Vedic addition

Vikram Devatha
First Edition
Vedic Addition

ii
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4.0/.
All Things Vedic
Auroville Collaborative
Saracon, Auroville, TN 605111, INDIA.
Tel: +91-413-2622571
Web: www.allthingsvedic.in/addition

4
Preface
Vedic Mathematics is a system of mathematics that allows
problems to be solved quickly and efficiently. It is based on the
work of Sri Bharathi Krishna Thirthaji Maharaja (1884 – 1964),
who devised the system from a close study of the Vedas. The
Vedas are ancient scriptures of India that deal with many
subjects. It is based on 16 sutras (aphorisms) from the Vedas
that provide a principle or a rule of working to solve a problem.
These sutras may be ancient in origin, but are still relevant to
modern day mathematics.
Vedic Math provides many different methods to solve any given
problem. The choice of method depends on the conditions that
the given problem satisfies. This is very much like planting a
tree – the choice of which tree to plant has to depend on the
nature of the soil and the environment. It is impossible to plant
the same tree everywhere without considering the
surroundings. Vedic math works in a similar manner.
Conventional mathematics generally provides a single method
to solve a mathematical problem. This method is applied
“blindly” whenever the student comes across the problem.
However, in vedic math, the student chooses which method to
employ. In multiplication, for instance, there are almost five
different methods that can be used, and the choice of method
depends entirely on what the student is comfortable with.
Learning such a system of mathematics at an early age can
greatly help in dispelling fears of mathematics in children and
can even make it more fun. Vedic math also allows us to
develop the ability of lateral thinking, enabling us be faster at
calculations and even to rely less on the calculator. ! !
This series of books is an attempt to present the material in a
modular fashion. Each book focusses on one specific arithmetic
operation - addition, subtraction, multiplication and division.
These books can be read in any order, but it is recommended
that addition and subtraction be read before multiplication and
division. This particular book is related to addition only, and
subsequent books will cover the other arithmetical operations.
Some of the vedic methods apply to specific sets of numbers,
while others are general methods and can be used in all cases.
How to use this book
Each chapter introduces one or two ideas, and takes you from
the simple to the more advanced methods. At times, you will be
posed a question, and I suggest that you pause, think and
arrive at an answer before continuing.

5
Content has been optimized for the iPad. There are essentially
two kinds of interactivity available in the iPad version:
screencasts and buttons.
A screencast is a digital recording of computer screen output,
explaining the Vedic Math techniques, along with an audio
narration. Screencasts are natively available on an iPad, and in
some versions of the pdf. If the screencasts do not play on your
computer or tablet, these are also available on
www.youtube.com/VedicAddition for reference. At times, it is
easier to explain orally, than in written words. Hence, each
method is illustrated using a screencast, as well as a written
explanation.
Buttons are used to display the solutions to exercises. If the
buttons do not work in your version of this eBook, all solutions
are provided in Chapter 6 as well.
Note for the teacher
If you plan on using this material in your classes, I would
suggest a minimum of two hours on each chapter. Supplement
the exercises presented in this book with your own. Though not
essential, I would suggest that the students understand the
concept of negative sign, before being introduced to Vedic
Math.
Prerequisites
No prior knowledge of Vedic Math is necessary to read and
understand the material I have presented in this book. I start
with the basics, and proceed to the more advanced techniques
of Vedic Math. It will be helpful to know the addition tables till
20+20 to fully grasp the techniques presented in this book.

