Were having a little fun this week, and delving into some of the mysteries of the mathematical world, Vedic Math is Based on the ancient Inian Vedas, the most famous of which being the “Rig Veda.”
Vedic mathematics & FastMaths
“FastMaths” is a system of reasoning and mathematical working based on ancient Indian
teachings called Veda. It is fast , efficient and easy to learn and use.
It is being taught in some of the most prestigious institutions in England and Europe. NASA
scientists applied its principles in the area of artificial intelligence.
Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly
found acceptance the world over. Experts suggest that it could be a handy tool for those
who need to solve mathematical problems faster by the day.
In what way FastMaths Methods are different from Conventional Methods?
FastMaths provides answer in one line where as conventional method requires several
steps.
What is Vedic Mathematics?
It is an ancient technique, which simplifies multiplication, divisibility, complex numbers,
squaring, cubing, square and cube roots. Even recurring decimals and auxiliary fractions can
be handled by Vedic mathematics. Vedic Mathematics forms part of Jyotish Shastra which is
one of the six parts of Vedangas. The Jyotish Shastra or Astronomy is made up of three
parts called Skandas. A Skanda means the big branch of a tree shooting out of the trunk.
Who Brought Vedic Maths to limelight?
The subject was revived largely due to the efforts of Jagadguru Swami Bharathikrishna
Tirthaji of Govardhan Peeth, Puri Jaganath (18841960). Having researched the subject for
years, even his efforts would have gone in vain but for the enterprise of some disciples who
took down notes during his last days.
What is the basis of Vedic Mathematics?
The basis of Vedic mathematics, are the 16 sutras, which attribute a set of qualities to a
number or a group of numbers. The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras
(Phrases) and 120 words laid down simple steps for solving all mathematical problems in
easy to follow 2 or 3 steps.
Vedic Mental or one or two line methods can be used effectively for solving divisions,
reciprocals, factorisation, HCF, squares and square roots, cubes and cube roots, algebraic
equations, multiple simultaneous equations, quadratic equations, cubic equations, biquadratic
equations, higher degree equations, differential calculus, Partial fractions,
Integrations, Pythogorus theoram, Apollonius Theoram, Analytical Conics and so on.
What is the speciality of Vedic Mathematics?
Vedic scholars did not use figures for big numbers in their numerical notation. Instead, they
preferred to use the Sanskrit alphabets, with each alphabet constituting a number. Several
mantras, in fact, denote numbers; that includes the famed Gayatri mantra, which adds to
108 when decoded.
How important is Speed?
How fast your can solve a problem is very important. There is a race against time in all the
competitions. Only those people having fast calculation ability will be able to win the race.
Time saved can be used to solve more problems or used for difficult problems.
Is it useful today?
Given the initial training in modern maths in today’s schools, students will be able to
comprehend the logic of Vedic mathematics after they have reached the 8th standard. It will
be of interest to every one but more so to younger students keen to make their mark in
competitive entrance exams.
India’s past could well help them make it in today’s world.
It is amazing how with the help of 16 Sutras and 16 subsutras, the Vedic seers were able
to mentally calculate complex mathematical problems.
Introduction :
Learn to calculate 1015 times faster.
“FastMaths” is a system of reasoning and mathematical working based on ancient Indian
teachings called Veda. It is fast , efficient and easy to learn and use.
Example 1 : Finding Square of a number ending with 5
To find the square of 75
Do the following
Multiply 5 by 5 and put 25 as your right part of answer.
Multiply 7 with the next higher digit ie (7+1)=8 gives
56 as the left part of the answer, Answer is 5625
Example 2 : Calculate 43 X 47
The answer is 2021 Same theory worked here too.
The above ‘rule’ works when you multiply 2 numbers with units digits add up
to 10 and tenth place same
Example 3 : Find 52 X 58 ? Answer = 3016 How long this take ?
Example 4: Multiply 52 X 11
Answer is 572
Write down the number being multiplied and put the total of the digits between 2 digits
52 X 11 is [ 5 and 5+2=7 and 2 ] , answer is 572
Example 5: Can you find the following within less than a minute?
a) 1001/13 ?
b) 1/19 ?
