Math tricks

MULTIPLICATION OF 11 WITH ANY NUMBER OF 3 DIGITS.

 Let me explain this rule by taking examples
1. 352*11 = 3---(3+5)---(5+2)---2 = 3872
Means insert the sum of first and second digits, then sum of second and third 

digits between the two terminal digits of the number
2. 213*11 = 2---(2+1)---(1+3)---3 = 2343 

EXAMPLE.

Here an extra case arises
Consider the following examples for that

1) 329*11 = 3--- (3+2) +1--- (2+9-10) ---9 = 3619
Means, if sum of two digits of the number is greater than 10, then add 1 to previous digit and subtract 10 to the associated digit.
2) 758*11 = 7+1---(7+5-10)+1---(5+8-10)---8 = 8338

TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 27 AND 37

 Let me explain this rule by taking examples
consider number 34568276, we have to calculate the reminder on diving this number by 27 and 37 respectively.
make triplets as written below starting from units place
34.........568..........276
now sum of all triplets = 34+568+276 = 878
divide it by 27 we get reminder as 14
divide it by 37 we get reminder as 27 

EXAMPLE.

other examples for the clarification of the rule
let the number is 2387850765
triplets are 2...387...850...765
sum of the triplets = 2+387+850+765 = 2004
on revising the steps we get
2......004
sum = 6
divide it by 27 we get reminder as 6
divide it by 37 we get reminder as 6

TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 7 11 AND 13

 Let me explain this rule by taking examples
consider number 34568276, we have to calculate the reminder on diving this number by 7 11 and 13 respectively.
make triplets as written below starting from units place
34.........568..........276
now alternate sum = 34+276 = 310 and 568
and difference of these sums = 568-310 = 258
divide it by 7 we get reminder as 6
divide it by 11 we get reminder as 5
divide it by 13 we get reminder as 11 

EXAMPLE.

other examples:-
consider the number 4523895099854
triplet pairs are 4...523...895...099...854
alternate sums are 4+895+854=1753 and 523+099=622
difference = 1131
revise the same tripling process
1......131
so difference = 131-1 = 130
divide it by 7 we get reminder as 4
divide it by 11 we get reminder as 9
divide it by 13 we get reminder as 0

TO CALCULATE REMINDER ON DIVIDING THE NUMBER BY 3

 Method:- first calculate the digit sum , then divide it by 3, the reminder in this case will be the required reminder

example:- 1342568
let the number is as written above
its digit sum = 29 = 11 = 2
so reminder will be 2 

EXAMPLE.TAKE SOME OTHERS

34259677858
digit sum of the number is 64 = 10 = 1
reminder is 1

similarly let the number is 54670329845
then digit sum = 53 = 8
when we divide 8 by 3 we get reminder as 2 so answer will be 2

SQUARE OF NUMBERS NEAR TO 100

 Let me explain this rule by taking examples
96^2 :-
First calculate 100-96, it is 4
so 96^2 = (96-4)----4^2 = 9216
similarly
106^2 :-
First calculate 106-100, it is 6
so 106^2 = (106+6)----6^2 = 11236 

EXAMPLE.

An other case arises
110^2 = (110+10)----100 = (120+1)----00 = 12100
similarly
89^2 = (89-11)----121 = (78+1)----21 = 7921