7
Some notes
Patterns in numbers
Ever seen a pattern in nature, such as the recurring phases of
the moon, and wondered at the beauty of nature? These
patterns exist in numbers too. Patterns such as the Fibonacci
Numbers and the Golden Mean are well known examples.
Learning how to recognize these patterns and using them to
solve problems is what Vedic Math is all about.
Number line and negative numbers
The number line is a straight line with zero at the center and
extending to infinity on either side. Numbers to the left of zero
are negative while those to the right are positive. Zero, a
number discovered in ancient India, is neither positive nor
negative.
Negative numbers are used extensively in Vedic Mathematics.
You will notice that in the above diagram, the negative sign is
placed above the digit rather than to its left as in conventional
math e.g. -3 has been written as 3̅̅. Similarly, –9 will be written
9̅̅, -32 as 3̅̅2̅, –10 as either 1̅0̅ or 1̅0 (since 0̅ = 0).
Number tables
There are two kinds of number tables that are essential for
mathematics – addition & subtraction tables and multiplication
& division tables. Today, schools generally advocate addition
tables till 10 + 10, and multiplication tables until 12 x 12. For
Vedic Math, you only need to know the tables up to 5 x 5.
Tables of higher numbers are not required. However,
knowledge of tables till 20 x 20 and 16 x 16 will be useful.
Answers in parts
Answers are normally obtained in parts, namely, the left hand
side (LHS), middle (mid) and the right hand side (RHS). Each
of these are obtained using different methods. For example,
998 x 992 = 990 / 016
Here the answer to the problem 998 x 992 has been obtained
mentally in two steps – one giving the left hand side of the
answer (990) and the second giving the right hand side (016).
The method used will be discussed in a later chapter.
Bases
There are two kinds of Bases – Standard Base and Special
Base. Examples of standard bases are 10, 100, 1000, 10000
and so on i.e. numbers start with a 1 and followed by zeroes.
Multiplication and division with these numbers are very simple
– the decimal point is shifted, either to the right or to the left
0 1 2 33̅ 2̅ 1̅

8
respectively. Vedic math also uses Special bases. These can
be any number, such as 50, 500, 5000, 25, 250, 2500 and so
on. More on this later.
Place value
Place-value notation, or positional-notation is a way of
representing numbers. The value of a digit, depends on its
place or position in the number. Beginning with the ones place
at the right, each place value is multiplied by increasing
powers of 10. Place value for the number 24.759 is shown
below
To the left of the decimal point, digits to the right have smaller
place value than those to the left by a factor of 10. However,
to the right of the decimal point, digits to the left have higher
place value than those to the right.
Columns
We will use the terms “Place value” and “Columns”
interchangeably. For instance, while adding the numbers, we
will refer to columns.
Direction
In conventional math, most arithmetic operations are
performed Right to Left, i.e. starting with the Units column,
and moving leftward to the Tens column, Hundreds column
and so on. For instance, while adding 2 numbers, the Units
column are added first, then the tens and so on. While
subtracting numbers, again the units column is subtracted
first, then the tens. Direction of operation is Right to Left.
In Vedic Math, arithmetical operations are performed Left to
Right. In so doing, digits with a higher Place Value are
processed first, and rightfully so, as they have a larger value.
2 4 . 7 5 9
4 5 7
9 8 6
+ 3 4 5
Units column
Tens columnHundreds column
Tens Units Decimal Tenths Hundredths Thousandths

9
Carryover
Unlike conventional math, carryover in Vedic Math can be
made either to the left or to the right. When a digit is to be
carried over, it is written in small case. For instance, in the
following number, the ‘2’ is a carry-over which is added to the
5.
5 2 4 6 = 7 4 6

11
Conventional method
Before we study the Vedic Math techniques of addition, let us
review the method most commonly used today. Add the
following numbers:
It is likely that you started the addition from the Units column.
The main elements in this method of addition are:
1. Addition starts with the rightmost column, usually the Units
column, unless there are decimals.
2. The carry over is added on top of the column to the left.
3. All the columns are added, and the answer is given from the
left.
Although the conventional method can be applied to all cases
of addition, it is not an efficient method.
1. Addition starts with the column of least importance i.e. the
Units column, and in cases with decimal figures, addition
starts with the decimal digits which have even lower place
value. In day-to-day situations, it is far more important to sum
the columns with the higher place value i.e. the hundreds
column, or the thousands column rather than the units
column.
2. Addition moves from the rightmost column to the left,
however the final answer is given starting with the leftmost
digit. This becomes a problem if a paper and pen are not
available, since you will need to remember the digits in
reverse order while giving the answer. This makes mental
addition cumbersome.
In the following chapters, you will learn the vedic techniques of
addition that will overcome the problems that arise with
conventional addition. With practice, you will perfect these new
techniques.
3
1
8
1
9
4 2 5
+ 6 7 0
1 4 8 4
Carryovers
Addition begins
with the units
column
3 8 9
4 2 5
+ 6 7 0

