Lesson8

Lesson8

Let us try a long multiplication 235465 x233297 =????
This is the conventional method and everybody know this method so I am skipping the explanation.
2 3 5 4 6 5
x_ 2_ 3_ 3_ 2_ 9_ 7_
1 6 4 8 2 5 5
21 1 9 1 8 5 x
47 0 9 3 0 x x
706 3 9 5 x x x
7063 9 5 x x x x
_4 7093_ 0_ x_ x_ x_ x- x_
_54933_ 2_ 7_ 8_ 1_ 0_ 5_

Now the real magic of vedic maths come here and you can solve this problem in few seconds
Steps Almost same as we do in previous lesson .Start from
right ,multiply 5 to7 (5x7=35) write 5 take carry3
2 3 5 4 6 5
x _ 2 _ 3 _ 3 _ 2 _ 9 _ 7
35
Now multiply 6 to 7 ,9 to 5 add together with carry 3
6x7+9x5 +3 =42 +45+3=90 write 90 before 5
2 3 5 4 6 5
x _ 2 _ 3 _ 3 _ 2 _ 9 _ 7
_ _ _ _ _ _ _ _ _ _ 9035
Now multiply 4to5 ,5 to2 ,6 to 9 add together with carry9
4x7+5x2+6x9+9= 28+10+54+9=101
2 3 5 4 6 5
x_2_3_3_2_ 9 _ 7
1019035
Now 5x7+4x9+6x2+5x3+10 =35 +36+12+15+10=108
2 3 5 4 6 5
x_2_3_3_2_ 9 _ 7
1081019035
Now 3x7+5x9+4x2+6x3+5x3+10=21 +45+8+18+15+10=117
2 3 5 4 6 5
x_2_3_3_2 _ 9 _ 7
1171081019035
2x7+3x9+5x2+4x3+6x3 +5x2+11=14+27+10+12+18+10+11=102
2 3 5 4 6 5
x_2_3_3_ 2 _ 9 _ 7
1021171081019035
2x9+3x2+5x3+4x3+6x2+10=18+6+15+12+12+10 =73
2 3 5 4 6 5
x_2_3_3 _ 2 _ 9 _ 7
731021171081019035
2x2+3x3+5x3+4x2+7= 4+9+15+8+7=43
2 3 5 4 6 5
x_2_3_ 3 _ 2 _ 9 _ 7
43731021171081019035
2x3+3x3+5x2+4=6+9+10+4=29
2 3 5 4 6 5
x_2_3 _ 3 _ 2 _ 9 _ 7
2943731021171081019035
2x3+3x2+2=6+6+2=14
2 3 5 4 6 5
x_2_ 3 _ 3 _ 2 _ 9 _ 7
142943731021171081019035
2x2+1=5
2 3 5 4 6 5
x_2_ 3 _ 3 _ 2 _ 9 _ 7
5142943731021171081019035
Our required answer is 5493327109
It looks quite boring and tedious .But certainly a great time saver, do practice and become master

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Lesson 7

Lesson7

VERTICALLY AND CROSSWISE MULTIPLICATION

Consider the conventional multiplication of two 2 digit numbers 12 and 23

shown below:

12

X 23

36

24x

276

This is normally called long multiplication but

actually the answer can be written straight down

using the VERTICALLY AND CROSSWISE

formula.

There are 3 steps:

a) Multiply vertically on the left: 2 x 3= 6

This gives the first figure of the answer.

b) Multiply crosswise and add: 1 x 3 + 2 x 2 = 7

This gives the middle figure.

c) Multiply vertically on the right: 1 x 2 = 3

This gives the last figure of the

l 21 x 26 = 546

The method is the same as above

except that we get a 2-figure number, 14, in the

middle step, so the 1 is carried over to the left

(4 becomes 5).

l 33 x 44 = 1452

There may be more than one carry in a sum:

Vertically on the left we get 12.

Crosswise gives us 24, so we carry 2 to the left

and mentally get 144.

Then vertically on the right we get 12 and the 1

here is carried over to the 144 to make 1452.

This is multiplication of 2 digits numbers .Now we learn 3 digits multiplication

3 Digits Multiplication

Let us try to understand this by an example.

123 x321=????

