Singleton.

Singleton
Singleton of a number is a single digit number which you get after adding all the digits of that number , if the resultant is not a single digit number than you again add it back.
Ex :
Singleton(23453) = 2+3+4+5+3 = 17 => 1+7 => 8
Singleton(343) = 3+4+3 = 10 => 1 + 0 => 1
Singleton(534533256) = 9 or 0
Note : While calculating the Singleton , you can banish those numbers which add up to 9 , Remember : Singleton(9+x) = Singleton(x)
So when you find Singleton(918754) , you can ignore
– 9
– 8 and 1
– 4 and 5
so , you are left with 7 , which is the Singleton

Multiplication of numbers with a series of 1’s.

Multiplication of Numbers with a series of 1’s

11, 111, 1111 etc.

It will require some practice to get mastery. Take different numbers and practice. Practice makes the man perfect.

 

32 x 11	First we write the right hand most digit ‘2’ as it is	2
	Next, we add 2 to the number in left 3 ( 2 + 3) i.e. (Unit + tens)	5
	Last we write the left hand most digit 3 as it is	3
Ans		352
43 x 11	First we write the right hand most digit’3’ as it is	3
	Next, we add 3 to the number in left 4 (4 + 3) = 7 i.e. (Unit + Tens)	7
	Last we write the left hand most digit 4 as it is	4
Ans		473
64 x 11		4
	6 + 4 = 10 write 0 and carry 1	0
	6 + 1 (carried)	7
Ans		704
652 x 11	We write down the last digit as it is	2
	Next, we add 2 to 5 and make it 7 (Unit + Tens)	7
	Next, we add 5 to 6 to get 11. Write 1 and carry 1 ( tens + Hundreds)	1
	Last we take 6 and add carried number to get 7	7
Ans		7172
3102 x 11	W write down 2 as it is	2
	We add 2 to 0 and make it 2 (U + T)	2
	We add 0 to 1and make it 1 (T + H)	1
	We add 1 to 3 and make it 4 ( H + TT)	4
	We write the first digit 3 as it is	3
Ans		34122
201432 X 111	We write down 2 as it is	2
	We move to the left and add (2 + 3 ) U + T)	5
	We move to the left and add ( 2 + 3 + 4) ( U + T + H)	9
	We move to the left and add (3 + 4 + 1)  (T + H + T)	8
	We move to the left and add (4 + 1 + 0 ) (H + T+TT)	5
	We move to the left and add (1+0+2) (T + TT + L)	3
	We move to the left and add (0 + 2) (TT + L)	2
	We write the last digit as it is 2 (L)	2
Ans		22358952

Squaring a number beginning with ‘5’.

Last time we have seen how to square a number that is ending with ‘5’

Now we will see how to square a number beginning with ‘5’

i.e. 50, 51, 52, 53, 54, 55, 56, 57, 58, 59

Square of 53	Add 25 to the digit in the units place and put it as the left-hand part. 25 + 3 = 28.  Left Part = 28
	Square the unit place digit and put it as the right hand part of the answer. The square of 3 is 9 but write 09.  Right Part = 09
	Left Part     Right Part     28                09
Ans	2809
Square of 57	Add 25 to the  digit in the units place and put it as the left hand part. 25 + 7 = 32  Left Part = 32
	Square the unit place digit and put it as the right hand part of the answer. The square of 7 is 49 and keep it as 49.   Right Part = 49
	Left Part         Right Part      32                     49
Ans	3249
Square of 56	Left Part                         Right Part 25 + 6 = 31                      6 x 6 = 36                                                                                               Ans : 3136
Square of 53	Left Part                         Right Part 25 + 3 = 28                      3 x 3 = 09                           Ans : 2809
Square of 52
Sauare of 55
Square of 58
Square of 59