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

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

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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

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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

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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

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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

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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

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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

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

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Multiplication of two numbers that differ by 6

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

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Multiplication of two numbers that differ by 4

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 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

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Multiplication of 125 with any number

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.

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Multiplication of 25 with any number

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.

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Multiplication of 5 with any number

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.

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Multiplication of 999 with any number

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

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Multiplication of 99 with any number

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

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Multiplication of 99 with any number

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

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Multiplication of 9 with any number

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

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Multiplication of 11 with any number.

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

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Square of any 2 digit number

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

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Square of a 2 digit number ending with 5

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

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