1. Which Number is 1 more than
a) 19
b) 40
c) 189
d) 23
e) 4589
2.Which number is 1 less than
a) 29
b) 48
c) 2339
d) 5
e) 65320
Assignments Answers
1. Which Number is 1 more than
a) 20 b) 41
c) 190 d) 24
e) 4590
2.Which number is 1 less than
a) 28 b) 47
c) 2338 d) 4
e) 65319
http://www.fastmaths.com
Chapter 1 : Numbers
1.2 Place Value
Since there are only 9 numbers and a zero we count in
groups of 10.
• Ten Units make a TEN,
• Ten Tens make a HUNDRED .
• Ten Hundreds make a THOUSAND.
1.Find the value of 4 in the following
a) 430
b) 947
c) 14
d) 125004
2. Write the following numbers in Words
a) 57
b) 7002
c) 405
d) 9
Example 1: Find Factors of 36 ?
Factors of 36
36 can be expressed as 1 X 36 = 36, 2 X 18 =
36, 3 X 12 = 36, 4 X 9 = 36, 6 X 6 = 36
Factors of 36 are 1,2,3,4,6,9,12,18,36.
The number 1 is a factor of every number
1.3.3.1 Factor pairs
Number 18 has 6 factors; 1,2,3,6, 9,18
18 can be expressed as 1 X 18 = 18, 2 X 9 = 18, 3 X 6 =
18
Arrange Pair factors like (1X18),( 2X9), (3X6).?These pair
of numbers is called factor pairs.
Factor pairs of 18 are (1X18),( 2X9), ( 3X6)
If you know one factor of a number, you can get another
using factor pairs.
If you know 44 can be divided by 4, than another factor of
44 must be 11 since 11X4 = 44
Assignments
List all factors and list factor pairs if any.
a) 64
b) 48
c) 128
d) 27
e) 37
Assignments Answers
List all factors and list factor pairs if any.
a) 64
• Factors 1,2,4,8,16,32,64
• Factor Pairs (1,64) (2,32) ( 4,16) (8,8)
b) 48
• Factors 1,2,3,4,6,8,12,16,24,48
• Factor Pairs (1,48) (2,24) (3,16) (4,12) (6,8)
c) 128
• Factors 1,2,4,8,16,32,64,128
• Factor Pairs (1,128) (2,64) (4,32) (8,16)
d) 27
• Factors 1,3,9,27
• Factor Pairs (1,27) (3,9)
e) 37
• Factors 1,37
• Factor Pairs (1,37)
http://www.fastmaths.com
Chapter 1 : Numbers
1.3.3.2 Highest common factor (HCF)
Suppose we have 2 numbers 70 and 99
70 = 2 X 5 X 7
99 = 3 X 3 X 11
Looking at the factors, there is no common factor except
number 1. There is no factor of one number, which is also a
factor of the other number, except for 1. Such pair of
numbers is called relatively prime; they are prime in
relation to each other.
Example 1: Check 18 and 30
18 = 2 X 3 X 3
30 = 2 X 3 X 5
So 18 and 30 are not relatively prime, they have factors in
common
Both numbers can be divided by 2, 3 and 2 X 3 = 6
Of these three factor numbers the number 6 is the highest
Common Factor (HCF)
Example 2: Check 48 and 72
48 = 2 X 2 X 2 X 2 X 3
72 = 2 X 2 X 2 X 3 X 3 ?
So 48 and 72 are not relatively prime, they have factors in
common. Of these factor numbers the number 2 X 2 X 2 X 3
= 24 is the highest Common Factor (HCF)
Example 3: Check 140 and 27
140 = 2 X 2 X 5 X 7
27 = 3 X 3 X 3
So 140 and 27 are relatively prime. The highest Common
Factor (HCF) = 1
When numbers are close together the HCF will
also be a factor of the sum and of the
difference of the numbers
Example 4: Find HCF of 411 and 417
The above note means the HCF will divide into 411 and 417
also 411 + 417 = 828
417 ? 411= 6
This means that HCF is either 6 or a factor of 6 ( 6 or 3 or 2
or 1).
