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Navasesh

Navasesh is a general method of verification formulated in Vedic mathematics. This can be used to verify various mathematical operations such as Addition, Subtraction, Multiplication etc.

Navasesh means ' nine and its remainder '.

Examples :

Navasesh of 23 ---> N(23) == N(2+3) == N(5) == 5

Navasesh of 82 ---> N(82) == N(8+2) == N(10) == N(1+0) == N(1) == 1

Navasesh of 49 ---> N(49) == N(4+9) == N(13) == N(1+3) == N(4) ==4

Navasesh of 105 ---> N(105) == N(1+0+5) == N(6) == 6

Addition

We know that 23 + 82 = 105

To verify :

N(23) + N(82) = N(5) + N(1) == N(5+1) == N(6) == 6

N(105) = N(6) == 6

Hence N(23) + N(82) = N(105)

Subtraction

We Know that 82 - 49 = 33

To verify :

N(82) - N(49) = N(1) - N(4) = N(1-4) == N(-3) == N(9-3) == N(6) == 6

( Note that -3 here has been converted to 9-3 such that negative number is eliminated)

N(33) = N(3+3) == N(6) == 6

Hence N(82) - N(49) = N(33)

Multiplication

We know that 23 * 49 = 1127

To verify :

N(23) * N(49) = N(5) * N(4) ==N(5 * 4) ==N(20) = N(2) =2

N(1127) = N(1+1+2+7) = N(11) = N(2) =2

Hence N(23) * N(49) = N(1127)

Sutra : Yaavadunam Taavaduunikruthya vargam cha yogayet

Meaning : Whatever the extent of its deficiency, lessen it further to that very extent; and also set up the square of that deficiency.

This sutra is a corollary of the Nikhilam sutra.

Consider a simple example 9²

Step 1 : Consider the nearest base (here 10).

Step 2 : As 9 has a deficiency of 1 (10 - 9 = 1), we should decrease it further by 1, and set down our LHS of the Answer as '8'.

Step 3 : On the RHS put the square of the deficiency (here 1).

we get 9² = 81.

Now Consider 102

1) Base is 100

2) Deficiency is '-2' (100 - 102 = -2)

Therefore we subtract '-2' from 102

102 - (-2) = 104

This is our RHS

3) Our LHS now becomes (-2)² which is 4

Since the base is 100 we write it as '04', so that we get 102² = 10404

If we have multiples or sub multiples of a base, we employ the same technique as in 'Aanurupyena'. (See Nikhilam Multiplication)

Consider 28²

1) Let 20 be the Working Base and 10 as the Main Base.

Therefore x = (Main Base)/(Working Base) = 10/20 = 1/2

2) Here the deficiency = 20 - 28 = -8

Therefore RHS = 28 - (-8) = 36

Divide by x i.e. by (1/2).

We get 36/(1/2) = 72. This is the required RHS.

3) LHS = (-8)² = 64

Since Main Base is 10, we put only '4' on the LHS and carry over '6' to the RHS

Therefore we get

28² = 72+6 | 4 == 784

Some More Examples

36² = 128 |₁ 6 = 1296 (Base = 40)

522 = 27 | 04 = 2704 (Base = 50)

9972 = 994 | 009 = 994009 (Base = 1000)

10042 = 1008 | 016 = 1008016 (Base =1000)

Meaning : "By one more than the previous one"

This sutra is used exclusively for numbers ending with 5.

For numbers ending with 5 the LHS will be 25.

The RHS will be the product of the other digits with its ekadhikena.

Examples :

25² = (2 * 3) | 25 = 625

35² = (3 * 4) | 25 = 1225

45² = (4 * 5) | 25 = 2025

55² = (5 * 6 ) | 25 = 3035

65² = (6 * 7) | 25 = 4225

75² = (7 * 8) | 25 = 5625

105² = (10 * 11) | 25 = 11025

125² = (12 * 13) | 25 = 15625

175² = (17 * 18) | 25 = 30625

Direct Cubing

This method is simple and easy.

If the number is (ab) its cube can be calculated as

a³ a²b ab² b³

2a²b 2ab²

Sum them up taking care of the carryovers.