13
Column-less addition
Add the following numbers in the method that you are familiar
with.
It is likely that you started adding from the Units column
(7+6+5), and then moved to the Tens column (5+8+9).
Sometimes, having to start from the units column may not be a
such a great idea. There may be cases where you need to start
from the Leftmost column (since that column has the highest
place value). In the following chapter, you will learn a method of
adding numbers from the Leftmost column. For now, let us see
if it is possible to add numbers starting from any column.
Example 1
Watch the screencast below to see the column-less method of
adding these numbers. This can also be viewed at http://
youtu.be/JmZQdFCLqvQ
Screencast 2.1 Column-less addition
4 5 7
9 8 6
+ 3 9 5

14
Step 1: Numbers are added column by column, starting with
the column of your choice. Lets add numbers in Column 2, then
Column 1 and lastly Column 3.
Adding digits in Column 2, 5+8+9 gives 22, written as a ‘small
2’ and a ‘big 2’.
Step 2: All the small digits are carried over to the previous
column, 1 is carried over to the 2 giving 3, 2 and 6 give 8, and
the 1 is carried over 0 to give 1. The answer is 1838.
Example 2
In some cases, there will be multiple carryovers. Try adding the
following numbers using the column-less method.
You will see that you will need to carryover twice to arrive at the
ﬁnal answer.
Column1 Column2 Column3
Step 1
Step 2
4 5 7
9 8 6
+ 3 9 5
16 2 2 18
1 8 3 8 2 6 7
7 7 8
+ 5 5 9

15
Watch the screencast below to see the solution. This can also
be viewed at http://youtu.be/BvyKC3SEfog
Step 1: Numbers are added column by column, starting with
the column of your choice.
1’ and a ‘big 8’. Adding digits in Column 1, 2+7+5 gives 14,
written as a ‘small 1’ and a ‘big 4’. Adding digits in Column 3,
7+8+9 gives 24, written as a ‘small 2’ and a ‘big 4’.
Step 2: All the small digits are carried over to the previous
column, 2 is carried over to the 8 giving 10. This is written as a
‘small 1’ and a ‘big 0’. The existing ‘1’ to the left of the 8 is
carried over to the Hundreds column giving 5, and the ‘1’ with
the ‘4’ is carried over to the Thousands column, 0+1 giving 1.
Step 3: The ‘small 1’ is carried over the 5, giving 6. The ﬁnal
answer is 1606.
Screencast 2.2 Double carry-over Step 1
Column1 Column3Column2
Step 2
2 6 7
7 7 8
+ 5 5 9
1 4 18 2 4
1 5 10 4
1 6 0 4Step 3

17
Two-Digit Method
In this chapter, you will learn a method of adding numbers
quickly and efﬁciently. You will see that numbers don’t have to
be added from the right to the left only, which is most likely what
you are accustomed to. Lets review two points from before.
Place value
Place-value notation, or positional-notation is a way of
representing numbers. The value of a digit, depends on its
place or position in the number. Beginning with the ones place
at the right, each place value is multiplied by increasing
powers of 10.
To the left of the decimal point, digits to the right have smaller
place value than those to the left by a factor of 10. However,
to the right of the decimal point, digits to the left have higher
place value than those to the right.
Direction
In conventional math, most arithmetic operations are
performed Right to Left, i.e. starting with the Units column,
and moving leftward to the Tens column, Hundreds column
and so on. For instance, while adding numbers, the Units
column are added first, then the Tens column, then the
Hundreds. While subtracting numbers, again the Units column
is subtracted first, then the Tens. Direction of operation is
Right to Left.
In Vedic Math, arithmetical operations are performed Left to
Right. Digits with a higher Place Value are processed first, and
rightfully so, as they have a larger value.
Let us examine this more closely with Addition. Add these two
sets of numbers.
It is likely that you added the above numbers from the Right to
the Left, i.e. starting with the Units column in both cases. Now
see if you can ﬁnd a way to add these numbers from the Left to
the Right. i.e. start adding from the Hundreds column in both
cases!
2 5 6
+ 8 9 4
6 3 8
+ 1 9 4

