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Thursday, 29 May 2014

Vedic maths : Lesson 6 : Multiplying Close Numbers

                                                           Multiplying Close Numbers

Here we learn how to calculate close numbers multiplication


Multiply 88 by 98.

     For this type of multiplications, Let us consider 100 as our main weapon ..
          
     Both 88 and 98 are close to 100.
     88 is 12 below 100 and 98 is 2 below 100.


                   98 - 12 = 86: you can subtract either way, you will always get the same answer.
        And the 24 in the answer is
                                             just 12 x 2: you multiply vertically.
                                                        So 88 x 98 = 8624



93 x96 =??

      9 3      7
           X
      9 6      4

------------------
       8928

89 28 our required answer is 8928 .Here our base is 100.



                            Why can we take only 100 as center, why not other numbers??

We can !! , but we have to take the closest number. consider following Example

                    Now we consider some other base
Example  54 x 48

Here 50 is closest number,

54 / +4----------- because, 50 +4
48 / -2------------because , 50-2

52 / -8----------- because, either 54-2  or  48+4 => 52, +4 X -2 = -8
x50    ------------because base is 50
                                                          Here our base is 50
2600 /-8               2600-8 =2592                Therefore the answer is 2592

Ex:- 53 X 57 

   Here 60 is the closest number for both 53 & 57

   Then Base is 50

   So, multiply 60 & 50

Now,  53 & 57 are 7&3 less to 60 respectively                    
                             
So,  7X3 = 21
      
3000 / +21              Therefore, the answer is 3021.





Again see one more example
48 /-2
45 /-5

43 /+10
x 50 Base is 50
2150 +10 = 2160

Sunday, 6 October 2013

Vedic Maths : Lesson 5 (Multiply Easily) :: MULTIPLICATION OF 9

MULTIPLICATION OF 9

Step1
 Prefix 0 before multiplicand

Step2 Take last digit, subtract it from 10 and write it at the extreme right

Step3 Take second last digit add one and subtract it from last digit write before step 1 figure

Step4 Now move toward left take third last digit and subtract it from right neighbor
          write before step 2 figure and repeat it up to first digit i.e 0

                                                            

                                                             123456 x9 = ??

0123456x9 =

Here subtract 6 from 10 ( 10-6=4 ) write 4 at the extreme right ...............................................4
Take 5 add 1 (5+1 =6) and subtract it to last digit 6 and write before ..4,6-6=0 .....................04
Take 4 subtract it from 5 and write before ....04 5-4 =1 . ......................................................104
Subtract 3 from 4 and write before ...104 4-3 =1 ................................................................1104
Subtract 2 from 3 and write before ..1104 3-2 =1 .............................................................11104
Subtract 1 from 2 and write before..11104 2-1 =1...........................................................111104
Subtract 0 from 1 and write before.111104 1-0 =1 1111104

                                          1111104 is our required answer






                                                              365 x9= ??

0365x9=
10-5 =5 ............5
6+1=7 subtract 7 from 5 , take carry from 6 now 5 become 15 ( 15- 7 =8 ) .......85
Now 6 become 5(adjust carry) subtract 3 from it 5-3 =2 ........285
3-0 =3 3285
3285 is our required answer

I think all of you understand this concept . It is a very useful tool ,with the help of this tool


now we learn multiplication of 36 ,.45 ,54. 63 . 72 ,81 and other multiple of 9

212x36  =  ( 4x9)x212  = 9x(848)      = 7632
212x45  =  (90/2)x212  = 9x(2120/2) =  9x1060  = 9540
43x54    =  (9x6)x43     = 9x(43x6)    = 9x 258    =2322
63x58    =  (9x7)x58     = 9x( 7x58)   = 9x 406   = 3654
72x23    =  (8x9)x23     = 9x(8x23)    = 9x184    = 1656
81 x59   =  (10-1)9 x59 = (590-59)x9 = 531x9    = 4779




Practice Test

2589 x9=           5897 x36 =            569x9=
256x45 =           987x63 =               177 x9=
458x54 =           458x9=                  2597x72=

Saturday, 28 September 2013

Vedic Maths : Lesson 4 (Multiply Easily)

Lesson 4

                                         MULTIPLICATION OF 12 TO 19


MULTIPLICATION BY 12:
The method is exactly the same as in the case of 11 except that you double each number before adding the right neighbor.

