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
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
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
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
Let me explain this trick by taking examples
67^2 = [6^2][7^2]+20*6*7 = 3649+840 = 4489
similarly
25^2 = [2^2][5^2]+20*2*5 = 425+200 = 625
Take one more example
97^2 = [9^2][7^2]+20*9*7 = 8149+1260 = 9409
Here [] is not an operation, it is only a separation between initial 2 and last 2 digits
Example.
Here an extra case arises
Consider the following examples for that
91^2 = [9^2][1^2]+20*9*1 = 8101+180 = 8281
Let me explain this rule by taking examples
To calculate 56×54:
Multiply 5 by 5+1. So, 5*6 = 30. Write down 30.
Multiply together the last digits: 6*4 = 24. Write down 24.
The product of 56 and 54 is thus 3024.
Example.
Understand the rule by 1 more example
78*72 = [7*(7+1)][8*2] = 5616
If the two numbers differ by 6 then their product is the square of their average minus 9.
Let me explain this rule by taking examples
10*16 = 13^2 - 9 = 160
22*28 = 25^2 - 9 = 616
Example.
Understand the rule by 1 more example
997*1003 = 1000^2 - 9 = 999991
If two numbers differ by 4, then their product is the square of the number in the middle (the average of the two numbers) minus 4.
Let me explain this rule by taking examples
22*26 = 24^2 - 4 = 572
98*102 = 100^2 - 4 = 9996
Example.
Understand the rule by 1 more example
148*152 = 150^2 - 4 = 22496
(This trick only works if you have memorised or can quickly calculate the squares of numbers. When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.Let me explain this rule by taking examples
18*20 = 19^2 - 1 = 361 - 1 = 360
25*27 = 26^2 - 1 = 676 - 1 = 675
Example.
Understand the rule by 1 more example 49*51 = 50^2 - 1 = 2500 - 1 = 2499
Let me explain this rule by taking examples
1) 234163*11 = 2---2+3---3+4---4+1---1+6---6+3---3 = 2575793
Means insert the sum of 2 successive digits and put 2 terminal digits in its place
2) 45345181*11 = 4---4+5---5+3---3+4---4+5---5+1---1+8---8+1---1 = 498796991
Example.
Here an extra case arises
Consider the following examples for that
3) 473927*11 = 4+1--- (4+7-10) +1--- (7+3-10) +1--- (3+9-10) +1--- (9+2-10)--- (2+7) ---7 = 5213197
4) 584536*11 = 5+1---(5+8-10)+1---(8+4-10)---(4+5)---(5+3)---(3+6)---6 = 6429896
Let me explain this rule by taking examples
27^2 = (27+3)*(27-3) + 3^2 = 30*24 + 9 = 720+9 = 729
In this method, we have to make a number ending with 0, that's why; we add 3 to 27.
Example.
Understand the rule by 1 more example
78^2 = (78+2)*(78-2) + 2^2 = 80*76 + 4 = 6080+4 = 6084