18
Example 1
In the following example, we add 769 and 583, from the Left to
Right i.e. we start with the Hundreds column, or the leftmost
column, and move column by column, to the right.
Watch the screencast below for an explanation. This can also
be viewed at http://youtu.be/qSd_glxGfDo
The process is broken down into 6 steps, shown in roman
numerals.
Step i: Start by adding the Hundreds column, 7+5 to get 12.
This is written as a 1 in the preceding column (thousands
column), and the 2 is carried over to the subsequent column
(tens column).
Step ii: The 2 and the 6 in the tens column are combined as
“26”. Add 26 and 8 to get 34.
Step iii: 34 written as a 3 in the preceding column (the
Hundreds column), and the 4 is carried over to the subsequent
column (Units column).
Step iv: The 4 and 9 are combined as 49. Add 49 and 3 to get
52
7 2
6 4
9
+ 5 8 3
1 3 5 2
Step i Step iii Step v Step vi
Step ii Step iv
Screencast 3.1 Adding 769 and 583

19
Step v: 52 is written as 5 in the previous column (tens column),
and the 2 is carried over to the subsequent column.
Step vi: Since there is no column to the right of the units
column, the 2 from the 52 is written in the units column.
Read the above steps again carefully, and apply this method to
add the following 325 and 948. The steps are explained in the
next page, but spend a few minutes trying to ﬁgure this out
yourself, before continuing.
Hint: start writing your answer one column ahead.
Example 2
Were you able to add 325 and 948 from Left to Right? These
numbers are again added Left to Right i.e. we start with the
leftmost column, and move to the right. Watch the screencast
below for an explanation. This is also available at http://
youtu.be/3mNpth3NwQ0
3 2 5
+ 9 4 8
Screencast 3.2 Adding 325 and 948

20
Here is the solution for this exercise:
Step i: Start by adding the hundreds column, 3+9 to get 12.
This is written as a 1 in the preceding column (Thousands
column), and the 2 is carried over to the subsequent column
(Tens column).
Step ii: The 2 that was carried over, and the 2 in the tens
column are combined as “22”. Add 22 and 4 to get 26.
Step iii: 26 written as a 2 in the preceding column (the
Hundreds column), and the 6 is carried over to the subsequent
column (Units column).
Step iv: The 6 and 5 are combined as 65. Add 65 and 8 to get
73
Step v: 73 is written as 7 in the previous column (Tens column),
and the 3 is carried over to the subsequent column.
Step vi: Since there is no column to the right of the units
column, the 3 is written in the units column.
Example 3
Try adding 4658 and 7589 using this method on your own now.
Make sure you add Left to Right.
The solution is explained in the next page, however, try to ﬁgure
this out before seeing the solution.
Step i Step iii Step v Step vi
Step ii Step iv
3 2
2 6
5
+ 9 4 8
1 2 7 3
4 6 5 8
+ 7 5 8 9

21
Watch the screenshot below for the solution. This is also
available at http://youtu.be/GyRFgxb-gy8
Step i and ii: Start by adding the leftmost column, 4+7 to get
11. This is written as a 1 in the previous column, and 1 is
carried over to the subsequent column (Tens column).
Step iii: The 1 that was carried over, and the 6 in the tens
column are combined to get “16”. 16 and 5 are added to get 21.
Step iv: 21 written as a 2 in the preceding column, and the 1 is
carried over to the subsequent column.
Step v: The 1 and 5 are combined as 15. 15 and 8 are added
to get 23
Step vi: 23 is written as 2 in the previous column, and the 3 is
carried over to the subsequent column.
Step vii, viii, ix: 38 and 9 are added to get 47 the last two digits
in the answer.
Step ii Step iv Step vi Step viii
Step iii Step vStep i Step vii
Step ix
4 1
6 1
5 3
8
+ 7 5 8 9
1 2 2 4 7Screencast 3.3 Adding 4658 and 7589