Step1     Prefix 0 before multiplicand 

Step2     Multiply last digit by 2 and write it at extreme right take carry if there is

Step3     Double and add the right neighbor with carry in step first repeat this up to the first
               digit i.e till 0

 
1234 x12= 01234x12 =

Here     2 multiply by 4 write 8 at extreme right .                                        ...... 8
Double 3 and add to 4 and write before                                                           ...8
6+4=10 here we write 0 before 8 and take 1 carry                                       .....08
Double 2 and add to 3 and add carry1 and write before 08 ,4 +3 +1 =8    .....808
Double 1 and add to 2 and write before ...808, 2+ 2 =4                            ....4808
Double 0 and add to 1 and write before .4808       0+1=1                           14808

                     14808 is our required answer


MULTIPLICATION FROM 13 TO 19:
The method is exactly the same as in the case of 12 except that you treble each degit before add in the
right neighbor, in the case of multiplication of 13 .We would quadruple (i.e. multiply by 4) and then add the right neighbor, in the case of multiplication of 14 .In case of 19 we would multiply by 9 and then add the right neighbor.

39942 X 13 = ?

 039942x13=
                                2x3 =6 ........................ 6
                                4x3+2 =14 .................46
                                9x3+4+1 =32 ...........246
                                9x3+9+3=39 ..........9246
                                3x3+9+3=21 ........19246
                                0x3+3+2=5........ 519246

                      519246 is our required answer.


34x17 =?             034x17

                               4x7 =28 ...............8
                               3x7+4+2 =27 .....78
                               0x7 +3+2=5..... 578
                    
                          578 is our required answer.

Now try these examples

1) 39942 X 13 = ?           039942 X 13           519246  
2) 43285 X 14 = ?           043285 X 14           605990
3) 58265 X 15 = ?           058265 X 15           873975       
4) 36987 X 16 = ?           036987 X 16           591792
5) 69873 X 17 = ?           069873 X 17           1187841    
6) 96325 X 18 = ?           096325 X 18           1733850
7) 74125 X 19 = ?           074125 X 19

 
 Practice Test

24678 x 13=              246x13x 15=                89x19 x18=
98745 x14=               987 x19 =                     266x16=
98745 x17=               8745x 12 =                   3435 x12=

Check your answer with the help of calculator

Wednesday, 25 September 2013

Vedic Maths : Lesson 3 (Multiply Easily)

Lesson3

Multiplication by 5
It's often more convenient instead of multiplying by 5 to multiply first by 10 and then divide by 2. For example, 237x5=2370/2=1185
Same way you can also multiply by 50

Multiplication by 4
Replace either with a repeated operation by 2.For example 124x4=248·2=4

Multiplication by 25
Multiply first by 100 and then divide by 4 For example37x25=3700/4=1850/2=925.

Multiplication by 8
Replace either with a repeated operation by 2. For example 124x8=248x4=496x2=992.

Multiplication by 45
Multiply first by 90and then divide by 2.For example37x45=37x90/2=3330/2=1665
Or see this method also 37 x45 = 37 (100/2 -10/2)= 3700/2-370/2=1850-185=1665

Multiplication by 55
Multiply first by 110and then divide by 2. For example37x55=37x110/2=4070/2=2035

Multiplication by 75
Multiply first by 300 and then divide by 4 .For example37x75=37x300/4=11100/4=2775

Multiplication by 125
Multiply first by 500 and then divide by 4 For example37x125=37x500/4=18500/4=4625

Multiplication by 150
Multiply first by 300 and then divide by 2 For example37x150=37x300/4=11100/2=5550

Multiplication by 175
Multiply first by 700 and then divide by 4 For example37x175=37x700/4=25900/4=6475

Multiplication by 225
Multiply first by 900 and then divide by 4 For example37x225=37x900/4=33300/4=8325

Multiplication by 275
Multiply first by 1100 and then divide by 4


For example37x275=37x1100/4=40700/4=10175
A Great Time Saver



Q A music shop has a sound system marked at Rs. 14000 on which a sales tax of 12.5% is chargeable. Find the total value a customer

would have to pay for the sound system.
sales tax = 14000x12.5 = 14000x125 = 14x 500 = 7000 =1750
100 1000 4 4
Rs 14000+1750 =Rs15750 Answer

Monday, 23 September 2013

Vedic Maths : Lesson 2 (Multiply Easily)

Lesson2
                                  Multiplying a number by 11

 To multiply any number by 11 we just put
the total of the two figures between the 2 figures.
32X11
Here first we write 2 of 32 extreme right ,now add up 3+2 =5 ,put 5 before 2 and write 3 extreme left .                                                   Required answer is 352
                                                                          

                                                                     322x11
Write extreme right 2 of 322 and add up 2&2 of 322 , 2+2=4 ,write 4 before 2 Now our partial answer is ...........42 .Again add up 3&2 of 322 .3+2 =5 write before ..42 .Now our partial answer becomes ..542 .Put 3 before 5 .                                                 
                                             Now our required answer is 3542

                                                                                                  


77 x 11 = 847
This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7147 = 847


