 1.         21 x 22 

(Here we take 20 as the base number as 10 in  Maths  Trick 1)

Base number - 20
21  =  20  + 1
22  =  20  + 2

Step 1 :  21      +1
              22      +2
( +1 is the difference between 21 and 20 and  +2 is the difference between 22 and 20)

Step 2  :   21 + 2    =  23   OR  22 + 1 = 23  (CROSS SUM)

Step 3. :   23 x 20   = 460  (20 is the base number)

Step 4  :   1  x  2     =    2  

Step 5  : (Add 460 and 2)    460 +2  = 462  

Yes . That is the answer.

We can forget all these steps after getting it .

Example 2. 
                      23  x  24

Step 1 :     23  +  4   =  27
Step 2 :     27 x 20   =  540  ( short cut:  27 x 2 = 54, 27 x 20 = 540)
Step 3 :     3 x 4       =    12
Step 4 :    540 +12   = 552
                                   ===
Example 3
                    28 x 29

28 + 9   =    37
37 x 20 =    740       (37x2 =74 , 37 x 20 = 740)
8 x 9     =      72
740  +  72 =  812

Yes. That is the answer.

Example 4.
                   26 x 29

The multiplication must only be in your head

26 + 9 = 35 x 20 = 700 + 54 = 754
                                                 ===
Exercise

1.      22 x 25

2.      23 x 27

3.      24 x 29

4.      28 x 21

5.      25 x 29 

MATHS TRICK 3

An easy way to square any number  ending with 5
The way of squaring can be done like this:

Example  1 
                       15 ²  = 15 x 15  =225
        short cut : 
Step 1.  Separate the 5 from the  number to be squared        1    5   
Step 2. The remaining portion of the number is multiplied by the immediate higher number  1 x 2 =2
Step 3.  Suffix 25 to the result of   Step 2       =       225
 

Example 2.

                           25 ²            =  2     5
                                    2 x 3 =  6   25
                                             =  625

Example 3.                 35 ²   = 3 x 4 = 12 25
                                             = 1225
Example 4.                 85 ²   = 8 x9 = 72  25
                                             = 7225
Example 5          115 ²    = 11 x 12   ( Here we apply the Maths Trick 1)
                          11 + 2 = 13 0  +
                            1 x 2  =      2
                                         ------                            
                                          132

                         115 ² = 13225
                                                                        Maths can be fun ! 


 Example 6.      225 ²       = 22 x 23 (Short cut for this multiplication will be later)
                                         = 506
                         225 ²        = 506 25
                                         = 50625
                                            ====