Consider (16)³

Writing it as above

1 6 36 216

12 72

1 18 108 216

Considering the carryovers

                   1  0  0  0                          1  8  0  0                          1  0  8  0                               2  1  6                         4  0  9  6

Therefore we get the answer as 4096

Is it divisible by four?

This little math trick will show you whether a number is divisible by four or not.

So, this is how it works.

Let's look at 1234

Does 4 divide evenly into 1234?

For 4 to divide into any number we have
to make sure that the last number is even

If it is an odd number, there is no way it will go in evenly.
So, for example, 4 will not go evenly into 1233 or 1235

Now we know that for 4 to divide evenly into any
number the number has to end with an even number.

Back to the question...

4 into 1234, the solution:

Take the last number and add it to 2 times the second last number

If 4 goes evenly into this number then you know that 4 will go evenly into the whole number.

So
4 + (2 X 3) = 10
4 goes into 10 two times with a remainder of 2 so it does not go in evenly.

Therefore 4 into 1234 does not go in completely.

Let?s try 4 into 3436546

So, from our example, take the last number, 6 and add it to
two times the penultimate number, 4

6 + (2 X 4) = 14
4 goes into 14 three times with two remainder.
So it doesn't go in evenly.

Let's try one more.

4 into 212334436

6 + (2 X 3) = 12
4 goes into 12 three times with 0 remainder.

Therefore 4 goes into 234436 evenly.

So what use is this trick to you?
Well if you have learnt the tutorial at Memorymentor.com about telling the day in any year, then you can use it in working out whether the year you are calculating is a leap year or not.

Multiplying by 12 - shortcut

So how does the 12's shortcut work?
Let's take a look.

12 X 7

The first thing is to always multiply the 1 of the twelve by the
number we are multiplying by, in this case 7. So 1 X 7 = 7.

Multiply this 7 by 10 giving 70. (Why? We are working with BASES here.
Bases are the fundamentals to easy calculations for all multiplication tables.
To find out more check out our Vedic Maths ebook at www.vedic-maths-ebook.com

Now multiply the 7 by the 2 of twelve giving 14. Add this to 70 giving 84.

Therefore 7 X 12 = 84

Let's try another:

17 X 12

Remember, multiply the 17 by the 1 in 12 and multiply by 10
(Just add a zero to the end)

1 X 17 = 17, multiplied by 10 giving 170.

Multiply 17 by 2 giving 34.

Add 34 to 170 giving 204.

So 17 X 12 = 204

lets go one more

24 X 12

Multiply 24 X 1 = 24. Multiply by 10 giving 240.
Multiply 24 by 2 = 48. Add to 240 giving us 288

24 X 12 = 288 (these are Seriously Simple Sums to do aren?t they?!)

Converting Kilos to pounds

In this section you will learn how to convert Kilos to Pounds, and Vice Versa.

Let?s start off with looking at converting Kilos to pounds.
86 kilos into pounds:

Step one, multiply the kilos by TWO.
To do this, just double the kilos.

86 x 2 = 172

Step two, divide the answer by ten.
To do this, just put a decimal point one place in from the right.

172 / 10 = 17.2

Step three, add step two?s answer to step one?s answer.

172 + 17.2 = 189.2

86 Kilos = 189.2 pounds

Let's try:

50 Kilos to pounds:

Step one, multiply the kilos by TWO.
To do this, just double the kilos.

50 x 2 = 100

Step two, divide the answer by ten.
To do this, just put a decimal point one place in from the right.

100/10 = 10

Step three, add step two's answer to step one's answer.

100 + 10 = 110

50 Kilos = 110 pounds

Adding Time

Here is a nice simple way to add hours and minutes together:

Let's add 1 hr and 35 minutes and 3 hr 55 minutes together.

What you do is this:
make the 1 hr 35 minutes into one number, which will give us 135 and do
the same for the other number, 3 hours 55 minutes, giving us 355

Now you want to add these two numbers together:

135
355
___
490

So we now have a sub total of 490.

What you need to do to this and all sub totals is
add the time constant of 40.

No matter what the hours and minutes are,
just add the 40 time constant to the sub total.

490 + 40 = 530

So we can now see our answer is 5 hrs and 30 minutes!

Community Contributions - Articles by goIITians

Is it divisible by four?

Multiplying by 12 - shortcut

Converting Kilos to pounds

Adding Time