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# Mathematics-BASIC

2. Subtraction

3. Multiplication

4. Division

[ Special thanks to Vedic Maths ]

( 1 ) :: -  In the case of instant subtraction method, we have to subtract all digits except the last digit from 9, and the last digit subtracted from 10 to get the correct result.

For example 1000 - 357 = 643

We simply take each figure in 357 from 9 and the last figure from 10.

1000       -     3          5             7
|           |              |
From 9      From 9      From 10
ans
=     6           4            3

So the answer is 1000 - 357 = 643

Similarly 10,000 - 1049 = 8951

10,000         -           1           0             4             9

From 9   From 9     From 9    From 10
|
|               |               |
=           8          9             5              1

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

( 2 ) ::- Using the vertically and Crosswise, we have to multiply the 2 numbers easily. Here is the steps

Suppose you need 7 x 6
7 is 3 below 10 and 6 is 4 below 10.
Think of it like this:

7           3

6           4
_______

The diagram below shows how you get it.

7            3
x     |
6           4
_________
3 + 1    2
You subtract crosswise 7- 4 or 6 - 3 to get 3,  the first figure of the answer.  And you multiply vertically: 3 x 4 to get 12, and this carry 1 in 12 is added to 3 and we get 4. So the final answer is 42.

(3) Using the above method, Vertically and Crosswise, we have to multiply numbers which close to 100. Below shows how to carried out that in simple manner

If you want to multiply 87 * 96

87    -13
*
96     -4
_______
83     52

So answer is 8352. How we get that, first you have to subtract 13 from 96 and 4 from 87. In both cases you will get same answer. right?. Yes. So in the next step you have to multiply 13 and 4 in regular manner. So answer is 52. When we concatenate the both number we will get the answer , ie. 8352.

( 4 ) How to multiply the numbers just over 100

eg 1 ) 105 * 108 = 11340

first step = ( 105 + 8 ) = 113

second step = ( 8 * 5 ) = 40

eg 2 ) 102 * 107 = 10914

first step = ( 102 + 7 ) = 109

second step = ( 2 * 7 ) = 14

( 5 ) Another method depicts how to squares the number that ends in 5 , using the formula called By One More Than The One Before.

852 = 7225
here I explain the steps from the answer.
=> first step is divide the answer into 2 equally parts, here 72 & 25

=> last value is always 25 ( 5 * 5 = 25 )

=> So find out the first value is tricky method. ie., 8 in the question's 10th place digit value is multiplied with the value just 1 more than its value, ie here 9. So 8 * 9 = 72

So final step proofs the result 7225

( 6 ) Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
eg 1 ) 32 * 38 = 1216

=> step1 is multiplying the last digits 2 * 8 = 16

=> step 2 is multiplying first digit with 1 more than its value, ie here 4. So 3 * 4 = 12

=> So final answer is 1216

( 7 ) Another multiplication method.

2          4  *

2          5
__________________
4    18    20                     = 600

So you all know answer is 600. But how to get this through this method.
we have to take only 1 digit from group and remaining digit is added to just near the digits. So here 2 is added to 18 and we will get 20. Then 2 is added to last digit 4 . So we will get the final answer 600

=> step1 <=> from 20 we take 0

=> step2 <=> 2 + 18 is 20 , then we again take 0 from 20, that is not the first 20.\

=> Last we added the remaining 2 to 4 and we get 6

=> so final answer is 600

( 8 ) :: - Another one is just like funny method. Multiplication with 11 ( 2 digit multiplication )

eg 1 ) 67 * 11 = 737

=> step 1 is take 6 & 7 from 67 and write it like this ( 6        7 )

=> step 2 is adding 6 and 7, we will get 13. So put this value in the middle of first step value. ie ( 6  13  7 )

=>step 3 is 1 from the 13 is added to 6 and we get 7, the last digit of final value

=> so final answer is ( 6+1  3   7 ) <=> ( 737 )

eg 2 )
26 * 11 = 286

=> step 1 is 2 & 6 is placed left and right.

=> then put sum of 2 & 6 in middle of that.

=> we get 286  