Maths Tricks , shortcut tricks for maths to make calculation easy and fast

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, 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, 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

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

 

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

 

Square of any 2 digit number

 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

 

Multiplication of 2 two-digit numbers where the first digit of both the numbers are same and the last digit of the two numbers sum to 10 (You can’t use this rule for other numbers)

 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

 

Multiplication of two numbers that differ by 6 (This trick only works if you have memorized or can quickly calculate the squares of numbers.

 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

 

Multiplication of two numbers that differ by 4 (This trick only works if you have memorized or can quickly calculate the squares of numbers.

 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

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Multiplication of two numbers that differ by 2 (This trick only works if you have memorized 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

 

Multiplication of 125 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 93*125 = 93000/8 = 11625. 
2. 137*125 = 137000/8 = 17125. 

Example. 
Understand the rule by 1 more example
3786*125 = 3786000/8 = 473250.

Multiplication of 25 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 67*25 = 6700/4 = 1675. 
2. 298*25 = 29800/4 = 7450. 

Example. 
Understand the rule by 1 more example
5923*25 = 592300/4 = 148075.

 

Multiplication of 5 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 49*5 = 490/2 = 245. 
2. 453*5 = 4530/2 = 2265. 

Example. 
Understand the rule by 1 more example
5649*5 = 56490/2 = 28245.

 

Multiplication of 5 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 49*5 = 490/2 = 245. 
2. 453*5 = 4530/2 = 2265. 

Example. 
Understand the rule by 1 more example
5649*5 = 56490/2 = 28245.

 

Multiplication of 999 with any number (You can\'t use this rule for other numbers)

 Let me explain this rule by taking examples
1. 51*999 = 51*(1000-1) = 51*1000-51 = 51000-51 = 50949.
2. 147*999 = 147*(1000-1) = 147000-147 = 146853. 

Example. 
Understand the rule by 1 more example
3825*999 = 3825*(1000-1) = 3825000-3825 = 3821175

 

Multiplication of 99 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 46*99 = 46*(100-1) = 46*100-46 = 4600-46 = 4554.
2. 362*99 = 362*(100-1) = 36200-362 = 35838. 

Example. 
Example. 
Understand the rule by 1 more example
2841*99 = 2841*(100-1) = 284100-2841 = 281259

 

Multiplication of 99 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 46*99 = 46*(100-1) = 46*100-46 = 4600-46 = 4554.
2. 362*99 = 362*(100-1) = 36200-362 = 35838. 

Example. 
Example. 
Understand the rule by 1 more example
2841*99 = 2841*(100-1) = 284100-2841 = 281259

 

Multiplication of 9 with any number (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
1. 18*9 = 18*(10-1) = 18*10-18 = 180-18 = 162.
2. 187*9 = 187*(10-1) = 1870-187 = 1683. 

Example. 
Example. 
Understand the rule by 1 more example
1864*9 = 1864*(10-1) = 18640-1864 = 16776

 

Multiplication of 11 with any number. (You can't use this rule for other numbers)

 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

Square of any 2 digit number (You can't use this rule for other numbers)

 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

Square of a 2 digit number ending with 5 (You can't use this rule for other numbers)

 Let me explain this rule by taking examples
35^2 = 3*(3+1) ---25 = 1225 

Example. 
Other example
95^2 = 9*(9+1) ---25 = 9025

Multiplication of 11 with any number of 3 digits. (You can't use this rule for other numbers)

 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

 

Multiplication of 11 with any number of 2 digits. (You can’t use this rule for other numbers)

 Let me explain this rule by taking examples
35*11 = 3---(3+5)---5 = 385
Means insert the sum of first and second digits between the two digits of the number
27*11 = 2---(2+7)---7 = 297 

Example. 
Here an extra case arises
Consider the following examples for that
39*11 = 3+1---(3+9-10)---9 = 429
Means, if sum of two digits of the number is greater than 10, then add 1 to first digit and subtract 10 to the inserted term.
78*11 = 7+1---(7+8-10)---8 = 858

 

Multiplication of any two numbers, both ranging from 11 to 19. (You can’t use this rule for other numbers)

 Let me explain this rule by taking examples
13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it. 

Example. 
18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252