22
Exercises in Two-Digit Addition
Try the following exercises, starting from the leftmost column,
and move to the right. Answers are provided in Chapter 6.
Attempt the following mentally, i.e. keep the carryovers in your
mind, and write down only the digits of the ﬁnal answer.
5 1 4 3
+ 2 6 2 9
4 3 5 8
+ 7 2 0 9
7 6 5 8
+ 1 2 7 9
3 0 2
5 7 3
4 2 6
+ 2 5 8
Click for solution
7 5 6
1 2 2
9 2 3
+ 4 0
Click for solution
Click for solution
Click for solution
3 0 9 2
+ 7 1 7 4
Click for solution
Click for solution
6 8 0 2
+ 5 4 1 6
Click for solution
9 3 2
+ 4 8 7 6
1245 + 3529 =
4427 + 1903 =
12.54 + 23.56 =
45.95 + 45.95 =
8.695 + 3.795 =
Click for solution
Click for solution
Click for solution
Click for solution
Click for solution
34.50 + 88.50 = Click for solution
Click for solution

23
Why is this called the Two-digit Method?
You may have wondered why this technique is called the “Two-
Digit method” of addition. It is so called because any column
that is added, must yield 2, and only 2 digits. For example, in
the following, the hundreds column sums to 3, but should be
written as ‘03’, with the ‘0’ in the thousands place, and the ‘3’
carried over to the tens column. Again while adding the Units
column, 02+7 gives 9, but must be written as ‘09’. The answer
will be incorrect otherwise.
What would happen if the sum of any column results in 3 digits?
This will result in a Reverse carryover.
Example 1
Try the following for instance, using the Two-Digit method of
addition.
You will have three digits when you sum Column 2, but in the 2-
digit method, you must have two, and only two digits as you
sum each Column.
The ﬁnal answer in this case is 1035. How would you handle
the three digits of Column 2 to arrive at this answer?
2 3
6 0
2
+ 1 4 7
0 4 0 9
2 5 7
3 4 2
+ 4 3 6

24
Watch the screenshot below for an explanation, and solution of
this issue. This is also available at http://youtu.be/gREz1ilAMcY
The following explains this in detail.
Step 1: Adding digits in Column 1, we get 9, a single digit.
Hence, a zero is inserted in front of the 9, making it a ‘09’. ‘0’ is
written in the preceding column, and the ‘9’ is carried over to
the Tens column.
Adding digits in Column 2, we get 95+4+3=102, three digits,
written as a ‘small 1’ and ‘big 0’ in the Hundreds column, and ‘2’
is carried over to the Units column.
Adding digits in Column 3, 27+2+6 gives 35, written as 3 in the
tens column and 5 in the Units column.
Step 2: The ‘small 1’ in the Hundreds column needs to be
carried over to the Thousands column. 0+1=1, giving the ﬁnal
answer as 1035. This is the Reverse Carryover since it moves
Screencast 3.4 Reverse Carryover
2 9
5 2
7
3 4 2
+ 4 3 6
0 10 3 5
1 0 3 5

25
from the right to the left, i.e. in the reverse direction as
compared to the other carryovers (the ‘9’ was carried over from
the left to the right, and so was the ‘2’).
Example 2
Try another example involving Reverse Carryover.
Try solving this on your own, before viewing the screenshot
given in the next page. Here’s a hint: the Reverse Carryover in
the above example arises due to the Units column.
The ﬁnal answer in this case is 1035. How would you handle
the three digits of Column 2 to arrive at this answer?
Watch the screenshot below for an explanation, and solution of
this issue. This is also available at http://youtu.be/
1pIpNeYS8Q0
1 6 6 2
4 3 5 8
+ 3 7 8 6
Screencast 3.5 Reverse carryover

