Mental Arithmetic Tricks Part-III

8/9/2019 Mental Arithmetic Tricks Part-III

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Vedic mathematics is the name given to the ancient system of

mathematics

Its a unique technique of calculations based on simple principles

and rules , with which any mathematical problem - be it arithmetic,algebra, geometry or trigonometry can be solved mentally

Instant calculations

All from 9 and the last from 10 to perform substractions.

e.g.1000-457=543

VERTICALLY AND CROSSWISE you dont need to the

multiplication tables beyond 5x5.

e.g. 8x7;7x6

VERTICALLY AND CROSSWISE to write the answer straight

down!

e.g.

Multiply crosswise & add to get the numerator, & multiply the

denominators to get the denominator.


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Multiplying a number by 11.

e.g.26 x 11=286;77x11=847;

i)we put the total of the 2-figures between the 2-figures;

Method for diving by 9.

e.g.43/9=4;232/9=25,(r.2+3+2=7)

i)The first figure of 43 is 4=>the answer

ii)Reminder 43=>4+3=7

Multiplying by 12

e.g. 12 X17;

i)We multiply the 1(of12)by the number were multiplying =>1x17=17;

ii)Then => 17x10=170;

iii)Multiply the 2x17=34;

iv)Add 170 +34=204


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Effect

You write down the following 8 digit number on a piece of paper:

1 2 3 4 5 6 7 9

Then ask a friend to circle one of the digits. Say that they circle

number 7.

You then ask your friend to multiply the 8 digit number by 63, and

magically the result ends up being:

1 2 3 4 5 6 7 9

x 6 3

7 7 7 7 7 7 7 7 7

with the answer as a row of the chosen number 7.

The Secret

When your friend circles a number, you need to multiply the

chosen number by 9 in your head - if 3 was chosen you would

work out 3 x 9 = 27. Then you need to ask your friend to multiply

the 8 digit number by the number you have just worked out. In the

case of 3 being chosen you ask your friend to multiply 12345679

by 27 and you magically get the answer 333333333.

Use one symbol to make the expression true

VEDIC MATHEMATICS : Digital Roots/Sums

Digital rootof a number is the single digit obtained by

repeatedly summing all the digits of a number.

Example:

Digital root of 2357 = 8

because (2 + 3 + 5 + 7 = 17) and (1 + 7 = 8)


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Digital root of 89149 = 4

because (8 + 9 + 1 + 4 + 9 = 31) and (3 + 1 = 4)

A number is divisible by 3 if its digital root is divisible by 3

(that is, it is 0, 3, 6, or 9).

1236 is divisible by 3 because 3 is divisible by 3.

Note (1+2+3+6 = 12) and (1+2 = 3).

Recall: 1x(999+1) + 2x(99+1) + 3x(9+1) + 6

A number is divisible by 9 if its digital root is divisible by 9(that is, it is 0 or 9).

The digital root of a number is the remainder obtained by dividing it

by 9.

1236 divided by 9 = R 3

Recall: 1x(999+1) + 2x(99+1) + 3x(9+1) + 6

Note that 9 is treated similar to 0.

36 divided by 9 = R 0

Digital roots can be calculated quickly by casting out 9s.

12173645 => (1+2+1+7+3+6+4+5)

= (2+9) = (1+1) = 2

12173645 => (1+1)=2


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VEDIC SQUARE

Table of digital root of single digit product

Digital root pattern for 4x1 x 4 = 4

2 x 4 = 8

3 x 4 = 3

4 x 4 = 7

5 x 4 = 2

6 x 4 = 6

7 x 4 = 1

8 x 4 = 5

9 x 4 = 9

Prasad Digital Roots 8

Properties of digital roots

Digital root of asquareis 1, 4, 7, or 9

Digital root of aperfect cubeis 1, 8 or 9
http://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Perfect_cubehttp://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Square_numberhttp://en.wikipedia.org/wiki/Perfect_cubehttp://en.wikipedia.org/wiki/Perfect_cubehttp://en.wikipedia.org/wiki/Perfect_cubehttp://en.wikipedia.org/wiki/Perfect_cubehttp://en.wikipedia.org/wiki/Square_number


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Digital root of aprime number(except 3) is 1, 2, 4, 5, 7, or 8

Digital root of apower of 2is 1, 2, 4, 5, 7, or 8

Justification for digital roots of a prime number

Recall that digital root of 3, 6, or 9 implies it is divisible by 3.

The digital root of 1, 2, 4, 5, 7, and 8 are realizable by the prime

numbers 19, 2 (11), 13, 5 (23), 7 (43), and 8 (17), respectively.

This is a necessary(but not sufficient) condition for a numberto be prime.

Additive Persistence of a Number

Additive persistence of a numberis the number of steps required

to reach the digital root.

Additive persistence of 52 = One,

because (5 + 2) =One=> (7)

Additive persistence of 5243 = Two,

because (5 + 2 + 4 + 3) =One=> (14) =Two=> (5)

The smallest number for additive persistence 0 through 4 are:

0 step => 0

1 step => 10

2 steps => 19

3 steps => 199

4 steps => 19999999999999999999999

19999999999999999999999
http://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Prime_numberhttp://en.wikipedia.org/wiki/Power_of_twohttp://en.wikipedia.org/wiki/Power_of_twohttp://en.wikipedia.org/wiki/Power_of_twohttp://en.wikipedia.org/wiki/Power_of_twohttp://en.wikipedia.org/wiki/Prime_number


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4 steps => 1999999999999999999999

(22 9s + 1)

5 steps => 1 followed by

(quotient19999999999999999999998

divide 9) 9s

=> 1 followed by

2222222222222222222222 9s

How big is the last number?

Larger than the number of stars in the universe?

10^21 (10 followed by 21 zeros)

YES.

Larger than the number of atoms in the universe?

10^80

YES.

Larger than googol 10^100?

YES.

Larger than googolplex 10 followed by10^100 0s?

NO, we have at last found a match!

Lattice Multiplication


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Answer = 264

0

2

2

2

0

2

1

4

02

0

4

46

2

0

Answer = 2958

3

4

8

7

24

3

2

21

2

8

85

9

2


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This number 3816547290 has the required uniqueproperty of being divisible by 10,9,8,7,6,5,4,3,2,1 by

striking off the right most digits successively i.e. remove 0,it is divisible by 9, remove 7290 it is divisible by 6 (that is

the number of digits remaining in the number) and so on.3816547290 divisible by 10381654729 divisible by 938165472 divisible by 83816547 divisible by 7381654 divisible by 638165 divisible by 53816 divisible by 4381 divisible by 338 divisible by 23 divisible by 1There are two known solutions using all nine digits for

1738 x 4 = 69521963 x 4 = 7852Three more 1 to 9 puzzles, each number is twice the previous one and the series

uses only 1 to 9 once.

219, 438, 657273, 546, 819327, 654, 981

1729 = 13+123 = 93+1031729 is the smallest number that can be expressed as the sum of two cubes in 2

distinct ways. Such numbers have been dubbed taxicab numbers.

Strange ways!

13= 12

13+ 23= (1 + 2)2

13+ 23 + 33 = (1 + 2 +3)2

13+ 23 + 33 + 43 = (1 + 2 +3 +4)2

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Mental Arithmetic Tricks Part-III