9765438213 * 98785615624 Make it easy !!!!

I don't know why on this milky way I am writing this post..... As I am neither erudite nor good at playing with numbers, but still I give a try... May be this post serves as trinket for those who don't brook calculator for holy calculations :) ..... But for the ppl who are preparing for some option based examination may be this post can add some thing into their cerebral circles.... I could not gather from where I have got these tricks , may be its plagiarized( Sorry for the Plagiarism), but if some one in my circumference crawls here.. Its kinda enlightenment (also I admit as no one will look here because they all are GODS of their own class)
Any way i wont consume much bytes and will start

1. Faster Multiplication

Suppose you have to multiply two 2 digit no's . If both the numbers have same Ten's digit the ideal way is to choose the suitable base. (Base can you on one's choice)

e.g
MULTIPLY
82
*85

(As both the numbers have same Ten's digit i.e '8' , and now to choose the base , we can choose the base depending upon the convenience lets choose the base as 80

Hence 82 can be written as 80 + 2 and 85 can be written as 80 + 5

Now trick
Step 1
82 + 2 (why + 2 , because we have chosen base as 80 and the given number is 82(80+2) and 85 + 5 (why + 5, because we have chosen base as 80 and the given number is 85(80+5)


Step 2
Cross Addition i.e either Add 82 + 5 OR 85 + 2 in both case the result is 87 ------(i)

Step 3
Now Multiply (i) with the base chosen i.e 80 hence 87 * 80 = 6960-----------(ii)

Step 4
Multiply + 2 with + 5 i.e +10 ------------ (iii)

Step 5
Now add ii and iii
i.e 6960 + 10 = 6970 is the result

||ly lets do multiplication of 108 with 98

Choose the base lets choose 100 as the base
So with respect to 100 base, 108 can be written as 100 + 8 and 98 can be written as 100 - 2

there fore
108 +8 ( 100 + 8 ) 98 -2 (100 - 2 )

Step 1
108 +8 (why +8 , because we have chosen base as 100 and the given number is 108(100+8) and 98 -2 (why -2, because we have chosen base as 100 and the given number is 98(100-2)

Step 2
Cross Addition i.e either Add 108 + (-2) OR 98 + 8in both case the result is 106 ------(i)

Step 3
Now Multiply (i) with the base chosen i.e 100 hence 106 * 100 = 10600-----------(ii)

Step 4
Multiply +8 with -2 i.e -16 ------------ (iii)

Step 5
Now add ii and iii
i.e 10600 + (-16) = 10584 is the result

2 .Square of a Number Less then Hundred

For this you have to mug up the Squares of Number less than equal to 25.

• Square range 26 to 49 The Formula is 25 - (50 - N) .(50 -N)^2 (Remember . is not decimal, its concatenation operator, you can see the usage of it while solving the square of the numbers) Lets take 27 square so directly use the formula N = 27 therefore 25 - (50 - 27).(50-27)^2 = > 25 - 23 . (23)^2 => 02. 529 => now add the Hundredth digit(5) of 529 to 02 i.e 7.29 hence the square of the number is 729. ||ly you can use the above formula to get the square of any number between that range.
  
• Square range 51 to 74 .The Formula is 25 + (N - 50). (N - 50) ^2 ( Remember . is not decimal, its a concatenation operator, you can see the usage of it while solving the square of the numbers). Lets calculate 68 Square . Use the direct Formula N = 68. therefore 25 + (68 - 50).(68-50)^2=> 25 + 18 . (18)^2 => 43.324 => Now add the hundredth digit (3) of 324 to 43 hence 43 +3.24 => 4624 is the Answer
  
• Square range 76 to 99. The Formula is N - (100-N).(100-N)^2 =>Lets calculate the square of the 84 . Hence 84 - (100 - 84).(100-84) ^2 => 84 - 16 . 256 => 68.256 => Now add the hundredth digit (2) of 256 to 68 , hence the it becomes 68+2.56 => 7056 is the answer
  

3. Squares of Numbers greater than 100 and less than 199

• Lets take 124*124
  124 + 24 . 24 *24 (Remember . is again not the decimal point, it's a concatenation operator) Now let me radiate few energy particles how I derived the above figure.
  

1. In case of finding the square of number greater than 100 but less than 199, choose the original three digit no(124) add to its last two digit number (24)! 124 + 24 = 148 ---(i)
2. Now square the last two digits of the numbers in this case its 24 * 24 = 576 -------(ii)
   
3. Now club i and ii, in such a way that the hundredth digit of ii gets added to i hence 148+5.76 => 153.76
4. Hence the answer is 15376 :)

• Lets take 156*156
  

156+56.56*56 (Remember . is again not the decimal point, it's a concatenation)

156+56 = 212.3136 => add the Thousand and Hundredth digit( 31) to 212 i.e212 + 31 . 36=>243.36 hence the answer is 24336


4. Any Number multiplied by 9

• If any number is multiplied by 9, here is the trick

Lets say 76 * 9
Add 0 to end of the multiplicand i.e 760 and now subtract the original multiplicand (76)from the number thats has been modified by adding the 0 at the end(760 ) hence 760 - 76 = 684 and 684 is the answer

Lets take another number e.g 15678 * 9
Add 0 to the end of the multiplicand hence the number becomes 156780 and now subtract the original multiplicand (15678) from the number that has been modified by adding 0 at the end(156780) hence 156780 - 15678 = 141102. Answer


Isn't it Great????


5. Any number multiplied by 99... series

1. Lets take 765 * 999 (In which both the numbers have same digits)
765-1. 999-764 (Remember . is not decimal its a concatenation operator)
Step 1
Let me expand how i derive the above one, Any number which we are going to multiply with 999 series. Subtract 1 from that number hence in that case the given number is 765 and hence the new number formed is 765-1 = 764 ------- i
Step 2
Now subtract ( i) from 99 series number , (99 series is nothing but 9, 99, 999, 9999 ...) in this case the number given is 999 . Therefore 999- 764 = 235 ------- ii
Step 3
Concatenate i and ii hence the answer is 764235
||ly you can take try numerous examples.

2. Lets take 8723 * 999 ( In which the Number of digits of 99 series number is less than the multiplicand)
Step 1.
Same as above one hence 8723 - 1 = 8722--------i
Step 2
Now subtract ( i) from 99 series number , (99 series is nothing but 9, 99, 999, 9999 ...) in this case the number given is 999 . Therefore 999- 8722= (-8)277(why -8 because the 99 series is three digit number ------- ii
Step 3
Concatenate i and ii if any carry forward is there then add to the i , in this case the carry forward is -8 hence 8722+(-8).277 = 8714277 is the answer

3. Lets take 759 * 9999 ( In which the number of 99 series digit is greater than the multiplicand)

Step 1:
Same as above one i.e 759 - 1 = 758 ------ i
Step 2:
Now subtract ( i) from 99 series number , (99 series is nothing but 9, 99, 999, 9999 ...) in this case the number given is 9999 . Therefore 9999- 0758= 9241( In this case the last three digits will form the last three digits of the multiplication answer) ------- ii
Step 3:
Concatenate i and ii, in this case 9 is the carry forward, so rather than adding it to i , it will be concatenated to i i.e 7589.241. hence the answer is 7589241

Will post the next series of faster mathematics soon.

From
Abhit