Multiplication of 22 ,33 ,44 ,55, 66 , 77 ,88
I think all of you understand this concept . It is a very useful tool ,with the help of this tool
now we learn multiplication of 22 ,33 .44 ,55. 66 . 77 ,88
22x45 =( 2x11)x45 = 11x(2x45)=11x90= 990
33x66 = (3x11)x66 = 11x(3x66)= 11x198= 2178
44x356=(4x11)x356= 11x(4x356)=11x 14 24=1 5664
55x58 =(5x11)x28 = 11x( 5x28) = 11x 140 = 1540
66x23 =(6x11)x23 = 11x(6x23) = 11x138 = 1518
Same way 77 =7x11 and 88=8x11
Multiplication of 11 is great time saver How ???
You can do calculations in Mensuration very fast by this tool
As you know value of p is 22/7 .You can break it as 2x11/7
Ex Find the area of circle of radius of 14 cm
(22/7)x14x14=11x2x2x14=11x56=616square cm
All calculation mentally, no rough work , a great time saver.

Practice Test 2
Solve mentally these questions
Note down calculation time by your watch
(Suggested time 180 seconds)
11 X 356         11 X 9587          587 X 22
33 X 52           44 X 897            758 X 88
121 X789*         11 X 9874                 487 x99
Find the volume of a sphere of radius of 10.5 cm*
*Hints 121 X 789 = 11 X11 X789 = 11 X 8679=95469
 
volume of sphere = 4pr3
3
=4 x 10.5 x10.5x10.5 x22
3 7
= 4 x0.5 x 10.5x 10.5 x 22
= 2x2 x0.5 x 10.5x10.5 x22
= (2x 10.5)(2x10.5 )(0.5x22)
= 21 x21 x11
= 441 x11
=4851 cube cm
It seems to quite lengthy , actually it takes very little time . It is very tough to calculate 10.5x10.5 x10.5 conventionally

Sunday, 22 September 2013

Vedic Maths : Lesson 1 (Multiply Easily)

Lesson1
These lessons are based on Vedic Maths" principles and other maths tricks.These principles are general in nature
and can be applied in many ways and very very useful in commercial arthematics. I hope all of you like these
lessons and make your calculation more fast and save lot of time in daily calculations and examinations or any
entrance test like CAT /IIT /BANK PO /ENGINEERING ENTRANCE TEST/PMT /MCA ENTRANCE TEST/MBA ENTRANCE
TEST etc etc



Method for multiplying numbers where the first figures are same and the last figures add to1 0
.
                                                         42 x 48 =
                         Both numbers here start with 4 and the last
                                  figures (2 and 8) add up to 10.
                            just multiply 4 by 5 (the next number up)
                            to get 20 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer

Method for multiplying numbers where the first figures add up 10 and the last figures are same 
                                                           44X64
                           Here first figures are 4 and 6 and their add up 10 and unit figures of both number are same Just multiplying the last figures 4x4=16
                                                     Put it at right hand side
Again multiplying the first figures and add common degit(4x6 )+4=24+4=28 put it at left hand side
                                         Now we get required answer  2816

            Similarly 36x76 , 6X6 =36 right hand side , (3x7)+6= 21+6=27 left hand side
                                              Required answer is 2736

                       NOTE : If multiplication of last figures is less than 10 add zero before unit digit
                                Ex 81x21 , 1x1=01,( 8x2)+1= 16+1=17 Required answer 1701


Method for multiplying numbers where the first number"s add up10 and and the second number's digits are same

                                                          46X55
                Here first number's add up is 10 and second number "s digits are common i.e 5
                          Just multiplying last figures of both numbers 6x5 =30 put it at right hand side
          Again multiplying first figures of both numbers and add common digit of second number
                                  ( 4x5)+5 =20+5 =25 put it left hand side
               Required answer is 2530 ( If multiplication is in unit in first step add zero before it)
                                                   108 x 109 = 11772
                                 The answer is in two parts: 117 and 72,
                                       117 is just 108 + 9 (or 109 + 8),
                                                 and 72 is just 8 x 9.
                                        Similarly 107 x 106 = 11342

HOW USEFUL IS THIS CALCULATION!
EXAMPLE 1

Compute the amount and the compound intrest on Rs 10000.00 on 2.years at4%per annum.









Now 4x4=16 and 4+4=8 put 10 it becomes Rs 10816.00
How simple ! no calculation no extra time !

                                                            Practice Test 1
                                                   Solve mentally these questions
                                        Note down your calculation time by watch
                                                  (Suggested time 90 seconds)
22 X 28        35 X 35            48 X 42
   73 X 33            12 X 92               48 X 28
       28 X 22               37 X 88                  91 X 66
          118 X105             109 X108                112 X106
                91 X 99                 33 X 37                   55X55
            
                                      Now check your answer with the help of a calculator