Step 1 We start from right and multiply last digits of both numbers vertically

3x1 =3

Step 2 Multiply last two digits crosswise and add together and write before step one figure

2x1+3x2=2 + 6 = 8

Step 3 Multiply first and last digits crosswise and middle digit vertically and add together and write total before

step 2 figure

1x1 +3x3 +2x2 =1+9+3=14

Step 4 Multiply first two digits crosswise and add together and write before step 3 figure also add carry

2x1 +3x2+1 =9

Step 5 Multiply first digits of both numbers vertically and write before step 4 figure

1 2 3

I

3 2 1

3 9 14 8 3 1x3=3

Our required answer is 39483

Practice Test

28 x89 28x62 56x48 236 x456 58x 78

259x 789 289 x89 * 87 x56 211 x879 25x89

Hint 289 x089

289

x 089

0x2 / 2x8+8x0=16 / 2x9+8x8+0x9=82 / 8x9+8x9=144 / 9x9=81

16+9=25 / 82+15=97 /144+8 =152 /81

= 25721

Back Home Next

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Lesson 6

Lesson6
Multiplying Close Numbers
Here we learn how to calculate close numbers multiplication like 96x92, 43x49 ,88x98
Multiply 88 by 98.
Both 88 and 98 are close to 100.
88 is 12 below 100 and 98 is 2 below 100.
As before the 86 comes from
(or 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
9 6 + 4
89 28 our required answer is 8928 .Here our base is 100. Now we consider some other base
Ex:- 53 / + 3
57 / + 7
60 / +21 Here base is shifted to 50 .so we multiply 60 by 50 and add 21 60x30 +21
× 50 Therefore, the answer is 3021.
3000 / +21
See one more example
54 / +4
48 / -2
52 / -8
x50 Here our base is 50
2600 /-8 2600-8 =2592 Therefore the answer is 2592
Again see one more example
48 /-2(1 of 2)
45 /-5
43 /+10
x 50 Base is 50
2150 +10 = 2160
We can do this example taking base 40
48 / +8
45/ + 5
53 / +40
x40
2120 +40 =2160 Why we take base 50 instead of 40 ? Reason is simple calculation of 50 is easy compare to 40.
Let us consider another example for practice.
Ex:- 82 / + 2 Shifted base = 80
76 / - 4
78 / (-8)
× 80
6240 / (-8) ie 6240
- 8
Answer is 6232
Advantages : -
(1) The computation time is reduced drastically.
(2) This method is particularly useful when the numbers under consideration are close to base.
(3) Very useful in finding the squares.
Disadvantage : -
The disadvantage of this method is that the numbers under consideration should be very close to each other. If there is a large
duration in the numbers from each other then it is very difficult to fix the base for ex:- 32 × 78 etc.
Practice Test
96x 98 97 x 88 91X93 96 x 93 89x92
52 X49 73x82 45x48 69x72 78x79
45x42 72x75 48 x52 95x88 82x75

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Lesson 5

Lesson5

MULTIPLICATION OF 9

Step1 Prifix 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 neighbour ,write before step 2
figure and repeat it up to first digit ie 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=

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Lesson 4

Lesson4

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 neighbour.
Step1 Prifix 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 neighbour with carry in step first repeat this upto the first
digit ie 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 1and add to 2 and write before ...708, 2+ 2 =4 ....4808
Double 0 and add to 1 and write before .708 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 neighbour, in the case of multiplication of 13 .We would quadruple (i.e. multiply by 4) and then add
the right neighbour, in the case of multiplication of 14 .In case of 19 we would multiply by 9 and then add
the right neighbour
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 = ? (2) 43285 X 14 = ?
2331 21132
039942 X 13 043285 X 14
519246 605990
(3) 58265 X 15 = ? (4) 36987 X 16 = ?
34132 25654
058265 X 15 036987 X 16
873975 591792
(5) 69873 X 17 = ? (6) 96325 X 18 = ?
57652 85224
069873 X 17 096325 X 18
1187841 1733850
(7) 74125 X 19 = ?
73124
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

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Lesson 3

EARN MONEY BY SIGN UP AND TAKING SURVRYS

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

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Lesson 2

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 2of 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

                                                                        322

                                                                        ||| |

                                                                        ||| |                                                       

                                                                       3542

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.

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