26
Step 1: Adding digits in Column 1, we get 8, a single digit.
Hence, a zero is inserted in front of the 8, making it a ’08’. ‘0’ is
written in the preceding column, and the ‘8’ is carried over to
the Hundreds column.
Adding digits in Column 2, we get 86+3+7=96, ‘9’ is written in
the preceding column, and the ‘6’ is carried over to the Tens
column.
Adding digits in Column 3, 66+5+8 gives 79, written as 7 in the
Hundreds column and 9 is carried over to the Units column.
Adding digits in Column 4, 92+8+6 gives 106. This is three
digits, and is written as a ‘small 1’ and ‘big 0’ in the Tens
column, and 6 in the Units column.
Step 2: The ‘small 1’ in the Tens column needs to be carried
over to the Hundreds column. 7+1=8, giving the ﬁnal answer as
9806. This is the Reverse Carryover since the 1 is carried over
from the right to the left, i.e. in the reverse direction as
compared to the other carryovers (the ‘8’ was carried over from
the left to the right, and so were the ‘6’ and ‘9’).
Although this still works, the Reverse Carryover prevents us
from arriving at the ﬁnal answer mentally, and hence, a paper
and pen become necessary.
The alternative is to use the Three-Digit method of addition.
How would that work? What would be the steps? Try the
following, and formulate a Three-Digit method of addition. The
goal is to sum these numbers mentally, and avoid the Reverse
Carryover.
1 8
6 6
6 9
2
4 3 5 8
+ 3 7 8 6
0 9 7 10 6
0 9 8 0 6
Step 1
Step 2
2 0 2
3 3 4
+ 5 6 7

28
Three-Digit method
The Three-Digit method of addition is a variation of the Two-
Digit method. In some cases, the Two-Digit method leads to a
Reverse Carryover in the ﬁnal step, which can be avoided using
this method.
Example 1
Let us revisit the question from the previous chapter. Were you
able to formulate the Three-Digit method for summing the
numbers below? The answer in this case is 1103. How can we
add these numbers, from left to right (starting with the
Hundreds column), and arrive at the answer mentally?
Watch the screencast below for an explanation of the Three-
Digit method. This can also be viewed at http://youtu.be/
9EdIMGNAJqc
Screencast 4.1 Three-Digit method
2 0 2
3 3 4
+ 5 6 7

29
Here are the detailed steps for the Three-Digit method
Step i: Adding digits in Column 1, 2+3+5 gives ‘10’, a two digit
number. In this method, the sum of each column must be
written as 3 digits. Hence, a zero is inserted in front of the ‘10’,
making it a ‘010’.
Step ii: The ‘0’ from the ‘010’ is written in the column before the
preceding column (Hundred-thousands column), and the ’10’ is
carried over the existing ‘0’ in the Tens column, now read as
‘100’.
Step iii and iv: Adding digits in Column 2, we get
100+3+6=109, ‘1’ is written in the column before the preceding
column (the Thousands column), and the ’09’ is carried over to
the Units column.
Step v: Adding digits in Column 3, 92+4+7 gives 103, written
as ‘1’ in the Hundreds column, ‘0’ in the Tens column and ‘3’ in
the Units column, giving 1103 as the ﬁnal answer.
Did you notice how the Three-Digit method helped us avoid the
Reverse Carryover? We were able to solve the addition moving
only from the left to the right.
Here is another example.
Example 2
Sum the following numbers using the Three-Digit method. The
answers are given in the next page, but try to solve this on your
own before continuing.
Hint: start writing your answer two columns ahead.
2 10
0 09
2
3 3 4
+ 5 6 7
0 1 1 0 3
Step i Step iii Step v
Step iv Step viStep ii
4 2 5 9
+ 8 7 9 3

30
Watch the screencast below for the solution. This can also be
viewed at http://youtu.be/N_qd2Z4kZ6o
Here is the detailed solution.
Step i: Adding digits in Column 1, 4+8 gives ’12’, a two digit
number. In this method, the sum of each column must be
written as 3 digits. Hence, a zero is inserted in front of the ’12’,
making it a ‘012’.
Step ii and iii: The ‘0’ from the ‘012’ is written in the column
before the preceding column, and the ’12’ is carried over to the
Hundreds column, next to the the existing ‘2, making it ‘122’.
Step iii, iv and v: Adding digits in Column 2, we get 122+7
giving 129. ‘1’ is written in the column before the preceding
column, and the ‘29’ is carried over to the Tens column next to
the ‘5’.
Screencast 4.2 Three-Digit method
4 12
2 29
5 04
9
+ 8 7 9 3
0 1 3 0 5 2
Step iii Step vStep i
Step iv
Step vi
Step viiStep vStep ii