Since 6 is not a factor of 411 and 417 , test for 3 or 2
HCF(411,417)= 3
Example 5: Find HCF of 90 and 102
This means the HCF will divide into 102 and 90 also
102 + 90 = 192
102 ? 90 = 12
This means that HCF is either 12 or a factor of 12 (12,
6,4,3,2,1)
3 is a common factor of 90 and 102
And 2 also, but not 4 ,Therefore 2X3 = 6, HCF = 6
HCF(90,102)= 6
Assignments
1. Find the following
a) HCF(80,20)=
b) HCF(68,24)=
c) HCF(88,38)=
d) HCF(88,82)=
e) HCF(63,18)=
Assignments Answers
1. Find the following
a) HCF(80,20)=20
80 = 2 X 2 X 2 X 2 X 5
20 = 2 X 2 X 5 ?
So 80 and 20 are not relatively prime, they have factors in
common. Of these factor numbers the number 2 X 2 X 5 =
20 is the highest Common Factor (HCF)
b) HCF(68,24)=4
68 = 2 X 2 X 17
24 = 2 X 2 X 6 ?
So 68 and 24 are not relatively prime, they have factors in
common. Of these factor numbers the number 2 X 2 = 4 is
the highest Common Factor (HCF)
c) HCF(88,38)= 2
88 = 2 X 2 X 2 X 11
38 = 2 X 19
So 88 and 38 are not relatively prime, they have factors in
common. Of these factor numbers the number 2 is the
highest Common Factor (HCF)
d) HCF(88,82)=2
88 = 2 X 2 X 2 X 11
82 = 2 X 41
So 88 and 82 are not relatively prime, they have factors in
common. Of these factor numbers the number 2 is the
highest Common Factor (HCF)
e) HCF(63,18)=9
63 = 3 X 3 X 7
18 = 2 X 3 X 3
So 63 and 18 are not relatively prime, they have factors in
common. Of these factor numbers the number 3 X 3 = 9 is
the highest Common Factor (HCF)

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Utilities
Vedic Maths Tutorial
Vedic Maths is based on sixteen sutras or principles. These principles are general in nature and can be applied in many ways. In practice many
applications of the sutras may be learned and combined to solve actual problems. These tutorials will give examples of simple applications of
the sutras, to give a feel for how the Vedic Maths system works. These tutorials do not attempt to teach the systematic use of the sutras.
For more advanced applications and a more complete coverage of the basic uses of the sutras, we recommend you study one of the texts
available.
N.B. The following tutorials are based on examples and exercises given in the book ‘Fun with figures’ by Kenneth Williams, which is a fun
introduction some of the applications of the sutras for children.
If you are having problems using the tutorials then you could always read the instructions.
Tutorial 1
Tutorial 2
Tutorial 3
Tutorial 4
Tutorial 5
Tutorial 6
Tutorial 7
Tutorial 1
Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.
l For example 1000 – 357 = 643
We simply take each figure in 357 from 9 and the last figure from 10.
So the answer is 1000 – 357 = 643
And thats all there is to it!
This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
l Similarly 10,000 – 1049 = 8951
l For 1000 – 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 – 83 becomes 1000 – 083 = 917
Vedic Maths Tutorial (interactive)
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Vedic Maths Tutorial (interactive)
Try some yourself:
1) 1000 – 777
=
2) 1000 – 283
=
3) 1000 – 505
=
4) 10,000 – 2345
=
5) 10000 – 9876
=
6) 10,000 – 1101
=
7) 100 – 57
=
8) 1000 – 57
=
9) 10,000 – 321
=
10) 10,000 – 38
=
Total Correct =
Return to Index
Tutorial 2
Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.
l Suppose you need 8 x 7
8 is 2 below 10 and 7 is 3 below 10.
Think of it like this:
The answer is 56.
The diagram below shows how you get it.
You subtract crosswise 83 or 7 – 2 to get 5,
the first figure of the answer.
And you multiply vertically: 2 x 3 to get 6,
the last figure of the answer.
That’s all you do:
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Vedic Maths Tutorial (interactive)
See how far the numbers are below 10, subtract one
number’s deficiency from the other number, and
multiply the deficiencies together.
l 7 x 6 = 42
Here there is a carry: the 1 in the 12 goes over to make 3 into 4.
