Lesson11

Lesson11

Can it Divide?

How can you quickly know if one number will divide evenly into another number, leaving no remainder? For example, will 3
divide evenly into 2,169,252? Well, I wouldn't have brought the subject up if I didn't know some curious shortcuts.I think all
of you know the division by 2 ,5 ,10 . Now we learn division by every possible number
Division by 2
No surprise here. Any number that ends in 0,2,4,6 or 8 is evenly divisible by 2.
Division by 3
Add the number's digits. If the sum is evenly divisible by 3, then so is the number. So, will 3 divide evenly into 2,169,252?
Yes it will, because the sum of the digits is 27, and 27 is divisble by 3. If you want, you can keep adding numbers until one
digit remains. For example, keep going with 27. 2 + 7 = 9, which is also evenly divisible by 3.
Division by 4
If the number's last 2 digits are 00 or if they form a 2-digit number evenly divisible by 4, then number itself is divisible by 4.
How about 56,789,000,000? Last 2 digits are 00, so it's divisible by 4. Try 786,565,544. Last 2 digits, 44, are divisible by 4
so, yes, the whole number is divisible by 4.
Division by 5
Any number that ends in a 0 or 5 is evenly divisible by 5. Easy enough.
Division by 6
The number has to be even. If it's not, forget it. Otherwise, add up the digits and see if the sum is evenly divisible by 3. It it
is, the number is evenly divisible by 6. Try 108,273,288. The digits sum to 39 which divides evenly into 13 by 3, so the
number is evenly divisible by 6. If you want, you can keep adding numbers until only one digit remains and do the same
thing. So in this case, 3 + 9 = 12 and 1 + 2 = 3, and 3 is evenly divisible by 3!
Division by 7
Multiply the last digit by 2. Subtract this answer from the remaining digits. Is this number evenly divisible by 7? If it is, then
your original number is evenly divisible by 7. Try 364. 4, the last digit, multiplied by 2 = 8. 36, the remaining digits,
minus 8 = 28. The last time I checked, 28 is evenly divisble by 7, and thus, so is 364!
Another example 1792 2 is the last digit multiply it by 2and subtract it from original number
1792
-4
1 7 5 repeat once again 5x2=10
- 10
7 7 is divisible by 7 so is 1792
Division by 8
If the number's last 3 digits are 000 or if they form a 3-digit number evenly divisible by 8, then the number itself is divisible
by 8. How about 56,789,000,000? Last 3 digits are 000, so it's divisible by 8. Try 786,565,120. The last 3 digits, 120, divide
by 8 into 15, so yes, the whole number is divisible by 8.
Division by 9
Sum the number's digits. If it divides by 9, you're in luck. As with the tests for 3 and 6, you can keep adding numbers until
you're left with only one digit. 9873 , 9+8+7+3=27 =2+7 =9 9873 is divisible by 9
Division by 10
Any number that ends in 0 is evenly divisible by 10.
Division by 11
Here are four ways for different types of numbers:
1. If the sum of every other digit, starting with the first, is equal to the sum of every other digit starting with the
second, then the number is evenly divisible by 11. Try 13057. 1+0+7 = 3+5, therefore it should divide evenly
by 11. And indeed it does: 13057 / 11 = 1187. 1+0+7-3-5=0
2. If the digits are different, count them from the right and then add the numbers in the odd positions and the
even positions. Subtract the smaller number from the larger. If the difference is evenly divisible by 11, so is
your original number. Take the number 181,907. The numbers 8,9, and 7 are in the odd positions. They sum
to 24. The numbers 1,1, and 0 are in the even positions. They sum to 2. Subtract 2 from 24 to get 22. 22
divides by 11 into 2, so 181,907 is evenly divisible by 11.
Division by 12
If the number can be evenly divided by 3 and 4, the same can also be said for 12. Use the methods for Division by 3 and
Division by 4 above. If they both work, your number is also evenly divisible by 12.
Division by 13
Multiply the last digit by 4 and add it from remaining digits Is this number evenly divisible by 13? If it is, then your original
number is evenly divisible by 13. Try 598
598
+32 (8x4=32)
9 1 Repeat once again
+ 4
13 so it is divisible by 13
Division by 15
If the number can be evenly divided by 3 and 5, the same can also be said for 15. Use the methods for Division by 3 and
Division by 5 above. If they both work, your number is also evenly divisible by 15.
Division by 17
Multiply the last digit by 5. Subtract this answer from the remaining digits. Is this number evenly divisible by 17? If it is, then
your original number is evenly divisible by 17. Try 663
663
- 15
51 it is divisible by 17 so 663 is divisible by 17
Division by 19
Multiply the last digit by 2. Add this answer from the remaining digits. Is this number evenly divisible by 19? If it is, then
your original number is evenly divisible by 19. Try 741
741
+ 2
76
+ 12
19 it is divisible by 19 so 741 is divisible by 19
Division by 23
Multiply the last digit by 7. Add this answer from the remaining digits. Is this number evenly divisible by 23? If it is, then
your original number is evenly divisible by 23. Try 667
667
+ 47
113