31
Step v and vi: Adding digits in Column 3, 295+9 gives ‘304’,
written as ‘3’ in the Thousands column, and ’04’ is carried over
to the Units column.
Step vi and vii: Adding digits in the Units column, 49+3 gives
‘52’. This is a two digit number, but we are using the Three-Digit
method. Hence, a ‘0’ is inserted in front of the number, making
it ‘052’, written along the Hundreds, Tens and Units column.
The answer is 13052.
Now try both these examples with the Two-Digit method, and
see which method may be more efﬁcient with practice.
Exercises in Three-Digit Addition
Try the following exercises using the Three-Digit method. Start
from the leftmost column, and move to the right. Write the sum
of each column as three digits by inserting a ‘0’ in case the sum
is two digits, and inserting two ‘0’s if it is a single digit. Answers
are provided in Chapter 6.
3 6 7
+ 4 3 7
Click for solution
1 4 5
+ 8 7 4
Click for solution
3 4 2 5
+ 8 2 7 8
Click for solution
1 3 0 4
+ 3 9 8
Click for solution
2 3 9
7 8 5
+ 2 3
Click for solution
2 5 7
1 2 8
+ 3 2 3
Click for solution

32
Common errors
Here is a list of some common errors that we make while using
the Vedic Math methods. Check if any of these apply to you.
Are there any other kinds of errors that you seem to make
often? Share your comments.
Concluding remarks on the Three-Digit method
One question that is likely to arise is, how does one decide
when to use the Three-Digit method over the Two-Digit
method? The Two-Digit method is surely easier, as there are
fewer digits to work with, but it may result in a Reverse
Carryover in some cases. Can we know in advance whether a
sum will give a Reverse Carryover? If so, then we can use the
Three-Digit method from the start, rather than having to switch
from the Two-Digit to the Three-Digit method mid way.
The answer is ‘yes’, there is a way to determine if a sum will
result in a Reverse Carryover by examining the numbers to be
added. But try to ﬁgure this out yourself, and mail me your
answer. A hint: Read up on “Digital Roots” presented in the
Book on Vedic Subtraction.
Writing the sum of a column as a single digit in the Two-!
Digit method, or as two digits in the Three-Digit method.
Make sure that the sum of every column is written as 2 digits
in the Two-Digit method, and as 3 digits in the Three-Digit
method.
Starting the answer in the same column as the column which
is summed. This will give errors. The answer must be written
in the preceding column in the Two-Digit method, or the
column before the preceding column in the Three-Digit
method.
Making an error while summing a column. At times we sum 2
and 3 as 6. Check your calculations and search where you
may have gone wrong.
Mistaking the Column-less methods with the Two-Digit or
Three-Digit methods. Unlike the conventional system, where
there is only one method to remember, Vedic Math provides
several methods for each arithmetic operation. We must
understand each method clearly, and apply accordingly.
X
X
X
X
Summing digits across different columns, rather than across
a single column. This usually happens when the numbers
are not written in an organized manner, most common in real
world situations.
X

33
Another question that is likely to arise is, how to choose among
the different Vedic Math techniques when faced with a problem.
You have learnt three methods of adding numbers - the
Column-less method, the Two-Digit method and the Three-Digit
method. Should you choose any of these methods for a
particular sum, or stick with the Conventional method? Or
chuck them all and pull out the calculator?
You will ﬁnd the answer to this question yourself, when you
have given the Vedic Math techniques a fair share of practice,
and attention.
Attempt some real world problems using these methods in the
following chapter.