Multply These:
1) 8
8 x
2) 9
7 x
3) 8
9 x
4) 7
7 x
5) 9
9 x
6) 6
6 x
Total Correct =
Here’s how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.
l
Suppose you want to multiply 88 by 98.
Not easy,you might think. But with
VERTICALLY AND CROSSWISE you can give
the answer immediately, using the same method
as above.
Both 88 and 98 are close to 100.
88 is 12 below 100 and 98 is 2 below 100.
You can imagine the sum set out like this:
As before the 86 comes from
subtracting crosswise: 88 – 2 = 86
(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
This is so easy it is just mental arithmetic.
Try some:
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Vedic Maths Tutorial (interactive)
1) 87
98 x
2) 88
97 x
3) 77
98 x
4) 93
96 x
5) 94
92 x
6) 64
99
7) 98
97 x
Total Correct =
Multiplying numbers just over 100.
l 103 x 104 = 10712
The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),
and 12 is just 3 x 4.
l Similarly 107 x 106 = 11342
107 + 6 = 113 and 7 x 6 = 42
Again, just for mental arithmetic
Try a few:
1) 102 x 107 =
1) 106 x 103 =
1) 104 x 104 =
4) 109 x 108 =
5) 101 x123 =
6) 103 x102 =
Total Correct =
Return to Index
Tutorial 3
The easy way to add and subtract fractions.
Use VERTICALLY AND CROSSWISE to write the answer straight down!
l
Multiply crosswise and add to get the top of the answer:
2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13.
The bottom of the fraction is just 3 x 5 = 15.
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Vedic Maths Tutorial (interactive)
You multiply the bottom number together.
So:
l
Subtracting is just as easy: multiply crosswise as before, but the subtract:
l
Try a few:
Total Correct =
Return to Index
Tutorial 4
A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.
l 752 = 5625
752 means 75 x 75.
The answer is in two parts: 56 and 25.
The last part is always 25.
The first part is the first number, 7, multiplied by the number “one more”, which is 8:
so 7 x 8 = 56
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Vedic Maths Tutorial (interactive)
l Similarly 852 = 7225 because 8 x 9 = 72.
Try these:
1) 452 =
2) 652 =
3) 952 =
4) 352 =
5) 152 =
Total Correct =
Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
l 32 x 38 = 1216
Both numbers here start with 3 and the last
figures (2 and 8) add up to 10.
So we just multiply 3 by 4 (the next number up)
to get 12 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.
Diagrammatically:
l And 81 x 89 = 7209
We put 09 since we need two figures as in all the other examples.
Practise some:
1) 43 x 47 =
2) 24 x 26 =
3) 62 x 68 =
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Vedic Maths Tutorial (interactive)
4) 17 x 13 =
5) 59 x 51 =
6) 77 x 73 =
Total Correct =
Return to Index
Tutorial 5
An elegant way of multiplying numbers using a simple pattern.
l 21 x 23 = 483
This is normally called long multiplication but
actually the answer can be written straight down
using the VERTICALLY AND CROSSWISE
formula.
We first put, or imagine, 23 below 21:
There are 3 steps:
a) Multiply vertically on the left: 2 x 2 = 4.
This gives the first figure of the answer.
b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3
This gives the last figure of the answer.
And thats all there is to it.
l Similarly 61 x 31 = 1891
l 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1
Try these, just write down the answer:
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Vedic Maths Tutorial (interactive)
1) 14
21 x
2) 22
31 x
3) 21
31 x
4) 21
22 x
5) 32
21 x
Total Correct =
Multiply any 2figure numbers together by mere mental arithmetic!
If you want 21 stamps at 26 pence each you can
easily find the total price in your head.
There were no carries in the method given above.
However, there only involve one small extra step.
l 21 x 26 = 546
The method is the same as above
except that we get a 2figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).
So 21 stamps cost £5.46.
Practise a few:
1) 21
47 x
2) 23
43 x
3) 32
53 x
4) 42
32 x
5) 71
72 x
Total Correct =
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.
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Vedic Maths Tutorial (interactive)
6) 32
56 x
7) 32
54 x
8) 31
72 x
9) 44
53 x
10) 54
64 x
Total Correct =
Any two numbers, no matter how big, can be
multiplied in one line by this method.
