Make Maths EZEE : 10 Steps

I have a big fan of MATHS and in my 15 years of life till now I have learnt some tricks from various book of vedic maths and few I found out myself .I want to share some 8 tricks that I remember................Hope you will like them .............

Step 1: Vedic Maths

WHAT IS Vedic maths?

"Welcome to the wonderful world of "Vedic" mathematics, a science that its founder claims was lost due to the advent of modern mathematics. Vedic mathematics is said by its founder to be a gift given to this world by the ancient sages of India, though there is no historical evidence whatsoever for this claim. It is a system for limited arithmetic and polynomial calculation which is simpler and more enjoyable than the equivalent algorithms of modern mathematics." this description is taken from Wikipedia.

Step 2: Squaring a Numbers Ending in 5

Multiply the first digit from left with digit + 1 and write 25 beside it.........

Thus 25 = 2 X 3 / 25 = 625.

In the same way,

35 = 3 X (3+1) /25 = 3 X 4/ 25 = 1225;

65 = 6 X 7 / 25 = 4225;

105 = 10 X 11/25 = 11025;

135 = 13 X 14/25 = 18225;

Step 3: Multiplying by 11

Multiplying by 11[edit]

Working from right to left

for 627 * 11

first write the digit 7 (right most) then (7+2) after that (6+2) then write 6 (left most digit)

6,(6+2),(7+2),7 = 6,8,9,7

thus ,

627 * 11 = 6897

Step 4: Multiplying by 5

This is a simple one , and most people can figure it out by themselves...........But still I will show it.....

eg. 5 * 46

we can easily find it out by dividing 46 by 2 and then add a zero

that is 230

for decimal

5 * 4.62

we will have to dividing it with 2 and then sifting the decimal one step right

2/ 4.62 = 2.31

and answer is 23.1

Step 5: Multiplying by 15

Multiplying by 15 can be broken down into a multiplication by 10 plus a multiplication by 5.

Multiplication with 10 can easily be done by putting a 0 at the end and multiplication with 5 is shown in the last step........

345 * 15 = 3450 + 1725 = 5175

Step 6: Vulgar Fractions Whose Denominators Are Numbers Ending in NINE :

First we recognize the last digit of the denominator of the type 1 / a9. Here the

last digit is 9.

For a fraction of the form in whose denominator 9 is the last digit, we take the case of 1 / 19 as follows: For 1 / 19, 'previous' of 19 is 1. And one more than of it is 1 + 1 = 2. Therefore 2 is the multiplier for the conversion. We write the last digit in the numerator as 1 and follow the steps leftwards.

Step. 1 : 1 12

Step. 2 : 21(multiply 1 by 2, put to left)

Step. 3 : 421(multiply 2 by 2, put to left)

Step. 4 : 8421(multiply 4 by 2, put to left)

Step. 5 : 168421 (multiply 8 by 2 =16, 1 carried over, 6 put to left)

Step. 6 : 1368421 ( 6 X 2 =12,+1 [carry over] = 13, 1 carried over, 3 put to left )

Step. 7 : 7368421 ( 3 X 2, = 6 +1 [Carryover] = 7, put to left) Step. 8 : 147368421 (as in the same process)

Step. 9 : 947368421 ( Do – continue to step 18)

Step. 10 : 18947368421

Step. 11 : 178947368421

Step. 12 : 1578947368421

Step. 13 : 11578947368421

Step. 14 : 31578947368421

Step. 15 : 631578947368421

Step. 16 : 12631578947368421

Step. 17 : 52631578947368421

Step. 18 : 1052631578947368421

Now from step 18 onwards the same numbers and order towards left continue.

Thus 1 / 19 = 0.052631578947368421

Step 7: All From 9 and the Last From 10

The formula can be very effectively applied in multiplication of numbers, which

are nearer to bases like 10, 100, 1000i.e., to the powers of 10 . The procedure of multiplication using the Nikhilam involves minimum number of steps, space, time saving and only mental calculation. The numbers taken can be either less or more than the base considered. The difference between the number and the base is termed as deviation. Deviation may be positive or negative.

Step 8: Multiplying Single Digit No.

Now the base is 10.

Since it is near to both the numbers,

7 we write the numbers one below the other

Take the deviations of both the numbers from the base and represent _ the minus sign before the deviations

7 -3

8 -2

remainders 3 and 2 implies that the numbers to be multiplied are both less than 10

The product or answer will have two parts, one on the left side and the other on the right. A vertical or a slant linei.e., a slash may be drawn for the demarcation of the two parts i.e.,

The R.H.S. of the answer is the product of the deviations of the numbers. It shall contain the number of digits equal to number of zeroes in the base. _ i.e.,

7 3

8 2

(3x2) = 6

Since base is 10,

6 can be taken as it is.

L.H.S of the answer is the sum of one number with the deviation of the other. It can be arrived at in any one of the four ways.

i) Cross-subtract deviation 2 on the second row from the original number7 in the first row i.e.,

7-2 = 5.

ii) Cross–subtract deviation 3 on the first row from the original number8 in the 20 second row (converse way of(i)) i.e.,

8 - 3 = 5

iii) Subtract the base 10 from the sum of the given numbers. i.e.,

(7 + 8) – 10 = 5 iv)

Subtract the sum of the two deviations from the base. i.e.,

10 – ( 3 + 2) = 5

Hence 5 is left hand side of the answer.

_Thus

7 3

8 2

‾‾‾‾‾‾‾‾‾‾‾‾

5 /

remember the first valve we found 6 and the second value is 5

so the result is 56

Step 9: Multiplying (54364576658736326353*99999999999999999999)

That seem tough, but it is not...

notice that both have 19 digit .....

this process is valid only when no. of. digit are equal and the second digit has only nine repeated.

lets start with a simple one 5245 * 9999

on the right sides write the number by following the "All from 9 and the last from 10" rule or subtract the (first number) from (second number + 1)..........

10000 - 5245 = 4755

"All from 9 and the last from 10" is a easier method for finding it..........

now subtract 1 from the first number that is

5245 - 1 = 5244

placing them one after the other

5244 4755

5245 * 9999 = 52444755

try out 54364576658736326353*99999999999999999999 on your own

LOGIC/REASON

5245 * 9999

= 5245 * (10000 - 1)

= 52450000 - 5245