35
Real world problems
One of the aims of this book is to make math easy to apply in
day-to-day situations when a calculator, or a paper and pen are
not available. This could be in the grocery store, or while paying
the bill in the restaurant, or while collecting change from the
pizza delivary guy. For the Vedic Math techniques to become
second nature, practice is necessary.
Answer the following real-world questions, using the techniques
you have learnt in the previous chapters. You will soon see, that
you don’t need to perform the entire addition, and from the
Units column as well, in most cases. Answers are provided in
Chapter 6.
Irresponsible clerk
John visited the medical diagnostic centre, and had a few x-
rays taken. While clearing the bill, the receptionist’s computer
crashed and she had the clerk make the bill manually. John has
a feeling the clerk has made an error while summing the
ﬁgures. Check to see if John is right!
Click for solution

36
The Woodchucks
The Woodchucks may have won the 2014 wood chucking
competition. The Iron Ladies chucked 1500 kg, a record in
itself. The data entered by the referees is given below. Did the
Woodchucks win?
Concluding remarks
You have now completed learning Addition in Vedic Math. You
learnt the Column-less method which can be used to sum any
column independently of the other columns, as well as the Two-
Digit and Three-Digit methods with which you can sum
numbers from Left to Right.
All of these methods can be explained using Algebra. In fact
Algebra is the foundation on which Vedic Math can be built. If
you are familiar with Algebra, try proving the Vedic Math
techniques using Algebra.
Use these methods in your day to day situations, and you will
improve with practice. You will ﬁnd that the other books in this
series, viz. Vedic Subtraction, Vedic Multiplication and Vedic
Division will assist you in doing other mental calculations in real
world situations.
Click for solution

38
Answers to exercises in Chapter 3
Here are solutions to the exercises on the Two-Digit Method of
addition.
5 7
1 7
4 7
3
+ 2 6 3 9
0 7 7 8 2
4 1
3 5
5 5
8
+ 7 2 0 9
1 1 5 6 7
7 8
6 8
5 2
8
+ 1 2 7 9
0 8 9 3 7
3 0
0 1
9 6
2
+ 7 1 7 4
1 0 2 6 6
6 1
8 2
0 3
2
+ 5 4 1 6
1 2 2 3 8
4
9 7
3 0
2
+ 4 8 7 6
0 5 8 0 8
3 4
0 4
2
5 7 3
4 2 6
+ 2 5 8
1 5 5 9
7 7
5 3
6
1 2 2
9 2 3
+ 4 0
1 8 4 1
14
27
46
5 + 3529 = 04774
45
43
23
7 + 1903 = 06340
13
2.5
50
4 + 23.56 = 036.10
48
5.0
98
5 + 45.95 = 091.90
8.1
63
98
5 + 3.795 = 12.490
31
4.2
50
0 + 88.50 = 123.00

39
Here are solutions to the exercises on the Three-Digit Method
of addition.
3 07
6 79
7
+ 4 3 7
0 0 8 0 4
1 09
4 01
5
+ 8 7 4
0 1 0 1 9
3 11
4 16
2 69
5
+ 8 2 7 8
0 1 1 7 0 3
1 01
3 16
0 69
4
+ 3 9 8
0 0 1 7 0 2
2 06
5 69
7
1 2 8
+ 3 2 3
0 0 7 0 8
2 09
3 03
9
7 8 5
+ 2 3
0 1 0 4 7

40
Here are solutions to the exercises on Real World problems
Irresponsible clerk
The clerk has indeed made an error. Add the balance column
starting from the left. 2+2 gives 04, with the ‘4’ carried over to
the tens column. In the Tens column we see there is a 4 and 8,
which is greater than 10. Hence, the Hundreds digit now
becomes 5. However, the clerk has mentioned the Total
Balance as 443, which is a mistake.
The Woodchucks
Summing the Hundreds column, we get 14. The ‘4’ is carried
over tot he Tens column. Summing the Tens column, we get
42+7+4+1 which exceeds 50. Hence, it is clear the
Woodchucks have won!

xlii
References
Glover, J., T. (2002) “Vedic Mathematics For Schools, Book 1”,
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi.
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi.
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi. 14
Gupta, A. (2006) “The Power of Vedic Maths – For Admission
Test, Professional & Competitive Examinations”, Jaico
Publishing House, India.
Jagadguru Swami Bharathi Krishna Thirthaji Maharaja (1992)
“Vedic Mathematics”, Motilal Banarsidass Publishers Pvt. Ltd.,
New Delhi.

Vedic addition

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