Return to Index
Tutorial 6
Multiplying a number by 11.
To multiply any 2figure number by 11 we just put
the total of the two figures between the 2 figures.
l 26 x 11 = 286
Notice that the outer figures in 286 are the 26
being multiplied.
And the middle figure is just 2 and 6 added up.
l So 72 x 11 = 792
Multiply by 11:
1) 43 =
2) 81 =
3) 15 =
4) 44 =
5) 11 =
Total Correct =
l 77 x 11 = 847
This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7147 = 847.
Multiply by 11:
1) 88 =
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Vedic Maths Tutorial (interactive)
2) 84 =
3) 48 =
4) 73 =
5) 56 =
Total Correct =
l 234 x 11 = 2574
We put the 2 and the 4 at the ends.
We add the first pair 2 + 3 = 5.
and we add the last pair: 3 + 4 = 7.
Multiply by 11:
1) 151 =
2) 527 =
3) 333 =
4) 714 =
5) 909 =
Total Correct =
Return to Index
Tutorial 7
Method for diving by 9.
l 23 / 9 = 2 remainder 5
The first figure of 23 is 2, and this is the answer.
The remainder is just 2 and 3 added up!
l 43 / 9 = 4 remainder 7
The first figure 4 is the answer
and 4 + 3 = 7 is the remainder – could it be easier?
Divide by 9:
1) 61 = remainder
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Vedic Maths Tutorial (interactive)
2) 33 = remainder
3) 44 = remainder
4) 53 = remainder
5) 80 = remainder
Total Correct =
l 134 / 9 = 14 remainder 8
The answer consists of 1,4 and 8.
1 is just the first figure of 134.
4 is the total of the first two figures 1+ 3 = 4,
and 8 is the total of all three figures 1+ 3 + 4 = 8.
Divide by 9:
6) 232 = remainder
7) 151 = remainder
8) 303 = remainder
9) 212 = remainder
10) 2121 = remainder
Total Correct =
l 842 / 9 = 812 remainder 14 = 92 remainder 14
Actually a remainder of 9 or more is not usually
permitted because we are trying to find how
many 9’s there are in 842.
Since the remainder, 14 has one more 9 with 5
left over the final answer will be 93 remainder 5
Divide these by 9:
1) 771 = remainder
2) 942 = remainder
3) 565 = remainder
4) 555 = remainder
5) 777 = remainder
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Vedic Maths Tutorial (interactive)
6) 2382 = remainder
7) 7070 = remainder
Total Correct =
Return to Index
Instructions
for using the tutorials
Each tutorial has test sections comprising of several questions each. Next to each question is a box (field) into which you can enter the answer
to the question. Select the first question in each test with the mouse to start a test. Enter the answer for the question using the numeric keys on
the keyboard. To move to the answer field of the next question in the test, press the ‘TAB’ key. Moving to the next question, will cause the
answer you entered to be checked, the following will be displayed depending on how you answered the question :
Correct
Wrong
Answer has more than one part (such as fractions and those answers with remainders). Answering remaining parts of the
question, will determine whether you answered the question correctly or not.
Some browsers will update the answer on ‘RETURN’ being pressed, others do not. Any problems stick to the ‘TAB’ key. Pressing ‘SHIFT
TAB’ will move the cursor back to the answer field for the previous question.
The button will clear all answers from the test and set the count of correct answers back to zero.
N.B. JavaScript is used to obtain the interactive nature of these tutorials. If you cannot get this to work then try the text/picture based version of
this tutorial.
Return to Index
Vedic Mathematics is greatly related to zero!
Zero has a greater relation to Vedic matrix,
Vedic matrix has a far greater relation to computers and digital count!
Everything is wellconnected relation!
How to relate zerostart positions with Vedic 2D square matrix 0…9 has been explained on site http://www.vedicmatrix.org
A 2dimensional square matrix having zerostart row and column numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, & 9) help users to relate memory to “merged row and column matrixpositions” as well as “computing principles” (revealed as Vedic sutras…)
For more related information please Google search “Vedic matrix” and Orkut forum ‘0’ topics via profile kkr–> communities–> forum
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