+ 21
23 it is divisible by 23 so 667 is divisible by 23
Division by 24
If the number can be evenly divided by 3 and 8, the same can also be said for 24. Use the methods for Division by 3 and
Division by 8 above. If they both work, your number is also evenly divisible by 24.
Division by 29
Multiply the last digit by 3. Add this answer from the remaining digits. Is this number evenly divisible by 29? If it is, then
your original number is evenly divisible by 19. Try 667
667
+ 21
87
+ 21
29 it is divisible by 29 so 667 is divisible by 29

Division by 31
Multiply the last digit by 3. Subtract this answer from the remaining digits. Is this number evenly divisible by 31? If it is, then
your original number is evenly divisible by 31. Try 744
744
- 1 2
62
6
0 it is divisible by 31 so 744 is divisible by 31
Division by 33
If the number can be evenly divided by 3 and 11, the same can also be said for 33. Use the methods for Division by 3 and
Division by 11 above. If they both work, your number is also evenly divisible by 33.
Division by 36
If the number can be evenly divided by 4 and 9, the same can also be said for 36. Use the methods for Division by 4 and
Division by 9 above. If they both work, your number is also evenly divisible by 36.
Division by 37
Multiply the last digit by 11. Subtract this answer from the remaining digits. Is this number evenly divisible by 37? If it is,
then your original number is evenly divisible by 37. Try 925
925
- 55
37 it is divisible by 31 so 925 is divisible by 37

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This is the blog of Quick Tips in which you will find Tips on solving day to day maths problems. And how to solve them fast without taking more time. In this blog you will also find how to write a blog and through them how to make a money. and also about online jobs, best internships , results ,collage ranking etc. if u have any doubt on this topics on this blog please mail me on .

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Lesson10

Lesson10
Squares

Finding square of any number is very very easy and you can calculate it very fast But before
going to concept ,you should do some home work . You are well conversant in squaring of
1 to 9
1x1 =1
2x2 =4
3x3 =9
4x4 =16
5x5 =25
6x6 =36
7x7 =47
8x8 =64
9x9 =81
These are square from 1 to 9 . Now learn square index of 1 to 9
Number Square Index Operation
1 2 First digit
squaring
1 to4
Multiply first
digit to next to
first digit
5 to9
2 4
3 6
4 8
5 0
6 2
7 4
8 6
9 8
Square Index is nothing except table of 2 .We just double
number in first part ie from 1 to 4 and leave ten 's digit in
second part ie from 5 to 9 after doubling .
Steps Now learn main concept by this example
21 x21 =????
Here our last digit (or unit digit ) is1 .Its square index
is 2 First we take square of 1 and write it extreme right then
we take first digit and multiply it by the square index write before
last figure then squaring first digit and write extreme left
If there is any carry add to it
1x1 =1 2x2 =4 22 =4 4 4 1 Answer
44 X44=????
Here square index of 4 is 8
4x4 = 16 4x8 +1(carry ) =32 +1 = 33 42 + 3 =16+3 =19 1936 Answer
93 X93 =????
Here square index of 3 is 6
3x3 =9 9x6 =54 92+ 5 =81 +5 =86 8649 Answer
These are the square where last digit is 1 to 4 now we learn squaring of those numbers
having last digit from 5 to 9.Method is same, instead of squaring first digit multiply to
next digit
36 X36 =
Here square index of 6 is 2
6x6 =36 3x2 + 3 =6+3=9 6X(6+1) = 6 x7 =42 42 96 answer
87 x 87 =
Here square index is 4
7x7=49 8x4+4 =32+4 =36 8x(8+1)+3 =72+3 =75 75 69 Answer
25x25 =
Here square index is 0 so no need of middle step
5x5 = 25 2x(2+1) = 6 625 answer
Now with the help of this concept we can calculate square of any number
236 x 236=????
Here square index of 6is 2
6x6 = 36 23 x2 +3 =46+3=49 23x24*+4 =552+4=556 55696 answer
*23x24 = ? By cross and vertical multiplication method(covered in lesson no 7)
4 / 14 /12 = 552

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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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